查看“︁Googolism - Part 3”︁的源代码

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== Linear omega level ==

=== Part 3.1: <math>f_{\omega}(f_3(10))</math> ~ <math>f_{\omega+1}(f_3(10))</math> ===

* <nowiki>Giggotri, {10, 10, {10, 100, 2}}</nowiki>
* Great grangol / Grangolsuplex, E100##2#2
* Grangolsuplexigong, E100,000##2#2
* Googoldexisuplex, E100##(E100#1#2)
* Googolplexidexisuplex, E100##(E100#2#2)
* Grangoldexisuplex, E100##(E100#100#2)
* Grangoldudexisuplex, E100##(E100#100#3)
* '''Moser''', 2[2[5, 2]] in a mega-gon
* Joyce's tetratri, g(2,1,1,4,3,3)
* Tritriplex, {3,3,1,2}
* Grand Moser, 3[3[5, 3]] in a Grand Mega-gon
* Great Moser, 4[4[5, 4]] in a Great Mega-gon
* Gong Moser, 5[5[5, 5]] in a Gong Mega-gon
* <nowiki>Gaggotri, {10, 10, {10, 100, 3}}</nowiki>
* Mosiston, 10 in a megiston-gon
* Great greagol / Greagolsuplex, E100##3#2
* Graham grahal / grabio, <math>g_2 = 3 \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{3 \uparrow\uparrow\uparrow\uparrow 3} 3</math>
* Greagolthrexisuplex, E100##(E100#100#100#2)
* Tritetplex, {4, 3, 1, 2}
* Zertrearmix, [0]↤[0]↤[3]
* <nowiki>Geegotri, {10, 10, {10, 100, 4}}</nowiki>
* Great gigangol / Gigangolsuplex, E100##4#2
* Tripentplex, {5, 3, 1, 2}
* <nowiki>Gigotri, {10, 10, {10, 100, 5}}</nowiki>
* Great gorgegol / Gorgegolsuplex, E100##5#2
* Trihexplex, {6, 3, 1, 2}
* <nowiki>Goggotri, {10, 10, {10, 100, 6}}</nowiki>
* Great gulgol / Gulgolsuplex, E100##6#2
* Triheptplex, {7, 3, 1, 2}
* <nowiki>Gagotri, {10, 10, {10, 100, 7}}</nowiki>
* Great gaspgol / Gaspgolsuplex, E100##7#2
* Trioctplex, {8, 3, 1, 2}
* Great ginorgol / Ginorgolsuplex, E100##8#2
* Triennplex, {9, 3, 1, 2}
* Great gargantuul / Gargantuulsuplex, E100##9#2
* Tridecalplex, {10,10,tridecal}
* Great googondol / Googondolsuplex, E100##10#2
* Little Graham grahal, [2,3,12,2] = F<sup>2</sup>(12)
* Grand Hyperhypillion, H*<sub>2</sub>(10,2)
* Primitolplex, s(3,3,2,2)
* Magthree, A(A(61,61),A(61,61))
* Double Centifact, 100**
* <nowiki>Boogolplex, {10,10,{10,10,100}}</nowiki>
* <nowiki>Gamminol, {12,100,{10,10,100}}</nowiki>
* TriGraham, g<sub>3</sub> = 3{3{3↑↑↑↑3}3}3
* Tris-hyperon, 100{X}100{X}100
* Gugolda-suplex / goolda-suplex, E100##100#2 = E100##gugold
* Kilohyperfaxul, (200![1])![1] ~ {10,198,hyperfaxul}
* Meser, 2[256[258]+2] = M(2,M(256,256))
* Charged Hayden, 999[999[999
* Gugolda-suplexichime, E1,000##1,000#2
* Myriodufact, 10,000**
* Gugolda-suplexitoll, E10,000##10,000#2
* Gugolda-suplexigong / goolda-suplexigong, E100,000##100,000#2
* Gongolplex, hyper(10,gongol,100)
* Joyce's pentatri, g(3,1,1,4,3,3)
* Googoldusuplex, E100##1#3
* Googoldusuplexigong, E100,000##1#3
* Googolplexidusuplex, E100##(E100#2)#2
* Googolduplexidusuplex, E100##(E100#3)#2
* Grangoldusuplex, E100##2#3
* Tritriplexian, {3,4,1,2}
* Grangoldexidusuplex, E100##(E100#100#2)#2
* Greagoldusuplex, E100##3#3
* Tritetduplex, {4, 4, 1, 2}
* Gigangoldusuplex, E100##4#3
* Gorgegoldusuplex, E100##5#3
* Bigrand Hyperhypillion, H*<sub>2</sub>(10,3)
* Joycian grand tridecal, g(3,1,1,11,10,10)
* Tridecalduplex, {10, 4, 1, 2}
* Googondoldusuplex, E100##10#3
* TriLittleGraham, [2,3,12,3] = F<sub>3</sub>(12)
* Primitolbiplex, s(3,4,2,2)
* Triple Centifact, 100***
* <nowiki>Boogolduplex, {10,10,{10,10,{10,10,100}}}</nowiki>
* Ter-hyperon, 100{X+1}4
* Gugolda-dusuplex / goolda-dusuplex, E100##100#3
* Megahyperfaxul, ((200![1])![1])![1] ~ {10,198,kilohyperfaxul}
* Muser, 2[2[256[258]+2]+2] = M(2,M(2,M(256,256)))
* Gugolda-dusuplexichime, E1,000##1,000#3
* Myriotrefact, 10,000***
* Gugolda-dusuplexitoll, E10,000##10,000#3
* Gugolda-dusuplexigong / goolda-dusuplexigong, E100,000##100,000#3
* Googoltrisuplex, E100##1#4
* Grangoltrisuplex, E100##2#4
* Mevenillion, 10<sup>3[3,3,3]*3+3</sup>
* ThaAwesome's Tetratri, 3[3,3]3
* Greagoltrisuplex, E100##3#4
* Golden grahal, g<sub>4</sub> = 3{3{3{3↑↑↑↑3}3}3}3
* Primitoltriplex, s(3,5,2,2)
* ThaAwesome's Tetratet, 4[4,4]4
* Golden crahal, [4,4,4,4] = gc(3)
* Tridecaltriplex, {10, 5, 1, 2}
* Little golden grahal, [2,3,12,4] = F<sup>4</sup>(12)
* Quadruple Centifact, 100****
* <nowiki>Boogoltriplex, {10,10,{10,10,{10,10,{10,10,100}}}}</nowiki>
* Gugolda-trisuplex, E100##100#4
* Juice infused Moser|Juice-infused Moser, 17[592[186[44[416
* Pen-hyperon, 100{X+1}5
* Gigahyperfaxul, (((200![1])![1])![1])![1] ~ {10,198,megahyperfaxul}
* Myrioterfact, 10,000****
* Primitolquadriplex, s(3,6,2,2)
* Gugolda-quadrisuplex, E100##100#5
* Quintuple Centifact, <math>100^* _5</math>
* Ex-hyperon, 100{X+1}6
* Terahyperfaxul, ((((200![1])![1])![1])![1])![1] ~ {10,198,gigahyperfaxul}
* Dihexar, <math>Q_{1,1}(6)</math>
* Epi-hyperon, 100{X+1}7
* Gugolda-quintisuplex, E100##100#6
* Petahyperfaxul, (((((200![1])![1])![1])![1])![1])![1] ~ {10,198,terahyperfaxul}
* '''Little Graham''' / Graham-Rothschild Number, F<sup>7</sup>(12), where F(n) = 2↑<sup>n</sup>3
* Gugolda-sextisuplex, E100##100#7
* Exahyperfaxul, ((((((200![1])![1])![1])![1])![1])![1])![1] ~ {10,198,petahyperfaxul}
* Gugolda-septisuplex, E100##100#8
* Dialogue-corporal, {10, 10, 1, 2}
* Uniance, 10[&1]
* Gugolda-octisuplex, E100##100#9
* Great grahal, [3,3,4,10] = G<sub>10</sub>
* Unaddom, <math>f_{\omega+1}(10)</math>
* One mow my, <math>g_{\Gamma_0}(10)</math>
* Great Hyperhypillion / Hypergrand Hyperhypillion, H* <sub>2</sub>(10,10)
* Gugolda-nonisuplex, E100##100#10
* Decuple Centifact, <math>100^* _{10}</math>
* Gugolda-decisuplex, E100##100#11
* Small fry-corporal, {10, 15, 1, 2}
* Quarter Graham, [3,3,4,16] = G<sub>16</sub>
* Great Exi-hyperhypillion, H* <sub>2</sub>(16,16)
* Guppy-corporal, {10, 20, 1, 2}
* Quinary-corporal, {5, 25, 1, 2}
* Joycian dimentri, g(27,1,1,4,3,3)
* Primibol, s(3,2,3,2)
* Half Graham, [3,3,4,32] = G<sub>32</sub>
* Mini-corporal, {10, 50, 1, 2}
* Octal-corporal, {8, 64, 1, 2}
* '''Graham's number''', G = g<sub>64</sub>
* Vsauce's Number, <math>g_{64}\times10^{10^{100}}!^{10^{10^{2\times10^{100}+100}}}</math>
* Bisuperiorgraham, G↑G
* Quadrisuperiorgraham, G↑↑5
* Graham-Conway number, {4,65,1,2}
* Prawn-corporal, {10, 65, 1, 2}
* Graham Jr., [2,3,12,64] = F<sup>64</sup>(12)
* Gugolda-tresexagintisuplex, E100##100#64
* xkcd number, A(G,G)
* Fyn, <u>1</u><sub>0</sub>(76)
* Ogocorporal, {10, 80, 1, 2}
* Corporalspeck, {10, 90, 1, 2}
* Corporalcrumb, {10, 95, 1, 2}
* Explodol, E(100)
* Corporalchunk, {10, 99, 1, 2}
* Corporal / Kil-Googol, {10,100,1,2} = 10[1,1]100
* Expandor / Cent-hyperon, 100{X+1}100
* Goourea / goolsol, s(10,100,2,2)
* Stasplex, g<sub>100</sub>
* Centuple Centifact, <math>100^* _{100}</math>
* Graatagold / graatagond / graatada, E100##100#100 = E100##100##2
* Astrex, #^* ((10))*100
* Great Cent-hyperhypillion, H* <sub>2</sub>(100,100)
* Wakoogol, <math>h_{100}(\underbrace{10,10,\cdots,10,10}_{\text{100 10's}})</math>
* ioannis.c|Output of ioannis.c, <math>\approx f_{\omega+1}(115)</math>
* Hexadecimal-corporal, {16, 256, 1, 2}
* Ungranika, <1,1> |488
* Corporalchime, {10, 1000, 1, 2}
* Graatagoldachime, E1,000##1,000#1,000
* Niftimal-corporal, {36, 1296, 1, 2}
* Pyrophord, g<sub>4707</sub>
* Corporaltoll, {10, 10000, 1, 2}
* Myriad Myriofact, <math>10000^* _{10000}</math>
* Graatagoldatoll, E10,000##10,000#10,000
* Joycian dulatri, g(19683,1,1,4,3,3)
* Corporalgong, {10, 100000, 1, 2}
* Graatagoldagong, E100,000##100,000#100,000 = E100,000##100,000##2
* Forcal, g<sub>1,000,000</sub>
* Graham forcal / Forahal, g<sub>1,000,001</sub>
* Graham graham forcal / Forado, g<sub>1,000,002</sub>
* Graham graham graham forcal / Foratrio, g<sub>1,000,003</sub>
* Borcal, g<sub>1,000,000,000</sub>
* Joycian trimentri, g(3<sup>27</sup>,1,1,4,3,3)
* Mevenogol, 10<sup>100</sup>[10<sup>100</sup>,10<sup>100</sup>,10<sup>100</sup>]
* Googolplux, g(g(3,2,g(2,50,100)),1,1,2,100,10)
* Googolsudexigong, E100,000##1#1#2
* Googolplexisudex, E100##100#(E100#2)
* Googolduplexisudex, E100##100#(E100#3)
* Clarkkkkson, ~ f<sub>ω+1</sub> (Lynz) (increases throughout time)

=== Part 3.2: <math>f_{\omega+1}(f_3(10))</math> ~ <math>f_{\omega+2}(f_3(10))</math> ===

* Yudkowsky's Number (Saibian), G(G(1))
* Googolpluc, g(g(g(2,2,3),2,g(2,100,10)),1,1,2,100,10)
* Grand hyperfaxul, 200(![1])<sup>200![1]+1</sup> ~ {10,hyperfaxul,1,2}
* Lower bound of Block subsequence theorem|n(4)
* Joycian decaltrix, g(g(11,10,10),1,1,11,10,10)
* Googolplum, g(g(g(3,3,3),2,g(2,100,10)),1,1,2,100,10)
* Goltreantrex, #^* ((10))^((10))* * ((10))* ((10))*100
* Grangolsudex, E100##2#1#2
* Grangoldexisudex, E100##100#(E100#100#2)
* Tritridex, {3, 3, 2, 2}
* Grand kilohyperfaxul, 200(![1])<sup>(200![1])![1]+1</sup> ~ {10,kilohyperfaxul,1,2}
* Greagolsudex, E100##3#1#2
* Tritetdex, {4, 4, 2, 2}
* Grand megahyperfaxul, 200(![1])<sup>((200![1])![1])![1]+1</sup> ~ {10,megahyperfaxul,1,2}
* Gigangolsudex, E100##4#1#2
* Grand gigahyperfaxul, 200(![1])<sup>(((200![1])![1])![1])![1]+1</sup> ~ {10,gigahyperfaxul,1,2}
* Gorgegolsudex, E100##5#1#2
* Grand terahyperfaxul, 200(![1])<sup>((((200![1])![1])![1])![1])![1]+1</sup> ~ {10,terahyperfaxul,1,2}
* Grand petahyperfaxul, 200(![1])<sup>(((((200![1])![1])![1])![1])![1])![1]+1</sup> ~ {10,petahyperfaxul,1,2}
* Grand exahyperfaxul, 200(![1])<sup>((((((200![1])![1])![1])![1])![1])![1])![1]+1</sup> ~ {10,exahyperfaxul,1,2}
* '''Conway's Tetratri''' / primibolplex, 3→3→3→3 ~ g<sub>g<sub>27</sub></sub>
* Gugolda-sudex, E100##100#1#2
* Googolsuplexisudex, E100##1#2#2
* Grangolsuplexisudex, E100##2#2#2
* Kudi-Chan's Number, ~ g<sub>g<sub>64</sub>+64</sub>
* Gugolda-suplexisudex, E100##100#2#2
* Gugolda-dusuplexisudex, E100##100#3#2
* Gugolda-trisuplexisudex, E100##100#4#2
* Corporalplex, {10,{10,100,1,2},1,2}
* Tris-expandor, 100{X+1}100{X+1}100
* Graatagolda-sudex / graatada-sudex, E100##100#100#2
* Graatagolda-sudexichime, E1,000##1,000#1,000#2
* Graatagolda-sudexitoll, E10,000##10,000#10,000#2
* Graatagolda-sudexigong, E100,000##100,000#100,000#2
* Force forcal, Forcal(2)
* Wakoogolplex, <math>h_{100}(\underbrace{10,10,\cdots,10,10}_{\text{wakoogol 10's}})</math>
* Clarkkkksonplex, ~ f<sub>ω+1</sub>(f<sub>ω+1</sub>(Lynz)) (increases throughout time)
* Googoldusudex, E100##1#1#3
* Grangoldusudex, E100##2#1#3
* Gugolda-dusudex, E100##100#1#3
* Bigrand hyperfaxul, 200(![1])<sup>200(![1])<sup>200![1]+1</sup>+1</sup> ~ {10,grand hyperfaxul,1,2}
* Gugolda-suplexidusudex, E100##100#2#3
* Bigrand kilohyperfaxul, 200(![1])<sup>200(![1])<sup>(200![1])![1]+1</sup>+1</sup> ~ {10,grand kilohyperfaxul,1,2}
* Gugolda-dusuplexidusudex, E100##100#3#3
* Bigrand megahyperfaxul, 200(![1])<sup>200(![1])<sup>((200![1])![1])![1]+1</sup>+1</sup> ~ {10,grand megahyperfaxul,1,2}
* Graatagolda-dusudex / graatada-dusudex, E100##100#100#3
* Graatagolda-dusudexichime, E1,000##1,000#1,000#3
* Graatagolda-dusudexitoll, E10,000##10,000#10,000#3
* Graatagolda-dusudexigong, E100,000##100,000#100,000#3
* Force force forcal, Forcal(3)
* Googoltrisudex, E100##1#1#4
* Terto-Grahal, G(G(G(G(1))))
* Gugolda-trisudex, E100##100#1#4
* Trigrand hyperfaxul, 200(![1])<sup>200(![1])<sup>200(![1])<sup>200![1]+1</sup>+1</sup>+1</sup> ~ {10,bigrand hyperfaxul,1,2}
* Graatagolda-trisudex, E100##100#100#4
* Trigrand kilohyperfaxul, 200(![1])<sup>200(![1])<sup>200(![1])<sup>(200![1])![1]+1</sup>+1</sup>+1</sup> ~ {10,bigrand kilohyperfaxul,1,2}
* Trigrand megahyperfaxul, 200(![1])<sup>200(![1])<sup>200(![1])<sup>((200![1])![1])![1]+1</sup>+1</sup>+1</sup> ~ {10,bigrand megahyperfaxul,1,2}
* Force force force forcal, Forcal(4)
* Quadgrand hyperfaxul, 200(![1])<sup>200(![1])<sup>200(![1])<sup>200(![1])<sup>200![1]+1</sup>+1</sup>+1</sup>+1</sup> ~ {10,6,2,2}
* Graatagolda-quadrisudex, E100##100#100#5
* Quintgrand hyperfaxul, 200(![1])<sup>200(![1])<sup>200(![1])<sup>200(![1])<sup>200(![1])<sup>200![1]+1</sup>+1</sup>+1</sup>+1</sup>+1</sup> ~ {10,7,2,2}
* Trihexar, <math>Q_{1,2}(6)</math>
* Graatagolda-quintisudex, E100##100#100#6
* Graatagolda-sextisudex, E100##100#100#7
* Graatagolda-septisudex, E100##100#100#8
* Biance, 10[&2]
* Multiexpandecal, {10,10,2,2} = {10,2,3,2}
* Baddom, <math>f_{\omega+2}(10)</math>
* Graatagolda-octisudex, E100##100#100#9
* Graatagolda-nonisudex, E100##100#100#10
* Graatagolda-decisudex, E100##100#100#11
* Primitrol, s(3,2,4,2)
* Unfyn, <u>1</u><sub>1</sub>(76)
* Mulporal / Kil-Doogol, {10,100,2,2} = 10[2,1]100
* Hypercentifact, <math>100^* _{(100,100)}</math>
* Greegold / greegond / greegada, E100##100#100#100 = E100##100##3
* Degranika, <2,1> |488
* Greegoldachime, E1,000##1,000#1,000#1,000
* Greegoldatoll, E10,000##10,000#10,000#10,000
* Greegoldagong, E100,000##100,000#100,000#100,000 = E100,000##100,000##3
* Suporcal, Forcal(1,000,000) = Forcal<sub>2</sub>(1)
* Force suporcal, Forcal(1,000,001)
* Force force suporcal, Forcal(1,000,002)
* Force force force suporcal, Forcal(1,000,003)
* Googolsuthrex, E100##1#1#1#2

=== Part 3.3: <math>f_{\omega+2}(f_3(10))</math> ~ <math>f_{\omega+5}(f_3(10))</math> ===

* Hypergraham, G<sup>Graham's number|G</sup>(64)
* Grangolsuthrex, E100##2#1#1#2
* Greagolsuthrex, E100##3#1#1#2
* Gigangolsuthrex, E100##4#1#1#2
* Gorgegolsuthrex, E100##5#1#1#2
* Googondolsuthrex, E100##10#1#1#2
* Gugolda-suthrex, E100##100#1#1#2
* Googolsuplexisuthrex, E100##1#2#1#2
* Gugolda-suplexisuthrex, E100##100#2#1#2
* Gugolda-dusuplexisuthrex, E100##100#3#1#2
* Graatagolda-suthrex, E100##100#100#1#2
* Googolsudexisuthrex, E100##1#1#2#2
* Gugolda-sudexisuthrex, E100##100#1#2#2
* Grand tritri, {3,3,3,2} = 3[3,1]3
* Primitrolplex, s(3,3,4,2)
* Graatagolda-sudexisuthrex, E100##100#100#2#2
* Graatagolda-dusudexisuthrex, E100##100#100#3#2
* Greegolda-suthrex / greegada-suthrex, E100##100#100#100#2
* Greegolda-suthrexichime, E1,000##1,000#1,000#1,000#2
* Greegolda-suthrexitoll, E10,000##10,000#10,000#10,000#2
* Greegolda-suthrexigong, E100,000##100,000#100,000#100,000#2
* Superior suporcal, Forcal<sub>2</sub>(2)
* Descendpent, {5, 4, 3, 2}
* '''Conway's Tetratet''', 4→4→4→4 = CG(4)
* Greegolda-dusuthrex, E100##100#100#100#3
* Greegolda-dusuthrexichime, E1,000##1,000#1,000#1,000#3
* Greegolda-dusuthrexitoll, E10,000##10,000#10,000#10,000#3
* Greegolda-dusuthrexigong, E100,000##100,000#100,000#100,000#3
* Superior superior suporcal, Forcal<sub>2</sub>(3)
* Superior superior superior suporcal, Forcal<sub>2</sub>(4)
* Quadhexar, <math>Q_{1,3}(6)</math>
* Triance, 10[&3]
* Traddom, <math>f_{\omega+3}(10)</math>
* Primitetol, s(3,2,5,2)
* Deufyn, <u>1</u><sub>2</sub>(76)
* Powporal / Kil-Toogol, {10,100,3,2} = 10[3,1]100
* Grinningold / grinningond / grinninda, E100##100#100#100#100 = E100##100##4
* Hectpeta-melpentis, 100[100#5]
* Treastrex, #^* * * ((10))*100
* Tregranika, <3,1>|488
* Grinningoldachime, E1,000##1,000#1,000#1,000#1,000
* Grinningoldatoll, E10,000##10,000#10,000#10,000#10,000
* Grinningoldagong, E100,000##100,000#100,000#100,000#100,000 = E100,000##100,000##4
* Megocal, Forcal<sub>2</sub>(1,000,000) = Forcal<sub>3</sub>(1)
* Force megocal, Forcal(1+Forcal<sub>2</sub>(999,999))
* Superior megocal, Forcal<sub>2</sub>(1,000,001)
* Superior superior megocal, Forcal<sub>2</sub>(1,000,002)
* Primitetolplex, s(3,3,5,2)
* Grinningolda-sutetrex / grinninda-sutetrex, E100##100#100#100#100#2
* Grinningolda-sutetrexichime, E1,000##1,000#1,000#1,000#1,000#2
* Grinningolda-sutetrexitoll, E10,000##10,000#10,000#10,000#10,000#2
* Grinningolda-sutetrexigong, E100,000##100,000#100,000#100,000#100,000#2
* Megaior megocal, Forcal<sub>3</sub>(2)
* Grinningolda-dusutetrex / grinninda-dusutetrex, E100##100#100#100#100#3
* Grinningolda-dusutetrexichime, E1,000##1,000#1,000#1,000#1,000#3
* Grinningolda-dusutetrexitoll, E10,000##10,000#10,000#10,000#10,000#3
* Grinningolda-dusutetrexigong, E100,000##100,000#100,000#100,000#100,000#3
* Grand tritet, {4,4,4,2}
* Megaior megaior megocal, Forcal<sub>3</sub>(3)
* Megaior megaior megaior megocal, Forcal<sub>3</sub>(4)
* Quinhexar, <math>Q_{1,4}(6)</math>
* Genesis / Tetriance, 10[&4]
* Quadraddom, <math>f_{\omega+4}(10)</math>
* Primipenol, s(3,2,6,2)
* Troifyn, <u>1</u><sub>3</sub>(76)
* Terporal / Kil-Tetoogol, {10,100,4,2} = 10[4,1]100
* Hecthexa-melhexis, 100[100#6]
* Golaagold / golaagond / golaada, E100##100##5
* Golaagoldachime, E1,000##1,000##5
* Golaagoldatoll, E10,000##10,000##5
* Golaagoldagong, E100,000##100,000##5
* Hypercal, Forcal<sub>4</sub>(1)
* Force hypercal, Forcal(1+Forcal<sub>2</sub>(Forcal<sub>3</sub>(999,999)-1))
* Superior hypercal, Forcal<sub>2</sub>(1+Forcal<sub>3</sub>(999,999))
* Megaior hypercal, Forcal<sub>3</sub>(1,000,001)
* Primipenolplex, s(3,3,6,2)
* Golaagolda-supentex / golaada-supentex, E100##100#100#100#100#100#2
* Golaagolda-supentexichime, E1,000##1,000#1,000#1,000#1,000#1,000#2
* Golaagolda-supentexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#2
* Golaagolda-supentexigong, E100,000##100,000#100,000#100,000#100,000#100,000#2
* Hyperior hypercal, Forcal<sub>4</sub>(2)
* Golaagolda-dusupentex / golaada-dusupentex, E100##100#100#100#100#100#3
* Golaagolda-dusupentexichime, E1,000##1,000#1,000#1,000#1,000#1,000#3
* Golaagolda-dusupentexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#3
* Golaagolda-dusupentexigong, E100,000##100,000#100,000#100,000#100,000#100,000#3
* Hyperior hyperior hypercal, Forcal<sub>4</sub>(3)
* Grand tripent, {5,5,5,2}
* Hyperior hyperior hyperior hypercal, Forcal<sub>4</sub>(4)
* Sexahexar, <math>Q_{1,5}(6)</math>
* Pentiance, 10[&5]
* Quintaddom, <math>f_{\omega+5}(10)</math>
* Pepporal, {10,100,5,2}
* Hecthepta-melheptis, 100[100#7]
* Gruelohgold / gruelohgond / gruelohda, E100##100##6
* Gruelohgoldachime, E1,000##1,000##6
* Gruelohgoldatoll, E10,000##10,000##6
* Gruelohgoldagong, E100,000##100,000##6
* Gorgcal, Forcal<sub>5</sub>(1)
* Force gorgcal, Forcal(1+Forcal<sub>2</sub>(Forcal<sub>3</sub>(Forcal<sub>4</sub>(999,999)-1)-1))
* Superior gorgcal, Forcal<sub>2</sub>(1+Forcal<sub>3</sub>(Forcal<sub>4</sub>(999,999)-1))
* Megaior gorgcal, Forcal<sub>3</sub>(1+Forcal<sub>4</sub>(999,999))
* Hyperior gorgcal, Forcal<sub>4</sub>(1,000,001)

=== Part 3.4: <math>f_{\omega+5}(f_3(10))</math> ~ <math>f_{\omega+11}(10)</math> ===

* Gruelohgolda-suhex, E100##100#100#100#100#100#100#2
* Gruelohgolda-suhexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#2
* Gruelohgolda-suhexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#2
* Gruelohgolda-suhexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#2
* Gorgcaior gorgcal, Forcal<sub>5</sub>(2)
* Gruelohgolda-dusuhex, E100##100#100#100#100#100#100#3
* Gruelohgolda-dusuhexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#3
* Gruelohgolda-dusuhexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#3
* Gruelohgolda-dusuhexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#3
* Gorgcaior gorgcaior gorgcal, Forcal<sub>5</sub>(3)
* Gorgcaior gorgcaior gorgcaior gorgcal, Forcal<sub>5</sub>(4)
* Septahexar, <math>Q_{2,0}(6)</math>
* Sextaddom, <math>f_{\omega+6}(10)</math>
* Hectocta-meloctis, 100[100#8]
* Gaspgold / gaspgond, E100##100##7
* Havering, 112![7]
* Gaspgoldachime, E1,000##1,000##7
* Gaspgoldatoll, E10,000##10,000##7
* Gaspgoldagong, E100,000##100,000##7
* Gulfcal, Forcal<sub>6</sub>(1)
* Gaspgolda-suheptex, E100##100#100#100#100#100#100#100#2
* Gaspgolda-suheptexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#2
* Gaspgolda-suheptexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
* Gaspgolda-suheptexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
* Gulfcaior gulfcal, Forcal<sub>6</sub>(2)
* Gaspgolda-dusuheptex, E100##100#100#100#100#100#100#100#3
* Gaspgolda-dusuheptexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#3
* Gaspgolda-dusuheptexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
* Gaspgolda-dusuheptexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
* Gulfcaior gulfcaior gulfcal, Forcal<sub>6</sub>(3)
* Gulfcaior gulfcaior gulfcaior gulfcal, Forcal<sub>6</sub>(4)
* Septaddom, <math>f_{\omega+7}(10)</math>
* Heptporal, {10,100,7,2}
* Hectenna-melenna. 100[100#9]
* Ginorgold / ginorgond, E100##100##8
* Ginorgoldachime, E1,000##1,000##8
* Ginorgoldatoll, E10,000##10,000##8
* Ginorgoldagong, E100,000##100,000##8
* Gaspocal, Forcal<sub>7</sub>(1)
* Ginorgolda-suoctex, E100##100#100#100#100#100#100#100#100#2
* Ginorgolda-suoctexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#2
* Ginorgolda-suoctexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
* Ginorgolda-suoctexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
* Gaspocaior gaspocal, Forcal<sub>7</sub>(2)
* Ginorgolda-dusuoctex, E100##100#100#100#100#100#100#100#100#3
* Ginorgolda-dusuoctexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#3
* Ginorgolda-dusuoctexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
* Ginorgolda-dusuoctexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
* Gaspocaior gaspocaior gaspocal, Forcal<sub>7</sub>(3)
* Gaspocaior gaspocaior gaspocaior gaspocal, Forcal<sub>7</sub>(4)
* Octaddom, <math>f_{\omega+8}(10)</math>
* Octporal, {10,100,8,2}
* Decazhel, 10[10#10]
* Hectdeka-meldeka, 100[100#10]
* Gargantuuld / gargantuund, E100##100##9
* Gargantuuldachime, E1,000##1,000##9
* Gargantuuldatoll, E10,000##10,000##9
* Gargantuuldagong, E100,000##100,000##9
* Ginorcal, Forcal<sub>8</sub>(1)
* Gargantuulda-suennex, E100##100#100#100#100#100#100#100#100#100#2
* Gargantuulda-suennexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#2
* Gargantuulda-suennexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
* Gargantuulda-suennexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
* Ginorcaior ginorcal, Forcal<sub>8</sub>(2)
* Gargantuulda-dusuennex, E100##100#100#100#100#100#100#100#100#100#3
* Gargantuulda-dusuennexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#3
* Gargantuulda-dusuennexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
* Gargantuulda-dusuennexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
* Ginorcaior ginorcaior ginorcal, Forcal<sub>8</sub>(3)
* Ginorcaior ginorcaior ginorcaior ginorcal, Forcal<sub>8</sub>(4)
* Nonaddom, <math>f_{\omega+9}(10)</math>
* Ennporal, {10,100,9,2}
* Googondold / googondond, E100##100##10
* Googondoldachime, E1,000##1,000##10
* Googondoldatoll, E10,000##10,000##10
* Googondoldagong, E100,000##100,000##10
* Googondolda-sudecex, E100##100#100#100#100#100#100#100#100#100#100#2
* Googondolda-sudecexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#2
* Googondolda-sudecexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
* Googondolda-sudecexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
* Googondolda-dusudecex, E100##100#100#100#100#100#100#100#100#100#100#3
* Googondolda-dusudecexichime, E1,000##1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#1,000#3
* Googondolda-dusudecexitoll, E10,000##10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
* Googondolda-dusudecexigong, E100,000##100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
* Grand tridecal, {10,10,10,2}
* Iterais, 10[&10] = 10[&&]
* Dekaddom / bultom, <math>f_{\omega+10}(10)</math>
* Decporal, {10,100,10,2}
* Googoadold, E100##100##11
* <nowiki>Solution, {{{{{42, 42, 1, 2}, 2, 2}, 3, 2}, 5, 2}, 10, 2}</nowiki>

=== Part 3.5: <math>f_{\omega+11}(10)</math> ~ <math>f_{\omega2}(f_3(10))</math> ===

* Ununaddom, <math>f_{\omega+11}(10)</math>
* Goograndold, E100##100##12
* Bunaddom, <math>f_{\omega+12}(10)</math>
* Grand dozenal, {12,12,12,2}
* Googreadold, E100##100##13
* Trunaddom, <math>f_{\omega+13}(10)</math>
* Googigandold, E100##100##14
* Quadrunaddom, <math>f_{\omega+14}(10)</math>
* Googorgedold, E100##100##15
* Quintunaddom, <math>f_{\omega+15}(10)</math>
* Googuldold, E100##100##16
* Sextunaddom, <math>f_{\omega+16}(10)</math>
* Googaspdold, E100##100##17
* Septunaddom, <math>f_{\omega+17}(10)</math>
* Googinordold, E100##100##18
* Octunaddom, <math>f_{\omega+18}(10)</math>
* Googargantuuld, E100##100##19
* Nonunaddom, <math>f_{\omega+19}(10)</math>
* Googonkosold, E100##100##20
* Vigaddom / zeribaddom, <math>f_{\omega+20}(10)</math>
* Unibaddom, <math>f_{\omega+21}(10)</math>
* Bibaddom, <math>f_{\omega+22}(10)</math>
* Tribaddom, <math>f_{\omega+23}(10)</math>
* Quadribaddom, <math>f_{\omega+24}(10)</math>
* Quintibaddom, <math>f_{\omega+25}(10)</math>
* Sextibaddom, <math>f_{\omega+26}(10)</math>
* Septibaddom, <math>f_{\omega+27}(10)</math>
* Octibaddom, <math>f_{\omega+28}(10)</math>
* Nonibaddom, <math>f_{\omega+29}(10)</math>
* Googontritold, E100##100##30
* Googonsartold, E100##100##40
* Chan.c numbers|chan-2.c, <math>\approx f_{\omega+48}(2)</math>
* Googonpetold, E100##100##50
* Googonextold, E100##100##60
* Googoneptold, E100##100##70
* Bi-Fyn, <u>2</u><sub>0</sub>(76)
* Googonogdold, E100##100##80
* Biggolspeck, {10,10,90,2}
* Googonentold, E100##100##90
* Biggolcrumb, {10,10,95,2}
* Biggolchunk, {10,10,99,2}
* Ternary-biggol, {3,3,100,2}
* Quarternary-biggol, {4,4,100,2}
* Quinary-biggol, {5,5,100,2}
* Octal-biggol / biggolbyte, {8,8,100,2}
* Gugolthra / gugonthra / googonhectold / goolthra, E100##100##100
* Biggol / Dukiloogol, {10,10,100,2} = 10[0,2]100
* Hektaddom, <math>f_{\omega+100}(10)</math>
* Dozenal-biggol / duodecimal-biggol, {12,12,100,2}
* Hexadecimal-biggol, {16,16,100,2}
* Grand trihectal, {100,100,100,2}
* Giaxul, 200![200] = 200![1,2] ~ {10,10,199,2}
* Kilogiaxul, (200![200])![200] ~ {10,3,200,2}
* Megagiaxul, ((200![200])![200])![200] ~ {10,4,200,2}
* Gigagiaxul, (((200![200])![200])![200])![200] ~ {10,5,200,2}
* Teragiaxul, ((((200![200])![200])![200])![200])![200] ~ {10,6,200,2}
* Petagiaxul, (((((200![200])![200])![200])![200])![200])![200] ~ {10,7,200,2}
* Exagiaxul, ((((((200![200])![200])![200])![200])![200])![200])![200] ~ {10,8,200,2}
* Ultron, <math>\approx f_{\omega+200}(100)</math>
* Grand Giaxul, 200(![200])<sup>200![200]+1</sup> ~ {10,giaxul,200,2}
* Grand Kilogiaxul, 200(![200])<sup>(200![200])![200]+1</sup> ~ {10,kilogiaxul,200,2}
* Grand Megagiaxul, 200(![200])<sup>((200![200])![200])![200]+1</sup>
* Grand Gigagiaxul, 200(![200])<sup>(((200![200])![200])![200])![200]+1</sup>
* Grand Teragiaxul, 200(![200])<sup>((((200![200])![200])![200])![200])![200]+1</sup>
* Grand Petagiaxul, 200(![200])<sup>(((((200![200])![200])![200])![200])![200])![200]+1</sup>
* Grand Exagiaxul, 200(![200])<sup>((((((200![200])![200])![200])![200])![200])![200])![200]+1</sup>
* Bigrand Giaxul, 200(![200])<sup>200(![200])<sup>200![200]+1</sup>+1</sup> ~ {10,Grand Giaxul,200,2}
* Bigrand Kilogiaxul, 200(![200])<sup>200(![200])<sup>(200![200])![200]+1</sup>+1</sup>
* Bigrand Megagiaxul, 200(![200])<sup>200(![200])<sup>((200![200])![200])![200]+1</sup>+1</sup>
* Trigrand Giaxul, 200(![200])<sup>200(![200])<sup>200(![200])<sup>200![200]+1</sup>+1</sup>+1</sup> ~ {10,4,201,2}
* Trigrand Kilogiaxul, 200(![200])<sup>200(![200])<sup>200(![200])<sup>(200![200])![200]+1</sup>+1</sup>+1</sup>
* Trigrand Megagiaxul, 200(![200])<sup>200(![200])<sup>200(![200])<sup>((200![200])![200])![200]+1</sup>+1</sup>+1</sup>
* Quadgrand Giaxul, 200(![200])<sup>200(![200])<sup>200(![200])<sup>200(![200])<sup>200![200]+1</sup>+1</sup>+1</sup>+1</sup> ~ {10,5,201,2}
* Quintgrand Giaxul, 200(![200])<sup>200(![200])<sup>200(![200])<sup>200(![200])<sup>200(![200])<sup>200![200]+1</sup>+1</sup>+1</sup>+1</sup>+1</sup> ~ {10,6,201,2}
* Bigranika, <0,2> |488
* Bwiggol / biggolchime, {10,10,1000,2}
* Kiladdom, <math>f_{\omega+1000}(10)</math>
* Biggoltoll, {10,10,10000,2}
* Skibidi toilet grimace ohio, <math>f_{\omega 2}(69420)</math>
* Biggolgong, {10,10,100000,2}
* Megaddom, <math>f_{\omega+1000000}(10)</math>
* Terribocal, Forcal<sub>1000000</sub>(1) = Forcal<sub>1,2</sub>(1)
* Biggolbong, {10,10,100000000,2}
* Gigaddom, <math>f_{\omega+10^9}(10)</math>
* Biggolthrong, {10,10,{10,11},2}
* Teraddom, <math>f_{\omega+10^{12}}(10)</math>
* Petaddom, <math>f_{\omega+10^{15}}(10)</math>
* Exaddom, <math>f_{\omega+10^{18}}(10)</math>
* Zettaddom, <math>f_{\omega+10^{21}}(10)</math>
* Yottaddom, <math>f_{\omega+10^{24}}(10)</math>
* Googolplexitris, E100##100##(E100)
* Googolplexplexitris, E100##100##(E100#2)

=== Part 3.6: <math>f_{\omega2}(f_3(10))</math> ~ <math>f_{\omega3}(f_3(10))</math> ===

* Duprimitol, s(3,2,2,3)
* Grangolplexitris, E100##100##(E100#100)
* Greagolplexitris, E100##100##(E100#100#100)
* Gigangolplexitris, E100##100##(E100#100#100#100)
* Great gugold / Gugolda-plexitris, E100##100##1#2
* Great graatagold, E100##100##2#2
* Great greegold, E100##100##3#2
* Grand tritriplex, {3,3,1,3}
* Great grinningold, E100##100##4#2
* Great golaagold, E100##100##5#2
* Great gruelohgold, E100##100##6#2
* Great gaspgold, E100##100##7#2
* Great ginorgold, E100##100##8#2
* Great gargantuuld, E100##100##9#2
* Great googondold, E100##100##10#2
* Gugolthra-plexitris, E100##100##100#2
* Biggolplex, {10,10,{10,10,100,2},2}
* Ultronplex, <math>\approx f_{\omega2}(f_{\omega+200}(100))</math>
* Terribocaior Terribocal, Forcal<sub>Terribocal</sub>(1) = Forcal<sub>1,2</sub>(2)
* Duprimitolplex, s(3,3,2,3)
* Gugolthra-duplexitris, E100##100##100#3
* Biggolduplex, {10,10,{10,10,{10,10,100,2},2},2}
* Gugolthra-triplexitris, E100##100##100#4
* Unadd-bultom, <math>f_{\omega2+1}(10)</math>
* Bi-Unfyn, <u>2</u><sub>1</sub>(76)
* Dukil-Googol / corplodal, 10[1,2]100 = {10,100,1,3}
* Graatagolthra / graatathra, E100##100##100##2
* Terribuporcal, Forcal<sub>2,2</sub>(1)
* Wonkapoogol, <math>h_x(h,\underbrace{10,10,\cdots,10,10}_{\text{100 10's}})(100)</math>
* Duprimibol, s(3,2,3,3)
* Graatagolthra-dexitris, E100##100##100#100#2
* Terribuperior Terribuporcal, Forcal<sub>2,2</sub>(2)
* Wonkapoogolplex, <math>h_x(h,\underbrace{10,10,\cdots,10,10}_{\text{wonkapoogol 10's}})(100)</math>
* Tetentri / duprimibolplex, s(3,3,3,3)
* Graatagolthra-dudexitris, E100##100##100#100#3
* Graatagolthra-tridexitris, E100##100##100#100#4
* Badd-bultom, <math>f_{\omega2+2}(10)</math>
* Bi-Deufyn, <u>2</u><sub>2</sub>(76)
* Dukil-Doogol / mulplodal, 10[2,2]100 = {10,100,2,3}
* Greegolthra / greegathra, E100##100##100##3
* Terribegocal, Forcal<sub>3,2</sub>(1)
* Tetratri, {3,3,3,3}
* Greegolthra-threxitris, E100##100##100#100#100#2
* Greegolthra-duthrexitris, E100##100##100#100#100#3
* Greegolthra-trithrexitris, E100##100##100#100#100#4
* Tradd-bultom, <math>f_{\omega2+3}(10)</math>
* Bi-Troifyn, <u>2</u><sub>3</sub>(76)
* Powplodal, {10,100,3,3}
* Grinningolthra / grinninthra, E100##100##100##4
* Terribypercal, Forcal<sub>4,2</sub>(1)
* Grinningolthra-tetrexitris, E100##100##100#100#100#100#2
* Grinningolthra-dutetrexitris, E100##100##100#100#100#100#3
* Grinningolthra-tritetrexitris, E100##100##100#100#100#100#4
* Terplodal, {10,100,4,3}
* Kirby-Paris hydra|Hydra(4) (lower bound), <math>> f_{\omega2+4}(5)</math>
* Hecta-pepto-hypermel, 100[100#####100]
* Golaagolthra / golaathra, E100##100##100##5
* Chan.c numbers|chan-3.c, <math>\approx f_{\omega2+4}(9998)</math>
* Terriborgecal, Forcal<sub>5,2</sub>(1)
* Golaagolthra-pentexitris, E100##100##100#100#100#100#100#2
* Golaagolthra-dupentexitris, E100##100##100#100#100#100#100#3
* Golaagolthra-tripentexitris, E100##100##100#100#100#100#100#4
* Pentplodal, {10,100,5,3}
* Gruelohgolthra / gruelohthra, E100##100##100##6
* Terribulfcal, Forcal<sub>6,2</sub>(1)
* Gruelohgolthra-hexitris, E100##100##100#100#100#100#100#100#2
* Gruelohgolthra-duhexitris, E100##100##100#100#100#100#100#100#3
* Gruelohgolthra-trihexitris, E100##100##100#100#100#100#100#100#4
* Septasexahexar, <math>Q_{3,0}(6)</math>
* Gaspgolthra, E100##100##100##7
* Terribaspcal, Forcal<sub>7,2</sub>(1)
* Gaspgolthra-heptexitris, E100##100##100#100#100#100#100#100#100#2
* Gaspgolthra-duheptexitris, E100##100##100#100#100#100#100#100#100#3
* Gaspgolthra-triheptexitris, E100##100##100#100#100#100#100#100#100#4
* Ginorgolthra, E100##100##100##8
* Terribinorcal, Forcal<sub>8,2</sub>(1)
* Ginorgolthra-octexitris, E100##100##100#100#100#100#100#100#100#100#2
* Ginorgolthra-duoctexitris, E100##100##100#100#100#100#100#100#100#100#3
* Ginorgolthra-trioctexitris, E100##100##100#100#100#100#100#100#100#100#4
* Gargantuulthra, E100##100##100##9
* Gargantuulthra-ennexitris, E100##100##100#100#100#100#100#100#100#100#100#2
* Gargantuulthra-duennexitris, E100##100##100#100#100#100#100#100#100#100#100#3
* Gargantuulthra-triennexitris, E100##100##100#100#100#100#100#100#100#100#100#4
* Hecta-dekato-hypermel, 100[100##########100]
* Googondolthra, E100##100##100##10
* Googondolthra-decexitris, E100##100##100#100#100#100#100#100#100#100#100#100#2
* Googondolthra-dudecexitris, E100##100##100#100#100#100#100#100#100#100#100#100#3
* Googondolthra-tridecexitris, E100##100##100#100#100#100#100#100#100#100#100#100#4
* Great tridecal, {10,10,10,3}
* Iteraduis, 10[&&10] = 10[&&&]
* Trultom / dekadd-bultom, <math>f_{\omega3}(10)</math>
* Googonkosolthra, E100##100##100##20
* Googontritolthra, E100##100##100##30
* Googonsartolthra, E100##100##100##40
* Googonpetolthra, E100##100##100##50
* Googonextolthra, E100##100##100##60
* Googoneptolthra, E100##100##100##70
* Tri-Fyn, <u>3</u><sub>0</sub>(76)
* Googonogdolthra, E100##100##100##80
* Googonentolthra, E100##100##100##90
* Gugoltesla / gugontesla / googonhectolthra / gooltesla, E100##100##100##100
* Baggol / Trukiloogol, {10,10,100,3} = 10[0,3]100
* Tri-astragold, #^^^((10))*100
* Juice infused Chain Arrows, <math>17 \rightarrow 592 \rightarrow 186 \rightarrow 44 \rightarrow 416</math>
* Trigranika, <0,3> |488
* Bwaggol, {10,10,1000,3}
* Baggoltoll, {10,10,10000,3}
* Baggolgong, {10,10,100000,3}
* Tribocal, Forcal<sub>1000000,2</sub>(1) = Forcal<sub>1,3</sub>(1)

=== Part 3.7: <math>f_{\omega3}(f_3(10))</math> ~ <math>f_{\omega5}(f_3(10))</math> ===

* Truprimitol, s(3,2,2,4)
* Gugoltesla-plexitetris, E100##100##100##100#2
* Baggolplex, {10,10,{10,10,100,3},3}
* Tribocaior Tribocal, Forcal<sub>1,3</sub>(2)
* Truprimitolplex, s(3,3,2,4)
* Tri-Unfyn, <u>3</u><sub>1</sub>(76)
* Cordetal, {10,100,1,4}
* Graatagoltesla / graatatesla, E100##100##100##100##2
* Tribuporcal, Forcal<sub>2,3</sub>(1)
* Truprimibol, s(3,2,3,4)
* Graatagoltesla-dexitetris, E100##100##100##100#100#2
* Truprimibolplex, s(3,3,3,4)
* Tri-Deufyn, <u>3</u><sub>2</sub>(76)
* Muldetal, {10,100,2,4}
* Greegoltesla / greegatesla, E100##100##100##100##3
* Tribegocal, Forcal<sub>3,3</sub>(1)
* Powdetal, {10,100,3,4}
* Greegoltesla-threxitetris, E100##100##100##100#100#100#2
* Hayden's Tetratri, 3(3)(3)3
* Tetentet, s(4,4,4,4)
* Tri-Troifyn, <u>3</u><sub>3</sub>(76)
* Grinningoltesla / grinnintesla, E100##100##100##100##4
* Tribypercal, Forcal<sub>4,3</sub>(1)
* Grinningoltesla-tetrexitetris, E100##100##100##100#100#100#100#2
* Supertet, {4,4,4,4}
* Tetdetal, {10,100,4,4}
* Golaagoltesla / golaatesla, E100##100##100##100##5
* Golaagoltesla-pentexitetris, E100##100##100##100#100#100#100#100#2
* Gruelohgoltesla / gruelohtesla, E100##100##100##100##6
* Gruelohgoltesla-hexitetris, E100##100##100##100#100#100#100#100#100#2
* Septasexa-sexahexar, <math>Q_{4,0}(6)</math>
* Gaspgoltesla, E100##100##100##100##7
* Gaspgoltesla-heptexitetris, E100##100##100##100#100#100#100#100#100#100#2
* Ginorgoltesla, E100##100##100##100##8
* Ginorgoltesla-octexitetris, E100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuultesla, E100##100##100##100##9
* Gargantuultesla-ennexitetris, E100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondoltesla, E100##100##100##100##10
* Gigantic tridecal, {10,10,10,4}
* Iteratris, 10[&&&10] = 10[&&&&]
* Quadrultom, <math>f_{\omega4}(10)</math>
* Googonkosoltesla, E100##100##100##100##20
* Googontritoltesla, E100##100##100##100##30
* Googonsartoltesla, E100##100##100##100##40
* Googonpetoltesla, E100##100##100##100##50
* Googonextoltesla, E100##100##100##100##60
* Googoneptoltesla, E100##100##100##100##70
* Googonogdoltesla, E100##100##100##100##80
* Googonentoltesla, E100##100##100##100##90
* Gugolpeta / gugonpeta / googonhectoltesla / goolpeta, E100##100##100##100##100
* Beegol / Tetrukiloogol, {10,10,100,4} = 10[0,4]100
* Bweegol, {10,10,1000,4}
* Beegolgong, {10,10,100000,4}
* Tetribocal, Forcal<sub>1,4</sub>(1)
* Quadprimitol, s(3,2,2,5)
* Gugolpeta-plexipentris, E100##100##100##100##100#2
* Beegolplex, {10,10,{10,10,100,4},4}
* Quadprimitolplex, s(3,3,2,5)
* Septahexar-unnar, <math>Q_{4,1}(6)</math>
* Corpental, {10,100,1,5}
* Graatagolpeta / graatapeta, E100##100##100##100##100##2
* Tetribuporcal, Forcal<sub>2,4</sub>(1)
* Quadprimibol, s(3,2,3,5)
* Graatagolpeta-dexipentris, E100##100##100##100##100#100#2
* Quadprimibolplex, s(3,3,3,5)
* Septahexar-duar, <math>Q_{4,2}(6)</math>
* Greegolpeta / greegapeta, E100##100##100##100##100##3
* Greegolpeta-threxipentris, E100##100##100##100##100#100#100#2
* Septahexar-trear, <math>Q_{4,3}(6)</math>
* Grinningolpeta / grinninpeta, E100##100##100##100##100##4
* Grinningolpeta-tetrexipentris, E100##100##100##100##100#100#100#100#2
* Hayden's Tetratet, 4(4)(4)4
* Tetenpent, s(5,5,5,5)
* Septahexar-quadrar, <math>Q_{4,4}(6)</math>
* Golaagolpeta / golaapeta, E100##100##100##100##100##5
* Golaagolpeta-pentexipentris, E100##100##100##100##100#100#100#100#100#2
* Tetrapent, {5,5,5,5}
* Septahexar-quintar, <math>Q_{4,5}(6)</math>
* Gruelohgolpeta / gruelohpeta, E100##100##100##100##100##6
* Gruelohgolpeta-hexipentris, E100##100##100##100##100#100#100#100#100#100#2
* Septahexar-sexar, <math>Q_{5,0}(6)</math>
* Gaspgolpeta, E100##100##100##100##100##7
* Gaspgolpeta-heptexipentris, E100##100##100##100##100#100#100#100#100#100#100#2
* Ginorgolpeta, E100##100##100##100##100##8
* Ginorgolpeta-octexipentris, E100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuulpeta, E100##100##100##100##100##9
* Gargantuulpeta-ennexipentris, E100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondolpeta, E100##100##100##100##100##10
* Googondolpeta-decexipentris, E100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* Gorged tridecal, {10,10,10,5}
* Quintultom, <math>f_{\omega5}(10)</math>
* Googonkosolpeta, E100##100##100##100##100##20
* Googontritolpeta, E100##100##100##100##100##30
* Googonsartolpeta, E100##100##100##100##100##40
* Googonpetolpeta, E100##100##100##100##100##50
* Googonextolpeta, E100##100##100##100##100##60
* Googoneptolpeta, E100##100##100##100##100##70
* Googonogdolpeta, E100##100##100##100##100##80
* Googonentolpeta, E100##100##100##100##100##90
* Gugolhexa / gugonhexa / googonhectolpeta / goolhexa, E100##100##100##100##100##100
* Bigol / Pentukiloogol, {10,10,100,5} = 10[0,5]100
* Bwigol, {10,10,1000,5}
* Bigolgong, {10,10,100000,5}
* Pentibocal, Forcal<sub>1,5</sub>(1)

=== Part 3.8: <math>f_{\omega5}(f_3(10))</math> ~ <math>f_{\omega7}(f_3(10))</math> ===

* Quinprimitol, s(3,2,2,6)
* Corhexal, {10,100,1,6}
* Gugolhexa-plexihexis, E100##100##100##100##100##100#2
* Quinprimitolplex, s(3,3,2,6)
* Septahexar-septar, <math>Q_{5,1}(6)</math>
* Graatagolhexa / graatahexa, E100##100##100##100##100##100#100
* Quinprimibol, s(3,2,3,6)
* Graatagolhexa-dexihexis, E100##100##100##100##100##100#100#2
* Quinprimibolplex, s(3,3,3,6)
* Septahexar-octar, <math>Q_{5,2}(6)</math>
* Greegolhexa / greegahexa, E100##100##100##100##100##100##3
* Greegolhexa-threxihexis, E100##100##100##100##100##100#100#100#2
* Septahexar-nonar, <math>Q_{5,3}(6)</math>
* Grinningolhexa / grinninhexa, E100##100##100##100##100##100##4
* Grinningolhexa-tetrexihexis, E100##100##100##100##100##100#100#100#100#2
* Septahexar-decar, <math>Q_{5,4}(6)</math>
* Golaagolhexa / golaahexa, E100##100##100##100##100##100##5
* Golaagolhexa-pentexihexis, E100##100##100##100##100##100#100#100#100#100#2
* Ascendhex, {3, 4, 5, 6}
* Tetenhex, s(6,6,6,6)
* Septahexar-undecar, <math>Q_{5,5}(6)</math>
* Gruelohgolhexa / gruelohhexa, E100##100##100##100##100##100##6
* Gruelohgolhexa-hexihexis, E100##100##100##100##100##100#100#100#100#100#100#2
* Tetrahex, {6,6,6,6}
* Septahexar-hexar, <math>Q_{1,0,0}(6)</math>
* Gaspgolhexa, E100##100##100##100##100##100##7
* Gaspgolhexa-heptexihexis, E100##100##100##100##100##100#100#100#100#100#100#100#2
* Ginorgolhexa, E100##100##100##100##100##100##8
* Ginorgolhexa-octexihexis, E100##100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuulhexa, E100##100##100##100##100##100##9
* Gargantuulhexa-ennexihexis, E100##100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondolhexa, E100##100##100##100##100##100##10
* Googondolhexa-decexihexis, E100##100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* Gulp tridecal, {10,10,10,6}
* Iterapentis, 10[&&&&&10] = 10[&&&&&&]
* Sextultom, <math>f_{\omega6}(10)</math>
* Googonkosolhexa, E100##100##100##100##100##100##20
* Googontritolhexa, E100##100##100##100##100##100##30
* Googonsartolhexa, E100##100##100##100##100##100##40
* Googonpetolhexa, E100##100##100##100##100##100##50
* Googonextolhexa, E100##100##100##100##100##100##60
* Googoneptolhexa, E100##100##100##100##100##100##70
* Googonogdolhexa, E100##100##100##100##100##100##80
* Googonentolhexa, E100##100##100##100##100##100##90
* Gugolhepta / gugonhepta / googonhectolhexa, E100##100##100##100##100##100##100
* Boggol / Hexukiloogol, {10,10,100,6} = 10[0,6]100
* Bwoggol, {10,10,1000,6}
* Hexibocal, Forcal<sub>1,6</sub>(1)
* Gugolhepta-plexiheptis, E100##100##100##100##100##100##100#2
* Boggolplex, {10,10,{10,10,100,6},6}
* Corheptal, {10,100,1,7}
* Graatagolhepta, E100##100##100##100##100##100##100#100
* Graatagolhepta-dexiheptis, E100##100##100##100##100##100##100#100#2
* Greegolhepta, E100##100##100##100##100##100##100##3
* Greegolhepta-threxiheptis, E100##100##100##100##100##100##100#100#100#2
* Grinningolhepta, E100##100##100##100##100##100##100##4
* Grinningolhepta-tetrexiheptis, E100##100##100##100##100##100##100#100#100#100#2
* Golaagolhepta, E100##100##100##100##100##100##100##5
* Golaagolhepta-pentexiheptis, E100##100##100##100##100##100##100#100#100#100#100#2
* Gruelohgolhepta, E100##100##100##100##100##100##100##6
* Gruelohgolhepta-hexiheptis, E100##100##100##100##100##100##100#100#100#100#100#100#2
* Gaspgolhepta, E100##100##100##100##100##100##100##7
* Gaspgolhepta-heptexiheptis, E100##100##100##100##100##100##100#100#100#100#100#100#100#2
* Tetrahept, {7,7,7,7}
* Ginorgolhepta, E100##100##100##100##100##100##100##8
* Ginorgolhepta-octexiheptis, E100##100##100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuulhepta, E100##100##100##100##100##100##100##9
* Gargantuulhepta-ennexiheptis, E100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondolhepta, E100##100##100##100##100##100##100##10
* Googondolhepta-decexiheptis, E100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* Gasp tridecal, {10,10,10,7}
* Septultom, <math>f_{\omega7}(10)</math>
* Googonkosolhepta, E100##100##100##100##100##100##100##20
* Googontritolhepta, E100##100##100##100##100##100##100##30
* Googonsartolhepta, E100##100##100##100##100##100##100##40
* Googonpetolhepta, E100##100##100##100##100##100##100##50
* Googonextolhepta, E100##100##100##100##100##100##100##60
* Googoneptolhepta, E100##100##100##100##100##100##100##70
* Googonogdolhepta, E100##100##100##100##100##100##100##80
* Googonentolhepta, E100##100##100##100##100##100##100##90
* Gugolocta / gugonocta / googonhectolhepta, E100##100##100##100##100##100##100##100
* Bagol / Heptukiloogol, {10,10,100,7} = 10[0,7]100
* Bwagol, {10,10,1000,7}
* Heptibocal, Forcal<sub>1,7</sub>(1)

=== Part 3.9: <math>f_{\omega7}(f_3(10))</math> ~ <math>f_{\omega10}(f_3(10))</math> ===

* Gugolocta-plexoctis, E100##100##100##100##100##100##100##100#2
* Coroctal, {10,100,1,8}
* Graatagolocta, E100##100##100##100##100##100##100##100#100
* Graatagolocta-dexoctis, E100##100##100##100##100##100##100##100#100#2
* Greegolocta, E100##100##100##100##100##100##100##100##3
* Greegolocta-threxoctis, E100##100##100##100##100##100##100##100#100#100#2
* Grinningolocta, E100##100##100##100##100##100##100##100##4
* Grinningolocta-tetrexoctis, E100##100##100##100##100##100##100##100#100#100#100#2
* Golaagolocta, E100##100##100##100##100##100##100##100##5
* Golaagolocta-pentexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#2
* Gruelohgolocta, E100##100##100##100##100##100##100##100##6
* Gruelohgolocta-hexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#100#2
* Gaspgolocta, E100##100##100##100##100##100##100##100##7
* Gaspgolocta-heptexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#100#100#2
* Ginorgolocta, E100##100##100##100##100##100##100##100##8
* Ginorgolocta-octexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuulocta, E100##100##100##100##100##100##100##100##9
* Gargantuulocta-ennexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondolocta, E100##100##100##100##100##100##100##100##10
* Googondolocta-decexoctis, E100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* Octultom, <math>f_{\omega8}(10)</math>
* Googonkosolocta, E100##100##100##100##100##100##100##100##20
* Googontritolocta, E100##100##100##100##100##100##100##100##30
* Googonsartolocta, E100##100##100##100##100##100##100##100##40
* Googonpetolocta, E100##100##100##100##100##100##100##100##50
* Googonextolocta, E100##100##100##100##100##100##100##100##60
* Googoneptolocta, E100##100##100##100##100##100##100##100##70
* Googonogdolocta, E100##100##100##100##100##100##100##100##80
* Googonentolocta, E100##100##100##100##100##100##100##100##90
* Bocgol, {10,10,100,8}
* Gugolenna / gugonenna / googonhectolocta / gooemeralnona, E100##100##100##100##100##100##100##100##100
* Octukiloogol, 10[0,8]100
* Bwocgol, {10,10,1000,8}
* Octibocal, Forcal<sub>1,8</sub>(1)
* Bocgolplex, {10,10,bocgol,8}
* Gugolenna-plexenna, E100##100##100##100##100##100##100##100##100#2
* Corental, {10,100,1,9}
* Graatagolenna, E100##100##100##100##100##100##100##100##100#100
* Graatagolenna-dexenna, E100##100##100##100##100##100##100##100##100#100#2
* Greegolenna, E100##100##100##100##100##100##100##100##100##3
* Greegolenna-threxenna, E100##100##100##100##100##100##100##100##100#100#100#2
* Grinningolenna, E100##100##100##100##100##100##100##100##100##4
* Grinningolenna-tetrexenna, E100##100##100##100##100##100##100##100##100#100#100#100#2
* Golaagolenna, E100##100##100##100##100##100##100##100##100##5
* Golaagolenna-pentexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#2
* Gruelohgolenna, E100##100##100##100##100##100##100##100##100##6
* Gruelohgolenna-hexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#100#2
* Gaspgolenna, E100##100##100##100##100##100##100##100##100##7
* Gaspgolenna-heptexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#2
* Ginorgolenna, E100##100##100##100##100##100##100##100##100##8
* Ginorgolenna-octexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuulenna, E100##100##100##100##100##100##100##100##100##9
* Gargantuulenna-ennexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondolenna, E100##100##100##100##100##100##100##100##100##10
* Googondolenna-decexenna, E100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* Nonultom, <math>f_{\omega9}(10)</math>
* Googonkosolenna, E100##100##100##100##100##100##100##100##100##20
* Googontritolenna, E100##100##100##100##100##100##100##100##100##30
* Googonsartolenna, E100##100##100##100##100##100##100##100##100##40
* Googonpetolenna, E100##100##100##100##100##100##100##100##100##50
* Googonextolenna, E100##100##100##100##100##100##100##100##100##60
* Googoneptolenna, E100##100##100##100##100##100##100##100##100##70
* Googonogdolenna, E100##100##100##100##100##100##100##100##100##80
* Googonentolenna, E100##100##100##100##100##100##100##100##100##90
* Gugoldeka / googonhectolenna / gugondeka / gooemeraldeca, E100##100##100##100##100##100##100##100##100##100
* Ennukiloogol, 10[0,9]100
* Bwengol, {10,10,1000,9}
* Bengolplex, {10,10,{10,10,100,9},9}
* Gugoldeka-plexideka, E100##100##100##100##100##100##100##100##100##100#2
* Cordecal, {10,100,1,10}
* Graatagoldeka, E100##100##100##100##100##100##100##100##100##100#100
* Graatagoldeka-dexideka, E100##100##100##100##100##100##100##100##100##100#100#2
* Greegoldeka, E100##100##100##100##100##100##100##100##100##100##3
* Greegoldeka-threxideka, E100##100##100##100##100##100##100##100##100##100#100#100#2
* Grinningoldeka, E100##100##100##100##100##100##100##100##100##100##4
* Grinningoldeka-tetrexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#2
* Golaagoldeka, E100##100##100##100##100##100##100##100##100##100##5
* Golaagoldeka-pentexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#2
* Gruelohgoldeka, E100##100##100##100##100##100##100##100##100##100##6
* Gruelohgoldeka-hexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#2
* Gaspgoldeka, E100##100##100##100##100##100##100##100##100##100##7
* Gaspgoldeka-heptexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#2
* Ginorgoldeka, E100##100##100##100##100##100##100##100##100##100##8
* Ginorgoldeka-octexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#2
* Gargantuuldeka, E100##100##100##100##100##100##100##100##100##100##9
* Gargantuuldeka-ennexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#2
* Googondoldeka, E100##100##100##100##100##100##100##100##100##100##10
* Googondoldeka-decexideka, E100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#100#2
* General / tetradecal, {10,10,10,10}
* Dekultom / bexom, <math>f_{\omega10}(10)</math>
* Googonkosoldeka, E100##100##100##100##100##100##100##100##100##100##20
* Googontritoldeka, E100##100##100##100##100##100##100##100##100##100##30
* Googonsartoldeka, E100##100##100##100##100##100##100##100##100##100##40
* Googonpetoldeka, E100##100##100##100##100##100##100##100##100##100##50
* Googonextoldeka, E100##100##100##100##100##100##100##100##100##100##60
* Googoneptoldeka, E100##100##100##100##100##100##100##100##100##100##70
* Googonogdoldeka, E100##100##100##100##100##100##100##100##100##100##80
* Googonentoldeka, E100##100##100##100##100##100##100##100##100##100##90
* Gugolendeka / googonhectoldeka / gooemeralelevened, E100###11
* Dekagranika, <0,10> |488
* Bexgol / dekukiloogol, {10,10,100,10} = 10[0,10]100
* Bwexgol, {10,10,1000,10}

=== Part 3.10: <math>f_{\omega10}(f_3(10))</math> ~ <math>f_{\omega^2}(f_3(10))</math> ===

* Bexgolplex, {10,10,{10,10,100,10},10}
* Hayden's General, 10(10)(10)10
* Iteradekis, 10[&&&&&&&&&&10] = 10[&&&&&&&&&&&]
* Gugoldodeka / gooemeraldozed, E100###12
* Tetradozenal, {12,12,12,12}
* Gugoltriadeka, E100###13
* Gugoltetradeka, E100###14
* Gugolpentadeka, E100###15
* Gugolhexadeka, E100###16
* Gugolheptadeka, E100###17
* Gugoloctadeka, E100###18
* Gugolennadeka, E100###19
* Troo-guppy, {10,10,10,20}
* Gugolicosa, E100###20
* Gugoltrianta, E100###30
* Pete.c numbers|pete-4.c, <math>\approx f_{\omega33}(10^5)</math>
* Gugolsaranta, E100###40
* Troo-gogol, {10,10,10,50}
* Gugolpeninta, E100###50
* Chan.c numbers|chan.c, <math>\approx f_{\omega50}(10^5)</math>
* Gugolexinta, E100###60
* White-aster, <math>\text{Ast}[5,\langle64\rangle]</math>
* Gugolebdominta, E100###70
* Greps, |1|<sub>0</sub>(76)
* Gugologdonta, E100###80
* Troogolspeck, {10,10,10,90}
* Gugoleneninta, E100###90
* Throogol / throogord / gugolhecta / goohoolgol, E100###100
* Grandogoogolplex, 10<sup>E100###100</sup>
* Grandogoogoldex, E100#(E100###100)
* Grandogoogolsuplex, E100##(E100###100)
* Grandogoogolsusuplex, E100##100##(E100###100)
* Grandogoogoltetrasuplex, E100##100##100##(E100###100)
* Troogol / Megoogol, {10,10,10,100} = 10[0,0,1]100
* Hektultom, <math>f_{\omega100}(10)</math>
* Tetrahectal, {100,100,100,100}
* Grid-hyperon, 100{X<sup>2</sup>}100
* Astuul, #{1}((10))*100
* Hektagranika, <0,100> |488
* Kaboodol, <math>f\rightarrow\underbrace{10\rightarrow\ldots10\rightarrow10}_{100}(100)</math>, where f(n) = hyper(n,n,n)
* Wakamoogol, <math>h\rightarrow\underbrace{10\rightarrow\cdots10\rightarrow10}_{\text{100 10's}}(100)</math>, where h is hyperlicious function
* Giabollaxul, 200$1
* Giabixul, 200![200,200] ~ {10,10,199,201}
* Kilogiabixul, (200![200,200])![200,200] ~ {10,3,200,201}
* Megagiabixul, ((200![200,200])![200,200])![200,200] ~ {10,4,200,201}
* Gigagiabixul, (((200![200,200])![200,200])![200,200])![200,200] ~ {10,5,200,201}
* Grand Giabixul, 200(![200,200])<sup>200![200,200]+1</sup> ~ {10,giabixul,200,201}
* Grand Kilogiabixul, 200(![200,200])<sup>(200![200,200])![200,200]+1</sup> ~ {10,kilogiabixul,200,201}
* Grand Megagiabixul, 200(![200,200])<sup>((200![200,200])![200,200])![200,200]+1</sup>
* Grand Gigagiabixul, 200(![200,200])<sup>(((200![200,200])![200,200])![200,200])![200,200]+1</sup>
* Bigrand Giabixul, 200(![200,200])<sup>200(![200,200])<sup>200![200,200]+1</sup>+1</sup> ~ {10,Grand Giabixul,200,201}
* Trigrand Giabixul, 200(![200,200])<sup>200(![200,200])<sup>200(![200,200])<sup>200![200,200]+1</sup>+1</sup>+1</sup> ~ {10,4,201,201}
* Collanika, <0,0,1>|488
* Throogolchime, E1000###1000
* Trwoogol, {10,10,10,1000}
* Kilultom, <math>f_{\omega1000}(10)</math>
* Throogoltoll, E10,000###10,000
* Troogoltoll, {10,10,10,10000}
* Level 5 gyatt rizz livvy dunne rizzing up baby gronk, <math>f_{\omega^2}(69420)</math>
* Throogolgong, E100,000###100,000
* Troogolgong, {10,10,10,100000}
* Gugolchilia-chila / gugolmega, E100###1,000,000
* Megultom, <math>f_{\omega1000000}(10)</math>
* Tris-Terribocal, Forcal<sub>1,1000000</sub>(1) = Forcal<sub>1,1,2</sub>(1)
* Gigultom, <math>f_{\omega10^9}(10)</math>
* Terultom, <math>f_{\omega10^{12}}(10)</math>
* Petultom, <math>f_{\omega10^{15}}(10)</math>
* Exultom, <math>f_{\omega10^{18}}(10)</math>
* Zettultom, <math>f_{\omega10^{21}}(10)</math>
* Yottultom, <math>f_{\omega10^{24}}(10)</math>
* Googolplexithird, E100###1#2

== Quadratic omega level ==

=== Part 3.11: <math>f_{\omega^2}(f_3(10))</math> ~ <math>f_{\omega^2 2}(f_3(10))</math> ===

* Chainol, s(3,2,2,1,2)
* Gugolda-plexithird, E100###2#2
* Great gugolthra, E100###3#2
* Tetratriplex, {3,3,1,1,2}
* Gugoltesla-plexithird / Great gugoltesla, E100###4#2
* Gugolpeta-plexithird / Great gugolpeta, E100###5#2
* Gugolhexa-plexithird / Great gugolhexa, E100###6#2
* Gugolhepta-plexithird / Great gugolhepta, E100###7#2
* Gugolocta-plexithird / Great gugolocta, E100###8#2
* Gugolenna-plexithird / Great gugolenna, E100###9#2
* Gugoldeka-plexithird / Great gugoldeka, E100###10#2
* Generalplex, {10,3,1,1,2}
* Tetrahectalplex, {100,3,1,1,2}
* Grand throogol / Grandogoogolgrandoplex / Throogolplexithird, E100###100#2
* Kaboodolplex, <math>f\rightarrow\underbrace{10\rightarrow10\ldots\rightarrow10}_{\text{kaboodol}}(100)</math>, where f(n) = hyper(n,n,n)
* Wakamoogolplex, <math>h\rightarrow\underbrace{10\rightarrow10\cdots\rightarrow10}_{\text{wakamoogol 10's}}(100)</math>, where h is hyperlicious function
* <nowiki>Troogolplex, {10,10,10,{10,10,10,100}}</nowiki>
* Tris-Terribocaior Tris-Terribocal, Forcal<sub>1,1,2</sub>(2)
* Googolduplexithird, E100###1#3
* Gugolda-duplexithird, E100###2#3
* Gugolthra-duplexithird, E100###3#3
* Gugoltesla-duplexithird, E100###4#3
* Gugolpeta-duplexithird, E100###5#3
* Chainolplex, s(3,3,2,1,2)
* Grand grand throogol / Throogolduplexithird, E100###100#3
* <nowiki>Troogolduplex, {10,10,10,{10,10,10,{10,10,10,100}}}</nowiki>
* Chainolbiplex, s(3,4,2,1,2)
* Chainoltriplex, s(3,5,2,1,2)
* Chainolquadriplex, s(3,6,2,1,2)
* Unadd-bexom, <math>f_{\omega^2+1}(10)</math>
* '''Fish number 1''', <math>\approx f_{\omega^2+1}(63)</math>
* Ungreps, |1|<sub>1</sub>(76)
* Meg-Googol, 10[1,0,1]100
* Cormegoporal / corgreygotial, {10,100,1,1,2}
* Thrangol / granhoolgol, E100###100#100
* Rexuul, #{1}* ((10))*100
* Tris-Terribuporcal, Forcal<sub>2,1,2</sub>(1)
* Googoldexithird, E100###1#1#2
* Grangoldexithird, E100###100#(E100#100)
* Greagoldexithird, E100###100#(E100#100#100)
* Gigangoldexithird, E100###100#(E100#100#100#100)
* Gorgegoldexithird, E100###100#(E100#100#100#100#100)
* Gulgoldexithird, E100###100#(E100##6)
* Gaspgoldexithird, E100###100#(E100##7)
* Ginorgoldexithird, E100###100#(E100##8)
* Gugolda-dexithird, E100###2#1#2
* Graatagolda-dexithird, E100###100#(E100##100#100)
* Greegolda-dexithird, E100###100#(E100##100#100#100)
* Chainbol, s(3,2,3,1,2)
* Grinningolda-dexithird, E100###100#(E100##100##4)
* Mouffles Monster, cg<sup>G</sup>(G)
* Gugolthra-dexithird, E100###3#1#2
* Gugoltesla-dexithird, E100###4#1#2
* Gugolpeta-dexithird, E100###5#1#2
* Gugolhexa-dexithird, E100###6#1#2
* Throogoldexithird, E100###100#1#2
* Grand thrangol / Thrangoldexithird, E100###100#100#2
* BOX_M̃, <math>\approx f_{\omega^2+1}(f_{\omega^2}(f_{\omega+2}(f_{\omega+1}(64))))</math>
* Chainbolplex, s(3,3,3,1,2)
* Badd-bexom, <math>f_{\omega^2+2}(10)</math>
* Deugreps, |1|<sub>2</sub>(76)
* Meg-Doogol, 10[2,0,1]100
* Mulmegoporal / mulgreygotial, {10,100,2,1,2}
* Threagol / greahoolgol, E100###100#100#100
* Tris-Terribegorcal, Forcal<sub>3,1,2</sub>(1)
* Chaintrol, s(3,2,4,1,2)
* Grand threagol, E100###100#100#100#2
* Chaintrolplex, s(3,3,4,1,2)
* Troigreps, |1|<sub>3</sub>(76)
* Thrigangol / giganhoolgol, E100###100#100#100#100
* Tris-Terribypercal, Forcal<sub>4,1,2</sub>(1)
* Grand thrigangol, E100###100#100#100#100#2
* Grand coral, 3AA3
* Powmegoporal / powergreygotial, {10,100,4,1,2}
* Throrgegol / gorgehoolgol, E100###100##5
* Grand throrgegol, E100###100#100#100#100#100#2
* Tetramegoporal / tetragreygotial, {10,100,5,1,2}
* Thrulgol / gulhoolgol, E100###100##6
* Grand thrulgol, E100###100#100#100#100#100#100#2
* Thraspgol, E100###100##7
* Grand thraspgol, E100###100#100#100#100#100#100#100#2
* Thrinorgol, E100###100##8
* Grand thrinorgol, E100###100#100#100#100#100#100#100#100#2
* Thrarantuul, E100###100##9
* Grand thrarantuul, E100###100#100#100#100#100#100#100#100#100#2
* Throogondol, E100###100##10
* Bigreps, |2|<sub>0</sub>(76)
* Thrugold / goolhoolda, E100###100##100 = E100###100###2
* Aperiomegoporal, {10,10,100,1,2}
* Meg-Kiloogol, 10[0,1,1]100
* Gooandol, 10[&<sub>1</sub>100]
* Astuulgold, #{1}^((10))*100
* Tris-Terrible-Terribocal, Forcal<sub>1000000,1,2</sub>(1) = Forcal<sub>1,2,2</sub>(1)
* Fa fel falafel, E[16]128###(100Factorial|!)##(2^89-1)
* Coke d Lout, {10,10,{3,3,3,3},1,2}
* Chainprimol, s(3,2,2,2,2)
* Grand thrugold, E100###100##100#2
* Chainprimolplex, s(3,3,2,2,2)
* Meg-Kil-Googol, 10[1,1,1]100
* Thraatagold / graatahoolda, E100###100##100##2
* Chainpribol, s(3,2,3,2,2)
* Chainpribolplex, s(3,3,3,2,2)
* Multimegoporal, {10,100,2,2,2}
* Threegold / greegahoolda, E100###100##100#100#100
* Thrinningold / grinninhoolda, E100###100##100#100#100#100
* Great coral, 3AAA3
* Throlaagold / golaahoolda, E100###100##100#100#100#100#100
* Thruelohgold / gruelohhoolda, E100###100##100#100#100#100#100#100
* Thraspgold, E100###100##100##7
* Thrinorgold, E100###100##100##8
* Thrargantuuld, E100###100##100##9
* Throogondold, E100###100##100##10
* Trigreps, |3|<sub>0</sub>(76)
* Thrugolthra / goolhoolthra, E100###100##100##100
* Meg-Dukiloogol, 10[0,2,1]100
* Tris-Terrible-Tribocal, Forcal<sub>1,3,2</sub>(1)
* Chainduprimol, s(3,2,2,3,2)
* Chainduprimolplex, s(3,3,2,3,2)
* Cor-megoexplodal / cor-explodogotial, {10,100,1,3,2}
* Thraatagolthra, E100###100##100##100#100
* Chaindupribol, s(3,2,3,3,2)
* Chaindupribolplex, s(3,3,3,3,2)
* Threegolthra, E100###100##100##100#100#100
* Conway's Su-tritri, 3 →<sub>3</sub> 3
* Grand tetratri, {3,3,3,3,2}
* Cyper coral, 3B3
* Thrinningolthra, E100###100##100##100#100#100#100
* Descend-hex, {6,5,4,3,2}
* Throlaagolthra, E100###100##100##100##5
* Thruelohgolthra, E100###100##100##100##6
* Thraspgolthra, E100###100##100##100##7
* Thrinorgolthra, E100###100##100##100##8
* Thrargantuulthra, E100###100##100##100##9
* Throogondolthra, E100###100##100##100##10
* Thrugoltesla / goolhooltesla, E100###100##100##100##100
* Meg-Trukiloogol, 10[0,3,1]100
* Hph ý¢p, {345,245,{536,546},3,2}
* Tomodachi, (22 {4, 4} 37)
* Cor-megodetal / cordetonagotial, {10,100,1,4,2}
* Thraatagoltesla, E100###100##100##100#100
* Threegoltesla, E100###100##100##100##3
* Thrinningoltesla, E100###100##100##100##4
* Throlaagoltesla, E100###100##100##100##5
* Thruelohgoltesla, E100###100##100##100##6
* Tris-Terrible-Tetribocal, Forcal<sub>1,4,2</sub>(1)
* Chaintruprimol, s(3,2,2,4,2)
* Chaintruprimolplex, s(3,3,2,4,2)
* Chaintrupribol, s(3,2,3,4,2)
* Chaintrupribolplex, s(3,3,3,4,2)
* Thrugolpeta / goolhoolpeta, E100###100###5
* Cor-megopental / corpentonagotial, {10,100,1,5,2}
* Thraatagolpeta, E100###100##100##100##100##2
* Threegolpeta, E100###100##100##100##100##3
* Thrinningolpeta, E100###100##100##100##100##4
* A Ljónvrri = {144,28,8,5,2}
* Thrugolhexa / goolhoolhexa, E100###100###6
* Thraatagolhexa, E100###100##100##100##100##100##2
* Threegolhexa, E100###100##100##100##100##100##3
* Thrugolhepta, E100###100###7
* Thraatagolhepta, E100###100##100##100##100##100##100##2
* Thrugolocta, E100###100###8
* Thraatagolocta, E100###100##100##100##100##100##100##100##2
* Thrugolenna, E100###100###9
* Thrugoldeka, E100###100###10
* Grand tetradecal, {10,10,10,10,2}
* Inspire, 10[&<sub>1</sub>&<sub>1</sub>]
* Thrugolicosa, E100###100###20
* Thrugoltrianta, E100###100###30
* Thrugolsaranta, E100###100###40
* Thrugolpeninta, E100###100###50
* Grepss, <sup>3</sup><u>1</u><sub>0</sub>(76)
* Throotrigol / tristo-throogol / tris-throogol / gootroolgol, E100###100###100 = E100####3
* Duriga, s(10,100,1,1,3)
* Triggol / Dumegoogol, {10,10,10,100,2} = 10[0,0,2]100
* Trwiggol / triggolchime, {10,10,10,1000,2}
* Triggoltoll, {10,10,10,10000,2}
* Triggolgong, {10,10,10,100000,2}
* Tris-Tribocal, Forcal<sub>1,1000000,2</sub>(1) = Forcal<sub>1,1,3</sub>(1)

=== Part 3.12: <math>f_{\omega^2 2}(f_3(10))</math> ~ <math>f_{\omega^2 3}(f_3(10))</math> ===

* Duchainol, s(3,2,2,1,3)
* Grand throotrigol, E100###100###100#2
* Triggolplex, {10,10,10,{10,10,10,100,2},2}
* Tris-Tribocaior Tris-Tribocal, Forcal<sub>1,1,3</sub>(2)
* Duchainolplex, s(3,3,2,1,3)
* Dumeg-Googol, 10[1,0,2]100
* Thrantrigol / tristo-thrangol / tris-thrangol, E100###100###100##2
* Duchainbol, s(3,2,3,1,3)
* Duchainbolplex, s(3,3,3,1,3)
* Threatrigol / tristo-threagol / tris-threagol, E100###100###100##3
* Thrigantrigol, E100###100###100##4
* Throrgetrigol, E100###100###100##5
* Thrultrigol, E100###100###100##6
* Thrasptrigol, E100###100###100##7
* Thrinortrigol, E100###100###100##8
* Thrargantrituul, E100###100###100##9
* Throogontridol, E100###100###100##10
* Thrutrigold / tristo-thrugold / tris-thrugold, E100###100###100##100 = E100###100###100###2
* Dumeg-Kiloogol, 10[0,1,2]100
* Cor-gigotial, {10,100,1,1,3}
* Tris-Trible-Terribocal, Forcal<sub>1,2,3</sub>(1)
* Duchainprimol, s(3,2,2,2,3)
* Duchainprimolplex, s(3,3,2,2,3)
* Orca trek kit, E[56]10###10###10##80##2
* Thraatatrigold / tristo-thraatagold / tris-thraatagold, E100###100###100##100##2
* Duchainpribol, s(3,2,3,2,3)
* Duchainpribolplex, s(3,3,3,2,3)
* Threetrigold / tristo-threegold / tris-threegold, E100###100###100##100##3
* Thrinnintrigold, E100###100###100##100##4
* Throlaatrigold, E100###100###100##100##5
* Thruelohtrigold, E100###100###100##100##6
* Thrasptrigold, E100###100###100##100##7
* Thrinortrigold, E100###100###100##100##8
* Thrargantrituuld, E100###100###100##100##9
* Throogontridold, E100###100###100##100##10
* Thrutrigolthra / tristo-thrugolthra / tris-thrugolthra, E100###100###100##100##100 = E100###100###100###3
* Dumeg-Dukiloogol, 10[0,2,2]100
* Tris-Trible-Tribocal, Forcal<sub>1,3,3</sub>(1)
* Duchainduprimol, s(3,2,2,3,3)
* Duchainduprimolplex, s(3,3,2,3,3)
* Thraatatrigolthra / tristo-thraatagolthra / tris-thraatagolthra, E100###100###100##100##100##2
* Duchaindupribol, s(3,2,3,3,3)
* Pententri / duchaindupribolplex, s(3,3,3,3,3)
* Pentatri, {3,3,3,3,3}
* Dutrearmix, [3]↤[3]↤[3]
* TriCoral, 3G3
* Thrutrigoltesla / tristo-thrugoltesla / tris-thrugoltesla, E100###100###100###4
* Tris-Trible-Tetribocal, Forcal<sub>1,4,3</sub>(1)
* Conway's Su-tritet, 4 →<sub>4</sub> 4
* Thrutrigolpeta / tristo-thrugolpeta / tris-thrugolpeta, E100###100###100###5
* Thrutrigolhexa / tristo-thrugolhexa / tris-thrugolhexa, E100###100###100###6
* Admire, 10[&<sub>1</sub>&<sub>1</sub>&<sub>1</sub>]
* Great tetradecal, {10,10,10,10,3}
* Grepsss, <sup>4</sup><u>1</u><sub>0</sub>(76)
* Throotergol / teristo-throogol / tessi-throogol, E100###100###100###100 = E100####4
* Traggol / Trumegoogol, {10,10,10,100,3} = 10[0,0,3]100
* Tri-astuul, #{1}{1}{1}((10))*100
* Tris-Tetribocal, Forcal<sub>1,1,4</sub>(1)

=== Part 3.13: <math>f_{\omega^2 3}(f_3(10))</math> ~ <math>f_{\omega^3}(f_3(10))</math> ===

* Truchainol, s(3,2,2,1,4)
* Traggolplex, {10,10,10,{10,10,10,100,3},3}
* Truchainolplex, s(3,3,2,1,4)
* Cor-terotial, {10,100,1,1,4}
* Thrantergol / teristo-thrangol / tessi-thrangol, E100###100###100###100##2
* Truchainbol, s(3,2,3,1,4)
* Truchainbolplex, s(3,3,3,1,4)
* Threatergol / teristo-threagol / tessi-threagol, E100###100###100###100##3
* Thrutergold / teristo-thrugold / tessi-thrugold, E100###100###100###100##100
* Trumeg-Kiloogol, 10[0,1,3]100
* Truchainprimol, s(3,2,2,2,4)
* Truchainprimolplex, s(3,3,2,2,4)
* Thraatatergold / teristo-thraatagold / tessi-thraatagold, E100###100###100###100##100##2
* Truchainpribol, s(3,2,3,2,4)
* Truchainpribolplex, s(3,3,3,2,4)
* Thrutergolthra / teristo-thrugolthra / tessi-thrugolthra, E100###100###100###100###3
* Truchainduprimol, s(3,2,2,3,4)
* Truchainduprimolplex, s(3,3,2,3,4)
* Truchaindupribol, s(3,2,3,3,4)
* Truchaindupribolplex, s(3,3,3,3,4)
* Hayden's Pentatri, 3(3)(3)(3)3
* Golden coral, 3D3
* Thrutergoltesla / teristo-thrugoltesla / tessi-thrugoltesla, E100###100###100###100###4
* Pententet, s(4,4,4,4,4)
* Thrutergolpeta / teristo-thrugolpeta / tessi-thrugolpeta, E100###100###100###100###5
* Conway's Su-tripent, 5 →<sub>5</sub> 5
* Thrutergolhexa / teristo-thrugolhexa / tessi-thrugolhexa, E100###100###100###100###6
* Desire, 10[&<sub>1</sub>&<sub>1</sub>&<sub>1</sub>&<sub>1</sub>]
* Grepssss, <sup>5</sup><u>1</u><sub>0</sub>(76)
* Throopetol / pesto-throogol / penri-throogol, E100###100###100###100###100 = E100####5
* Treegol / Tetrumegoogol, {10,10,10,100,4} = 10[0,0,4]100
* Tris-Pentibocal, Forcal<sub>1,1,5</sub>(1)
* Thranpetol / pesto-thrangol / penri-thrangol, E100###100###100###100###100##2
* Thrupetold / pesto-thrugold / penri-thrugold, E100###100###100###100###100##100
* Thrupetolthra / pesto-thrugolthra / penri-thrugolthra, E100###100###100###100###100###3
* Thrupetoltesla, E100###100###100###100###100###4
* Thrupetolpeta, E100###100###100###100###100###5
* Pentenpent, s(5,5,5,5,5)
* Superpent, {5,5,5,5,5}
* Conway's Su-trihex, 6 →<sub>6</sub> 6
* Grep-5-s, <sup>6</sup><u>1</u><sub>0</sub>(76)
* Throohexol / existo-throogol / exi-throogol, E100###100###100###100###100###100 = E100####6
* Trigol / Pentumegoogol, {10,10,10,100,5} = 10[0,0,5]100
* Tris-Hexibocal, Forcal<sub>1,1,6</sub>(1)
* Cor-exotial / corhatotial, {10,100,1,1,6}
* Thranhexol / existo-thrangol / exi-thrangol, E100###100###100###100###100###100##2
* Mulhatotial, {10,100,2,1,6}
* Thruhexold / existo-thrugold / exi-thrugold, E100###100###100###100###100###100##100
* Thruhexolthra / existo-thrugolthra / exi-thrugolthra, E100###100###100###100###100###100###3
* Pentenhex, s(6,6,6,6,6)
* Hexarplex, <math>Q_{1,0,0,0}(6)</math>
* Hayden's Pentapent, 5(5)(5)(5)5
* Conway's Su-trisept, 7 →<sub>7</sub> 7
* Throoheptgol / episto-throogol / epti-throogol, E100####7
* Troggol, {10,10,10,100,6}
* Cor-zettotial, {10,100,1,1,7}
* Ascend-hept, {3,4,5,6,7}
* Pentahept, {7,7,7,7,7}
* Conway's Su-trioct, 8 →<sub>8</sub> 8
* Throogogdol / ogisto-throogol / okti-throogol, E100####8
* Tragol, {10,10,10,100,7}
* Cor-yottotial, {10,100,1,1,8}
* Conway's Su-triennet, 9 →<sub>9</sub> 9
* Trocgol, {10,10,10,100,8}
* Throogentol / giyottatogoogol, E100####9
* <nowiki>Wreak oaf meson, {{12,12,12},8,8,8,8}</nowiki>
* Trocgolplex, {10,10,10,{10,10,10,100,8},8}
* Cor-xenotial, {10,100,1,1,9}
* Trengol, {10,10,10,100,9}
* Throodekol / ginovatogoogol, E100####10
* Trengolplex, {10,10,10,{10,10,10,100,9},9}
* Coruzotial, {10,100,1,1,10}
* Thrudekold, E100###100###100###100###100###100###100###100###100###100##100
* Thrudekolthra, E100###100###100###100###100###100###100###100###100###100###3
* Thrudekoltesla, E100###100###100###100###100###100###100###100###100###100###4
* Thrudekolpeta, E100###100###100###100###100###100###100###100###100###100###5
* Pentadecal, {10,10,10,10,10}
* Trexom, <math>f_{\omega^3}(10)</math>
* Conway's Su-tridecal, 10 →<sub>10</sub> 10
* Trexgol, {10,10,10,100,10}
* Trexgolplex, {10,10,10,{10,10,10,100,10},10}
* Gitenatogoogol / throoendekol, E100####11
* Coru-uotial, {10,100,1,1,11}
* Gitenakilotogoogol / throododekol, E100####12
* Coru-udotial, {10,100,1,1,12}
* Pentadozenal, {12,12,12,12,12}
* Throotriadekol, E100####13
* Throotetradekol, E100####14
* Throopentadekol, E100####15
* Throohexadekol, E100####16
* Throogicosol, E100####20
* Cor-dzotial, {10,100,1,1,20}
* Throotriantol, E100####30
* Throosarantol, E100####40
* Throopenintol, E100####50
* Throogexintol, E100####60
* Fish number 2, <math>\approx f_{\omega^3}(63)</math>
* Throogebdomintol, E100####70
* Aya, <u>1<sup>[1]</sup></u><sub>0</sub>(76)
* Throogogdontol, E100####80
* Throogenenintol, E100####90
* Quadroogolspeck, {10,10,10,10,90}
* Quadroogolchunk, {10,10,10,10,99}
* Tetroogol / tetroogorth / teroogol / throohectol, E100####100
* Quadroogol / Gigoogol, {10,10,10,10,100} = 10[0,0,0,1]100
* Pentahectal, {100,100,100,100,100}
* Cube-hyperon, 100{X<sup>3</sup>}100
* Galaxiol, #{2}((10))*100
* Giatrollaxul, 200$2
* Juice-infused SAN, s(17, 592, 186, 44, 416)
* Juice-infused BEAF, {17, 592, 186, 44, 416}
* Juice-infused HAN, 17(186)(44)(416)592
* Titanika, <0,0,0,1>|488
* Burrito, {555,555,555,555,555}
* Throochilol, E100####1000
* Quadrwoogol, {10,10,10,10,1000}
* Throomyriol, E100####10,000
* Quadroogolgong, {10,10,10,10,100000}
* Teris-Terribocal, Forcal<sub>1,1,1000000</sub>(1) = Forcal<sub>1,1,1,2</sub>(1)
* Throoterol, E100####10<sup>12</sup>
* Throopettol, E100####10<sup>15</sup>
* Throo-exol, E100####10<sup>18</sup>
* Googolplexifourth, E100####1#2

== Polynomial omega level ==

=== Part 3.14: <math>f_{\omega^3}(f_3(10))</math> ~ <math>f_{\omega^3 2}(f_3(10))</math> ===

* Throogolplexifourth, E100####2#2
* Thrangolplexifourth, E100####(E100###100#100)
* Thrugolda-plexifourth, E100####(E100###100##100)
* Choinol, s(3,2,2,1,1,2)
* Throotrigolplexifourth, E100####3#2
* Pentatriplex, {3,3,1,1,1,2}
* Throotergolplexifourth, E100####4#2
* Throopetolplexifourth, E100####5#2
* Pentadecalplex, {10,3,1,1,1,2}
* Grand tetroogol, E100####100#2
* <nowiki>Quadroogolplex, {10,10,10,10,{10,10,10,10,100}}</nowiki>
* Pentahectalplex, {100,3,1,1,1,2}
* Choinolplex, s(3,3,2,1,1,2)
* Choinalbiplex, s(3,4,2,1,1,2)
* Gig-Googol, 10[1,0,0,1]100
* Corpowerinatial, {10,100,1,1,1,2}
* Tetrangol / terangol, E100####100#100
* Teris-Terribuporcal, Forcal<sub>2,1,1,2</sub>(1)
* Pesty Pitt / Aluminium phosphide, {Drava,Drava,1,1,1,2}
* Choinbol, s(3,2,3,1,1,2)
* Choinbolplex, s(3,3,3,1,1,2)
* Tetreagol / tereagol, E100####100#100#100
* Teris-Terribegorcal, Forcal<sub>3,1,1,2</sub>(1)
* C-tri, C(3, 3, 3)
* Tetrigangol, E100####100#100#100#100
* Tetrorgegol, E100####100##5
* Tetrulgol, E100####100##6
* Tetraspgol, E100####100##7
* Tetrinorgol, E100####100##8
* Tetrargantuul, E100####100##9
* Tetroogondol, E100####100##10
* C-decal, C(10, 10, 10)
* Tetrugold / terugold, E100####100##100
* Gig-Kiloogol, 10[0,1,0,1]100
* Booandol, 10[&<sub>2</sub>100]
* Teris-Terrible-Terribocal, Forcal<sub>1,2,1,2</sub>(1)
* Choinprimol, s(3,2,2,2,1,2)
* Choinprimolplex, s(3,3,2,2,1,2)
* Tetraatagold / teraatagold, E100####100##100#100
* Tetreegold / tereegold, E100####100##100#100#100
* Tetrinningold / terinningold, E100####100##100#100#100#100
* Corexpandainatial, {10,100,1,2,1,2}
* Choinpribol, s(3,2,3,2,1,2)
* Choinpribolplex, s(3,3,3,2,1,2)
* Tetrugolthra / terugolthra, E100####100###3
* Teris-Terrible-Tribocal, Forcal<sub>1,3,1,2</sub>(1)
* Choinduprimol, s(3,2,2,3,1,2)
* Choinduprimolplex, s(3,3,2,3,1,2)
* Corexplodainatial, {10,100,1,3,1,2}
* Choindupribol, s(3,2,3,3,1,2)
* Choindupribolplex, s(3,3,3,3,1,2)
* Tetrugoltesla / terugoltesla, E100####100###4
* Teris-Terrible-Tetribocal, Forcal<sub>1,4,1,2</sub>(1)
* Cordetodainiatial, {10,100,1,4,1,2}
* Tetrugolpeta, E100####100###5
* Corpentodainiatial, {10,100,1,5,1,2}
* Tetrugolhexa, E100####100###6
* Tetrithroogol / teri-throogol, E100####100###100
* Gig-Megoogol, 10[0,0,1,1]100
* Teris-Terrible-Tris-Terribocal, Forcal<sub>1,1,2,2</sub>(1)
* Choichainol, s(3,2,2,1,2,2)
* Choichainolplex, s(3,3,2,1,2,2)
* Cormegodainiatial, {10,100,1,1,2,2}
* Choichainbolplex, s(3,3,3,1,2,2)
* Cormegoexpandatial, {10,100,2,2,2,2}
* Choichainpribolplex, s(3,3,3,2,2,2)
* Choichaindupribolplex, s(3,3,3,3,2,2)
* Tetrithrootrigol / teri-tristo-throogol / teri-tris-throogol, E100####100###100###100
* Teris-Terrible-Tris-Tribocal, Forcal<sub>1,1,3,2</sub>(1)
* Cor-gigodainatial, {10,100,1,1,3,2}
* Choiduchaindupribolplex, s(3,3,3,3,3,2)
* Descenhept, {7,6,5,4,3,2}
* Tetrithrootergol / teri-teristo-throogol / teri-tessi-throogol, E100####100###100###100###100
* Teris-Terrible-Tris-Tetribocal, Forcal<sub>1,1,4,2</sub>(1)
* Corterodainatial, {10,100,1,1,4,2}
* Tetrithroopetol / teri-pesto-throogol / teri-penri-throogol, E100####100###100###100###100###100
* Corpexodainatial, {10,100,1,1,5,2}
* Tetrithroohexol / teri-existo-throogol / teri-exi-throogol, E100####100###100###100###100###100###100
* Tetrithrooheptgol, E100####100####7
* Ayaa, <u>1<sup>[2]</sup></u><sub>0</sub>(76)
* Tetrootrigol / tristo-teroogol / tris-teroogol, E100####100####100 = E100#####3
* Quadriggol / Dugigoogol, {10,10,10,10,100,2} = 10[0,0,0,2]100

* Teris-Tribocal, Forcal<sub>1,1,1,3</sub>(1)

=== Part 3.15: <math>f_{\omega^3 2}(f_3(10))</math> ~ <math>f_{\omega^4}(f_3(10))</math> ===

* Quadriggolplex, {10,10,10,10,{10,10,10,10,100,2},2}
* Corpowiairatial, {10,100,1,1,1,3}
* Tetrantrigol, E100####100####100#100
* Tetreatrigol, E100####100####100#100#100
* Tetrutrigold, E100####100####100##100
* Tetratrithroogol / tristo-teri-throogol / tris-teri-throogol, E100####100####100###100
* Cormegodairatial, {10,100,1,1,2,3}
* Tetratrithrootrigol / tristo-teri-tristo-throogol / tris-teri-tris-throogol, E100####100####100###100###100
* Corgigodairatial, {10,100,1,1,3,3}
* Corgigoexplodainitial, {10,100,1,3,3,3}
* Hexentri, s(3,3,3,3,3,3)
* Hexatri, {3,3,3,3,3,3}
* Ayaaa, <u>1<sup>[3]</sup></u><sub>0</sub>(76)
* Tetrootergol / teristo-teroogol / tessi-teroogol, E100####100####100####100 = E100#####4
* Quadraggol / Trugigoogol, {10,10,10,10,100,3} = 10[0,0,0,3]100
* Tri-galaxiol, #{2}{2}{2}((10))*100
* Teris-Tetribocal, Forcal<sub>1,1,1,4</sub>(1)
* Corpowiaitionatial, {10,100,1,1,1,4}
* Tetrantergol, E100####100####100####100#100
* Tetraterithroogol / teristo-teri-throogol / tessi-teri-throogol, E100####100####100####100###100
* Hexentet, s(4,4,4,4,4,4)
* Hayden's Hexatri, 3(3)(3)(3)(3)3
* Hexatet, {4,4,4,4,4,4}
* Ayaaaa, <u>1<sup>[4]</sup></u><sub>0</sub>(76)
* Tetroopetol / pesto-teroogol / penri-teroogol, E100#####5
* Quadreegol, {10,10,10,10,100,4}
* Teris-Pentibocal, Forcal<sub>1,1,1,5</sub>(1)
* Corpowiaientatial, {10,100,1,1,1,5}
* Hexenpent, s(5,5,5,5,5,5)
* Hexapent, {5,5,5,5,5,5}
* Tetroohexol / existo-teroogol / exi-teroogol, E100#####6
* Quadrigol, {10,10,10,10,100,5}
* Corpowiaihexatial, {10,100,1,1,1,6}
* Hexenhex, s(6,6,6,6,6,6)
* Superhex, {6,6,6,6,6,6}
* Tetrooheptgol / episto-teroogol / epti-teroogol, E100#####7
* Quadroggol, {10,10,10,10,100,6}
* Corpowiaiheptatial, {10,100,1,1,1,7}
* Hayden's Hexahex / hyperhex, 6(6)(6)(6)(6)6
* Tetroogogdol / ogisto-teroogol / okti-teroogol, E100#####8
* Quadragol, {10,10,10,10,100,7}
* Corpowiaioctatial, {10,100,1,1,1,8}
* Ascendoct, {3,4,5,6,7,8}
* Tetroogentol, E100#####9
* Quadrocgol, {10,10,10,10,100,8}
* Quadrocgolplex, {10,10,10,10,{10,10,10,10,100,8},8}
* Tetroodekol, E100#####10
* Quadrengol, {10,10,10,10,100,9}
* Quadrengol], {10,10,10,10,{10,10,10,10,100,9},9}
* Hexadecal, {10,10,10,10,10,10}
* Quadrexom, <math>f_{\omega^4}(10)</math>
* Quadrexgol, {10,10,10,10,100,10}
* Quadrexgolplex, {10,10,10,10,{10,10,10,10,100,10},10}
* Hexadozenal, {12,12,12,12,12,12}
* Issou, <u>1<sup>[0,1]</sup></u><sub>0</sub>(76)
* Pentoogol / pentoogith / petoogol, E100#####100
* Quintoogol / Teroogol (Username5243), {10,10,10,10,10,100} = 10[0,0,0,0,1]100
* Hectargum-quadrexom, <math>f_{\omega^4}(100)</math>
* Hexahectal, {100,100,100,100,100,100}
* Tessa-hyperon, 100{X<sup>4</sup>}100
* Cosmol, #{3}((10))*100
* Giaquadrollaxul, 200$3
* Onion-infused BEEF, {210,42,141,113,214,300}
* Mostranika, <0,0,0,0,1> |488
* Quintwoogol, {10,10,10,10,10,1000}
* Petris-Terribocal, Forcal<sub>1,1,1,1,2</sub>(1)

=== Part 3.16: <math>f_{\omega^4}(f_3(10))</math> ~ <math>f_{\omega^\omega}(f_3(10))</math> ===

* Hexadecalplex, {10,3,1,1,1,1,2}
* Grand pentoogol, E100#####100#2
* <nowiki>Quintoogolplex, {10,10,10,10,10,{10,10,10,10,10,100}}</nowiki>
* Corheptogatial, {10,100,1,1,1,1,2}
* Pentrangol, E100#####100#100
* Trooandol, 10[&<sub>3</sub>100]
* Pentugold, E100#####100##100
* Pentithroogol, E100#####100###100
* 冬の数, s(12, 12, 1, 2, 12, 1, 2)
* Pentitetroogol, E100#####100####100
* Descent-oct, {8,7,6,5,4,3,2}
* Pentootrigol, E100#####100#####100
* Quintiggol / Duteroogol, {10,10,10,10,10,100,2} = 10[0,0,0,0,2]100
* Petris-Tribocal, Forcal<sub>1,1,1,1,3</sub>(1)
* Corcuboheptogatial, {10,100,1,1,1,1,3}
* Leudaren flashes, {3,9,1,1,3,3,3}
* Heptatri, {3,3,3,3,3,3,3}
* Pentootergol, E100#####100#####100#####100
* Quintaggol, {10,10,10,10,10,100,3}
* Petris-Tetribocal, Forcal<sub>1,1,1,1,4</sub>(1)
* Cortessoheptogatial, {10,100,1,1,1,1,4}
* Hayden's Heptatri, 3(3)(3)(3)(3)(3)3
* Pentoopetol, E100#####100#####100#####100#####100 = E100######5
* Quinteegol, {10,10,10,10,10,100,4}
* Corpentoheptogatial, {10,100,1,1,1,1,5}
* Quintigol, {10,10,10,10,10,100,5}
* Supersept, {7,7,7,7,7,7,7}
* Quintagol, {10,10,10,10,10,100,7}
* Hayden's Heptahept / hyperhept, 7(7)(7)(7)(7)(7)7
* Ascendenn, {3,4,5,6,7,8,9}
* Heptadecal, {10,10,10,10,10,10,10}
* Quintexom, <math>f_{\omega^5}(10)</math>
* Lower wun, {1111!,11,1,1,1,11!,11}
* Issouplex, <u>1<sup>[0,0,1]</sup></u><sub>0</sub>(76)
* Hexoogol / hexoogixth / ectoogol, E100######100
* Sextoogol / Petoogol (Username5243), {10,10,10,10,10,10,100} = 10[0,0,0,0,0,1]100
* Heptahectal, {100,100,100,100,100,100,100}
* Peta-hyperon, 100{X<sup>5</sup>}100
* Hyperiol, #{4}((10))*100
* Sextwoogol, {10,10,10,10,10,10,1000}
* Ectris-Terribocal, Forcal<sub>1,1,1,1,1,2</sub>(1)
* Grand hexoogol, E100######100#2
* Hexangol, E100######100#100
* Hexithrinorgol / Kilts en vos, E100######100###100##8
* Descenenn, {9,8,7,6,5,4,3,2}
* Hexootrigol, E100######100######100
* Sextiggol, {10,10,10,10,10,10,100,2}
* Ectris-Tribocal, Forcal<sub>1,1,1,1,1,3</sub>(1)
* Octatri, {3,3,3,3,3,3,3,3}
* Sextaggol, {10,10,10,10,10,10,100,3}
* Ectris-Tetribocal, Forcal<sub>1,1,1,1,1,4</sub>(1)
* Hayden's Octatri, 3(3)(3)(3)(3)(3)(3)3
* Sexteegol, {10,10,10,10,10,10,100,4}
* Sextigol, {10,10,10,10,10,10,100,5}
* Bairn and Ride, {14,14,14,53,2,5,3,8}
* Superoct, {8,8,8,8,8,8,8,8}
* Chicken chasseur, {3,6,1,1,1,1,4,9}
* Hyperogd, 8(8)(8)(8)(8)(8)(8)8
* Ascend-deck, {3,4,5,6,7,8,9,10}
* Octadecal, {10,10,10,10,10,10,10,10}
* Sextexom, <math>f_{\omega^6}(10)</math>
* Issouduplex, <u>1<sup>[0,0,0,1]</sup></u><sub>0</sub>(76)
* Heptoogol / heptoogenth / zettoogol, E100#######100
* Septoogol / Ectoogol (Username5243), {10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,1]100
* Ultrol, #{5}((10))*100
* Septwoogol, {10,10,10,10,10,10,10,1000}
* Zetris-Terribocal, Forcal<sub>1,1,1,1,1,1,2</sub>(1)
* Grand heptoogol, E100#######100#2
* Heptrangol, E100#######100#100
* Ultra-galaxiol, #{5}{2}((10))*100
* Ultra-cosmol, #{5}{3}((10))*100
* Ultra-hyperiol, #{5}{4}((10))*100
* Pentooandol, 10[&<sub>5</sub>100]
* Heptootrigol, E100#######100#######100
* Septiggol, {10,10,10,10,10,10,10,100,2}
* Bi-ultrol, #{5}{5}((10))*100
* Ultra-hyper-cosmo-galaxi-cosmo-hyper-ultrol, #{5}{4}{3}{2}{3}{4}{5}((10))*100
* Zetris-Tribocal, Forcal<sub>1,1,1,1,1,1,3</sub>(1)
* Enneatri, {3,3,3,3,3,3,3,3,3}
* Tri-ultrol, #{5}{5}{5}((10))*100
* Heptootergol, E100#######100#######100#######100
* Septaggol, {10,10,10,10,10,10,10,100,3}
* Zetris-Tetribocal, Forcal<sub>1,1,1,1,1,1,4</sub>(1)
* Hayden's Ennatri, 3(3)(3)(3)(3)(3)(3)(3)3
* Superenn, {9,9,9,9,9,9,9,9,9}
* Hyperenn, 9(9)(9)(9)(9)(9)(9)(9)9
* Ennadecal, {10,10,10,10,10,10,10,10,10}
* Septexom, <math>f_{\omega^7}(10)</math>
* Issoutriplex, <u>1<sup>[0,0,0,0,1]</sup></u><sub>0</sub>(76)
* Ogdoogol / yottoogol, E100########100
* Octoogol / Zettoogol (Username5243), {10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,1]100
* Octwoogol, {10,10,10,10,10,10,10,10,1000}
* Yotris-Terribocal, Forcal<sub>1,1,1,1,1,1,1,2</sub>(1)
* Ogdahepti-hexapenti-tetrithroogol / yotti-zetti-ecti-peti-teri-throogol, E100########100#######100######100#####100####100###100
* Yotris-Tribocal, Forcal<sub>1,1,1,1,1,1,1,3</sub>(1)
* Ogdatri-hexi-pentateri-tetrapetithrinortrigolthra / tristo-yotti-ecti-teristo-peti-pesto-teri-tristo-thrinorgolthra / tris-yotti-ecti-tessi-peti-penri-teri-tris-thrinorgolthra, E100########100########100######100#####100#####100#####100####100####100####100####100###100###100##100##100##8
* Decatri, {3,3,3,3,3,3,3,3,3,3}
* Yotris-Tetribocal, Forcal<sub>1,1,1,1,1,1,1,4</sub>(1)
* Hayden's Dekatri, 3(3)(3)(3)(3)(3)(3)(3)(3)3
* '''Iteral''' / superdecal, {10,10,10,10,10,10,10,10,10,10} = {10,10 (1) 2}
* Octexom, <math>f_{\omega^8}(10)</math>
* Hyperdecal / hiteral, 10(10)(10)(10)(10)(10)(10)(10)(10)10
* Entoogol, E100#########100
* Nonoogol / Yottoogol (Username5243), {10,10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,0,1]100
* Nonwoogol, {10,10,10,10,10,10,10,10,10,1000}
* Undecatri, {3,3,3,3,3,3,3,3,3,3,3}
* Nonexom, <math>f_{\omega^9}(10)</math>
* Wun, {1111!!,11!!!,11!,11!!!!,11!!!,11111!,1,1,1,11!,11}
* Dektoogol, E100##########100
* Decoogol / Xennoogol, {10,10,10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,0,0,1]100
* Decwoogol, {10,10,10,10,10,10,10,10,10,10,1000}
* Dodecatri, {3,3,3,3,3,3,3,3,3,3,3,3}
* Dektadekientadekiogdadekiheptadekihexadekipentadekitetradekithrooogondekoldeka, E100##########100##########100##########100##########100##########100##########100##########100##########100##########100#########100#########100#########100#########100#########100#########100#########100#########100#########100########100########100########100########100########100########100########100########100########100#######100#######100#######100#######100#######100#######100#######100#######100#######100######100######100######100######100######100######100######100######100######100#####100#####100#####100#####100#####100#####100#####100#####100#####100####100####100####100####100####100####100####100####100####100###100###100###100###100###100###100###100###100###100##100##100##100##100##100##100##100##100##100#100#100#100#100#100#100#100#100#100
* Dekexom / bitetrom, <math>f_{\omega^{10}}(10)</math>
* Superdozen, {12,12,12,12,12,12,12,12,12,12,12,12}
* Endektoogol, E100#^#11
* Wekoogol, 10[0,0,0,0,0,0,0,0,0,0,1]100
* Pete.c numbers|pete-5.c, <math>\approx f_{\omega^{11}}^{16}(999)</math>
* Dekooandol, 10[&<sub>10</sub>100]
* Shiki no kazu|秋の数, 100![9, 10, 11]
* Shiki no kazu|春の数, {3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5}
* Superhexadecal, {16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
* Icosolus, E100#^#20
* Vigintoogol, {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,100}
* Pete.c numbers|pete-6.c, <math>\approx f_{\omega^{23}}(9\times2^{9999})</math>
* Ultatri, {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
* Hayden's Dupertri, 3(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)3
* Linel, s(3,2,2{2}2)
* Triantolus, E100#^#30
* Trigintoogol, {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,100}
* Supernifty, {36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36}
* Sarantolus, E100#^#40
* Quadragintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (41 entries)
* Penintolus, E100#^#50
* Quinquagintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (51 entries)
* Okojo numbers|Okojo-stoat number, <math>\approx f_{\omega^\omega}(53)</math>
* Exintolus, E100#^#60
* Sexagintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (61 entries)
* Ebdomintolus, E100#^#70
* Septuagintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (71 entries)
* Lvapofr, <u>1<sup>[(2)[1</sup></u><sub>0</sub>(76)
* Ogdontolus, E100#^#80
* Octogintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (81 entries)
* Goobolspeck, {10,90 (1) 2}
* Enenintolus, E100#^#90
* Nonagintoogol, {10,10,10,10,10, ... ... ,10,10,10,10,10,100} (91 entries)
* Goobolcrumb, {10,95 (1) 2}
* Goobolchunk, {10,99 (1) 2}
* Ternary-goobol, {4, 100 (1) 2}
* Octal-goobol, {8, 100 (1) 2}
* Hexadecimal-goobol, {16, 100 (1) 2}
* Goobol, {10,100 (1) 2}
* Hay-Goobol, 10(10)(10)(10) ... (10)(10)(10)10 (98 (10)'s)
* Godgahlah / hectolus, E100#^#100
* Linoogol, 10[0{1}1]100
* Goobolbunch, {10,101 (1) 2}
* Centoogol, {10,10,10,10,10,...,10,10,10,10,10,100} (101 entries)
* Godsoogol, 10[&<sub>100</sub>10]
* Hektexom, <math>f_{\omega^{100}}(10)</math>
* Hyper-hyperon, 100{X<sup>X</sup>}100
* Titanicol / centrol, #{0:1}((10))*100
* Angelah, E111#^#111
* Goobolswarm, {10,110 (1) 2}
* Yan Grrrls, E2023#^(180)(Qami Qami) = E2023#^(180)(E2021#224)
* Ducentoogol, {10,10,10,10,10,...,10,10,10,10,10,100} (201 entries)
* Hugedollaxul, <math>200\$[0]</math>
* Giatrixul, 200![200,200,200] ~ {10,203 (1) 2}
* Kilogiatrixul, (200![200,200,200])![200,200,200]
* Megagiatrixul, ((200![200,200,200])![200,200,200])![200,200,200]
* Gigagiatrixul, (((200![200,200,200])![200,200,200])![200,200,200])![200,200,200]
* Grand Giatrixul, 200(![200,200,200])<sup>200![200,200,200]+1</sup>
* Grand Kilogiatrixul, 200(![200,200,200])<sup>(200![200,200,200])![200,200,200]+1</sup>
* Grand Megagiatrixul, 200(![200,200,200])<sup>((200![200,200,200])![200,200,200])![200,200,200]+1</sup>
* Grand Gigagiatrixul, 200(![200,200,200])<sup>(((200![200,200,200])![200,200,200])![200,200,200])![200,200,200]+1</sup>
* Bigrand Giatrixul, 200(![200,200,200])<sup>200(![200,200,200])<sup>200![200,200,200]+1</sup>+1</sup>
* Trigrand Giatrixul, 200(![200,200,200])<sup>200(![200,200,200])<sup>200(![200,200,200])<sup>200![200,200,200]+1</sup>+1</sup>+1</sup>
* The linearity, {10,10,10,10,10,...,10,10,10,10,10,100} (235 entries)
* Ultratri, 3(3)(3)(3...(3)(3)(3)3 (333 (3)'s)
* Goobolding, {10,500 (1) 2}
* Nether Update, <math>f_{\omega^{\omega}}(576)</math>
* Devilgahlah, E666#^#666
* Goobolchime, {10,1000 (1) 2}
* Chilliatolus, E100#^#1000
* Milloogol, {10,10,10,10,10,...,10,10,10,10,10,100} (1,001 entries)
* Godgahlahchime, E1000#^#1000
* Kilexom, <math>f_{\omega^{1000}}(10)</math>
* Goobolbell, {10,5000 (1) 2}
* Gooboltoll, {10,10000 (1) 2}
* Myriatolus, E100#^#10000
* Godgahlahtoll, E10000#^#10000
* Ice spice what the dog doin skibbidy toilet in real life (only in ohio), <math>f_{\omega^{69420}}(69420)</math>
* Goobolgong, {10,100000 (1) 2}
* Godgahlahgong, E100000#^#100000
* Superis-Terribocal, Forcal<sub>1[2]2</sub>(1)
* Microogol, {10,10,10,10,10,...,10,10,10,10,10,100} (1,000,001 entries)
* Megexom, <math>f_{\omega^{1000000}}(10)</math>
* Goobolbong, {10,100000000 (1) 2}
* Gigexom, <math>f_{\omega^{10^9}}(10)</math>
* Goobolthrong, {10,10<sup>11</sup> (1) 2}
* Terexom, <math>f_{\omega^{10^{12}}}(10)</math>
* Goobolgandingan, {10,10<sup>14</sup> (1) 2}
* Petexom, <math>f_{\omega^{10^{15}}}(10)</math>
* Exexom, <math>f_{\omega^{10^{18}}}(10)</math>
* Zettexom, <math>f_{\omega^{10^{21}}}(10)</math>
* Yottexom, <math>f_{\omega^{10^{24}}}(10)</math>
* Array reversed zootzoot, <math>\{3,4,5,6,7,\ldots \ldots \ldots,10^{100}-3,10^{100}-2,10^{100}-1,10^{100}\}</math>
* Array zootzoot, <math>\{10^{100},10^{100}-1,10^{100}-2,10^{100}-3,\ldots \ldots \ldots,6,5,4,3,2\}</math>
* Goobo-googol, {10,googol(1)2}
* Googahlah, E100#^#(10<sup>100</sup>)
* Googoloogol, {10,10,10,10,10,...,10,10,10,10,10,100} (10<sup>100</sup>+1 entries)
* Deckgoobol, {10,{10,10,2}(1)2}

== Exponentiated linear omega level ==

=== Part 3.17: <math>f_{\omega^\omega}(f_3(10))</math> ~ <math>f_{\omega^\omega + \omega}(f_3(10))</math> ===

* pete-7.c, <math>f_{\omega^\omega}(2\uparrow\uparrow36)</math>
* Goobo-giggol, {10,{10,100,2}(1)2}
* Dupertri, {3,3,2 (1) 2}
* Duperdecal, {10,3,2 (1) 2}
* Linelplex, s(3,3,2{2}2)
* Hayden's Trupertri, 3(3)(3)(3) ... (3)(3)(3)3 (Hayden's Dupertri 3's)
* Goobolplex, {10,{10,100 (1) 2} (1) 2}
* Duperhect, {100,3,2(1)2}
* Grand godgahlah, E100#^#100#2
* Goobolplexigong, {10,{10,100000(1)2}(1)2}
* Grand godgahlahgong, E100000#^#100000#2
* Trupertri, {3,4,2(1)2}
* Truperdecal, {10,4,2 (1) 2}
* Goobolduplex, {10, {10, {10, 100 (1) 2} (1) 2} (1) 2}
* Truperhect, {100,4,2(1)2}
* Grand grand godgahlah / two-ex-grand godgahlah, E100#^#100#3
* Goobolduplexigong, {10,{10,{10,{10,100000(1)2}(1)2}(1)2}(1)2}
* Grand grand godgahlahgong, E100000#^#100000#3
* Quadruperdecal, {10,5,2 (1) 2}
* Gooboltriplex, {10, goobolduplex (1) 2}
* Grand grand grand godgahlah / three-ex-grand godgahlah, E100#^#100#4
* Quintuperdecal, {10,6,2 (1) 2}
* Grand grand grand grand godgahlah / four-ex-grand godgahlah, E100#^#100#5
* Goobolquintiplex, {10, goobolquadriplex (1) 2}
* Gooboldeciplex, {10, goobolnoniplex (1) 2}
* Goobolvigintiplex, {10, goobolnovemdeciplex (1) 2}
* Gooboltrigintiplex, {10, goobolnovemvigintiplex (1) 2}
* Goobolquinquagintiplex, {10, goobolnovemquadragintiplex (1) 2}
* Gibbol, {10,100,2 (1) 2}
* Lin-Googol, 10[1{1}1]100
* Grandgahlah, E100#^#100#100
* Titanicoltrex, #{0:1}* ((10))*100
* Goobolcentiplex, {10, goobolnovemnonagintiplex (1) 2}
* Hundred-ex-grand godgahlah, E100#^#100#101
* Gibbolchime, {10,1000,2(1)2}
* Goobolmilliplex, {10, goobolnovemnonagintinongentiplex (1) 2}
* Eleven-thousand-eight-hundred-sixty-two-ex-grand godgahlahgong, E100000#^#100000#11863
* Gibbolgong, {10,100000,2(1)2}
* Grandgahlahgong, E100,000#^#100,000#100,000
* Goobolmegaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (1,000,001 times)
* Goobolgigaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (1,000,000,001 times)
* Goobolteraplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (1,000,000,000,001 times)
* Goobolpetaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (10<sup>15</sup> + 1 times)
* Goobolexaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (10<sup>18</sup> + 1 times)
* Goobolzettaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (10<sup>21</sup> + 1 times)
* Goobolyottaplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (10<sup>24</sup> + 1 times)
* Superis-Terribuporcal, Forcal<sub>2[2]2</sub>(1)
* Godgahlah-ex-grand godgahlah, E100#^#100#(1+E100#^#100)
* Gooboldex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobol times)
* Gooboldexiplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobol + 1 times)
* Gooboldexiduplex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobol + 2 times)
* Goobolplexidex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobolplex times)
* Goobolduplexidex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobolduplex times)
* Gibbolplex, {10,{10,100,2 (1) 2},2 (1) 2}
* Grand grandgahlah, E100#^#100#100#2
* Gooboldudex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (gooboldex times)
* Grand grand grandgahlah, E100#^#100#100#3
* Gooboltridex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (gooboldudex times)
* Goobolquintidex, {10, {10, {10, … {10, 100 (1) 2} (1) 2} (1) 2} … (1) 2} (goobolquadridex times)
* Latri, {3,3,3 (1) 2}
* Lintrienel, s(3,3,3{2}2)
* Gabbol, {10,100,3 (1) 2}
* Lin-Doogol, 10[2{1}1]100
* Greagahlah, E100#^#100#100#100
* Gabbolgong, {10,100000,3(1)2}
* Greagahlahgong, E100,000#^#100,000#100,000#100,000
* Goobolthrex
* Goobolthrexiplex
* Goobolplexithrex
* Gooboldexithrex
* Gabbolplex, {10,{10,100,3 (1) 2},3 (1) 2}
* Grand greagahlah, E100#^#100#100#100#2
* Goobolduthrex
* Gooboltrithrex
* Superis-Terribmegocal, Forcal<sub>3[2]2</sub>(1)
* Lower latet, {4,4,4(1)2}
* Geebol, {10,100,4 (1) 2}
* Gigangahlah, E100#^#100#100#100#100
* Geebolgong, {10,100000,4(1)2}
* Grand gigangahlah, E100#^#100#100#100#100#2
* Superis-Terribypercal, Forcal<sub>4[2]2</sub>(1)
* Gibol, {10,100,5 (1) 2}
* Gorgegahlah, E100#^#100#100#100#100#100
* Grand gorgegahlah, E100#^#100#100#100#100#100#2
* Gobbol, {10,100,6 (1) 2}
* Gulgahlah, E100#^#100#100#100#100#100#100
* Grand gulgahlah, E100#^#100#100#100#100#100#100#2
* Gabol, {10,100,7 (1) 2}
* Gaspgahlah, E100#^#100##7
* Gocbol, {10,100,8(1)2}
* Ginorgahlah, E100#^#100##8
* Genbol, {10,100,9(1)2}
* Gargangahlah, E100#^#100##9
* Tridecbol, {10,10,10(1)2}
* Gexbol, {10,100,10(1)2}
* Googongahlah, E100#^#100##10
* Beggard antre khi, (0)(1)(2)(3)(1)(2)[15]
* Boobol, {10,10,100 (1) 2}
* Woobol, {10,100,100(1)2}
* Gugoldgahlah, E100#^#100##100
* Lin-Kiloogol, 10[0,1{1}1]100
* Wibbol, {10,100,200(1)2}
* Wabbol, {10,100,300(1)2}
* Weebol, {10,100,400(1)2}
* Wibol, {10,100,500(1)2}
* Wobbol, {10,100,600(1)2}
* Wabol, {10,100,700(1)2}
* Bwoobol, {10,10,1000(1)2}
* Boobolplex, {10,10,{10,10,100 (1) 2} (1) 2}
* Grand gugoldgahlah, E100#^#100##100#2

=== Part 3.18: <math>f_{\omega^\omega + \omega}(f_3(10))</math> ~ <math>f_{\omega^\omega 2}(f_3(10))</math> ===

* Corboral, {10,100,1,2(1)2}
* Graatagoldgahlah, E100#^#100##100#100
* Titanicolgoltrex, #{0:1}^* ((10))*100
* Greegoldgahlah, E100#^#100##100#100#100
* Grinningoldgahlah, E100#^#100##100#100#100#100
* Golaagoldgahlah, E100#^#100##100#100#100#100#100
* Gruelohgoldgahlah, E100#^#100##100##6
* Gaspgoldgahlah, E100#^#100##100##7
* Ginorgoldgahlah, E100#^#100##100##8
* Gargantuuldgahlah, E100#^#100##100##9
* Googondoldgahlah, E100#^#100##100##10
* Gugolthragahlah, E100#^#100##100##100
* Bibbol, {10,10,100,2 (1) 2}
* Graatagolthragahlah, E100#^#100##100##100#100
* Greegolthragahlah, E100#^#100##100##100#100#100
* Lintetenel, s(3,3,3,3{2}2)
* Grinningolthragahlah, E100#^#100##100##100#100#100#100
* Golaagolthragahlah, E100#^#100##100##100##5
* Gruelohgolthragahlah, E100#^#100##100##100##6
* Gugolteslagahlah, E100#^#100##100##100##100
* Babbol, {10,10,100,3 (1) 2}
* Graatagolteslagahlah, E100#^#100##100##100##100#100
* Greegolteslagahlah, E100#^#100##100##100#100##100#100
* First row supertet / latet {4,4,4,4(1)2} = {4,4(1)3}
* Gugolpetagahlah, E100#^#100###5
* Beebol, {10,10,100,4 (1) 2}
* Gugolhexagahlah, E100#^#100###6
* Bibol, {10,10,100,5 (1) 2}
* Gugolheptagahlah, E100#^#100###7
* Bobbol, {10,10,100,6 (1) 2}
* Gugoloctagahlah, E100#^#100###8
* Babol, {10,10,100,7 (1) 2}
* Gugolennagahlah, E100#^#100###9
* Bocbol, {10,10,100,8(1)2}
* Gugoldekagahlah, E100#^#100###10
* Benbol, {10,10,100,9(1)2}
* Generadual, {10,10,10,10(1)2}
* Bexbol, {10,10,100,10(1)2}
* Throogahlah / throogogahlah, E100#^#100###100
* Troobol, {10,10,10,100 (1) 2}
* Lin-Megoogol, 10[0,0,1{1}1]100
* Titanic Astuul, #{0:1}{1}((10))*100
* Trwoobol, {10,10,10,1000(1)2}
* Grand throogahlah, E100#^#100###100#2
* Troobolplex, {10,10,10,{10,10,10,100 (1) 2} (1) 2}
* Thrangahlah, E100#^#100###100#100
* Cormegotidual, {10,100,1,1,2(1)2}
* Threagahlah, E100#^#100###100#100#100
* Thrigangahlah, E100#^#100###100#100#100#100
* Thrugoldgahlah, E100#^#100###100##100
* Thraatagoldgahlah, E100#^#100###100##100#100
* Thrugolthragahlah, E100#^#100###100##100##100
* Thrugolteslagahlah, E100#^#100###100##100##100##100
* Throotrigahlah, E100#^#100###100###100
* Tribbol, {10,10,10,100,2 (1) 2}
* Linpentenel, s(3,3,3,3,3{2}2)
* Throotergahlah, E100#^#100###100###100###100
* Trabbol, {10,10,10,100,3 (1) 2}
* Throopetogahlah, E100#^#100###100###100###100###100
* First row superpent / lapent, {5,5(1)3}
* Throohexogahlah, E100#^#100####6
* Throoheptogahlah, E100#^#100####7
* Throogogdogahlah, E100#^#100####8
* Throogentogahlah, E100#^#100####9
* Trocbol, {10,10,10,100,8(1)2}
* Throodekogahlah, E100#^#100####10
* Trenbol, {10,10,10,100,9(1)2}
* Pentadecadual / trexbol, {10,10,10,10,10(1)2}
* Tetroogahlah / teroogahlah / teroogogahlah, E100#^#100####100
* Quadroobol, {10,10,10,10,100 (1) 2}
* Lin-Gigoogol, 10[0,0,0,1{1}1]100
* Titanic Galaxiol, #{0:1}{2}((10))*100
* Quadrwoobol, {10,10,10,10,1000(1)2}
* Tetrangahlah, E100#^#100####100#100
* Tetrugoldgahlah, E100#^#100####100##100
* Tetrithroogahlah, E100#^#100####100###100
* Tetrootrigahlah, E100#^#100####100####100
* Quadribbol, {10,10,10,10,100,2 (1) 2}
* Tetrootergahlah, E100#^#100####100####100####100
* Quadrabbol, {10,10,10,10,100,3 (1) 2}
* Tetroopetogahlah, E100#^#100####100####100####100####100
* Tetroohexogahlah, E100#^#100#####6
* Tetrooheptogahlah, E100#^#100#####7
* Tetroogogdogahlah, E100#^#100#####8
* Pentoogahlah / petoogahlah / petoogogahlah, E100#^#100#####100
* Quintoobol, {10,10,10,10,10,100 (1) 2}
* Titanic Cosmol, #{0:1}{3}((10))*100
* Quintwoobol, {10,10,10,10,10,1000(1)2}
* Pentootrigahlah, E100#^#100#####100#####100
* Pentootergahlah, E100#^#100#####100#####100#####100
* Pentoopetogahlah, E100#^#100#####100#####100#####100#####100
* Hexoogahlah / ectoogahlah / ectoogogahlah, E100#^#100######100
* Sextoobol, {10,10,10,10,10,10,100 (1) 2}
* Titanic Hyperiol, #{0:1}{4}((10))*100
* Sextwoobol, {10,10,10,10,10,10,1000(1)2}
* Heptoogahlah / zettoogahlah / zettoogogahlah, E100#^#100#######100
* Septoobol, {10,10,10,10,10,10,10,100 (1) 2}
* Septwoobol, {10,10,10,10,10,10,10,1000(1)2}
* Ogdoogahlah / yottoogahlah / yottoogogahlah, E100#^#100########100
* Octoobol, {10,10,10,10,10,10,10,10,100 (1) 2}
* Octwoobol, {10,10,10,10,10,10,10,10,1000(1)2}
* Entoogahlah, E100#^#100#^#9
* Nonwoobol, {10,10,10,10,10,10,10,10,10,1000(1)2}
* Dektoogahlah, E100#^#100#^#10
* Decoobol, {10,10,10,10,10,10,10,10,10,10,100(1)2}
* Lvapofrbi, <u>1<sup>[(3)[1</sup></u><sub>0</sub>(76)
* Gootrol, {10,100 (1) 3}
* Gotrigahlah, E100#^#100#^#100
* Dulinoogol, 10[0{1}2]100
* Gootrolplex, {10,{10,100 (1) 3} (1) 3}

=== Part 3.19: <math>f_{\omega^\omega 2}(f_3(10))</math> ~ <math>f_{\omega^{\omega+1}}(f_3(10))</math> ===

* Dulinel, s(3,2,2{2}3)
* Dulinelplex, s(3,3,2{2}3)
* Gitrol, {10,100,2 (1) 3}
* Dulin-Googol, 10[1{1}2]100
* Grangotrigahlah / grantrigahlah, E100#^#100#^#100#100
* Dulintrienel, s(3,3,3{2}3)
* Gatrol, {10,100,3 (1) 3}
* Greagotrigahlah / greatrigahlah, E100#^#100#^#100#100#100
* Geetrol, {10,100,4 (1) 3}
* Gigangotrigahlah / gigantrigahlah, E100#^#100#^#100#100#100#100
* Gietrol, {10,100,5 (1) 3}
* Gorgegotrigahlah / gorgetrigahlah, E100#^#100#^#100#100#100#100#100
* Gotrol, {10,100,6 (1) 3}
* Gulgotrigahlah / gultrigahlah, E100#^#100#^#100##6
* Gaitrol, {10,100,7 (1) 3}
* Gaspgotrigahlah / gasptrigahlah, E100#^#100#^#100##7
* Goctrol, {10,100,8(1)3}
* Ginorgotrigahlah, E100#^#100#^#100##8
* Gentrol, {10,100,9(1)3}
* Gargangotrigahlah, E100#^#100#^#100##9
* Gextrol, {10,100,10(1)3}
* Googongotrigahlah, E100#^#100#^#100##10
* Bootrol, {10,10,100 (1) 3}
* Wootrol, {10,100,100(1)3}
* Gugoldgotrigahlah / gugoldtrigahlah, E100#^#100#^#100##100
* Bwootrol, {10,10,1000(1)3}
* Graatagoldgotrigahlah, E100#^#100#^#100##100#100
* Greegoldgotrigahlah, E100#^#100#^#100##100#100#100
* Grinningoldgotrigahlah, E100#^#100#^#100##100#100#100#100
* Golaagoldgotrigahlah, E100#^#100#^#100##100#100#100#100#100
* Gugolthragotrigahlah, E100#^#100#^#100##100##100
* Bitrol, {10,10,100,2 (1) 3}
* Dulintetenel, s(3,3,3,3{2}3)
* Batrol, {10,10,100,3 (1) 3}
* Beetrol, {10,10,100,4 (1) 3}
* Throogotrigahlah / throotrigahlah, E100#^#100#^#100###100
* Trootrol, {10,10,10,100 (1) 3}
* Trwootrol, {10,10,10,1000(1)3}
* Thrangotrigahlah, E100#^#100#^#100###100#100
* Threagotrigahlah, E100#^#100#^#100###100#100#100
* Thrugoldgotrigahlah, E100#^#100#^#100###100##100
* Thrugolthragotrigahlah, E100#^#100#^#100###100##100##100
* Throotrigotrigahlah, E100#^#100#^#100###100###100
* Tritrol, {10,10,10,100,2 (1) 3}
* Throotergotrigahlah, E100#^#100#^#100####4
* Tritrol, {10,10,10,100,3 (1) 3}
* Throopetotrigahlah, E100#^#100#^#100####5
* Throohexotrigahlah, E100#^#100#^#100####6
* Tetroogotrigahlah / terootrigahlah / teroogotrigahlah, E100#^#100#^#100####100
* Quadrootrol, {10,10,10,10,100 (1) 3}
* Tetrootrigotrigahlah, E100#^#100#^#100####100####100
* Tetrootergotrigahlah, E100#^#100#^#100#####4
* Tetroopetotrigahlah, E100#^#100#^#100#####5
* Pentoogotrigahlah / petootrigahlah / petoogotrigahlah, E100#^#100#^#100#####100
* Quintootrol, {10,10,10,10,10,100 (1) 3}
* Pentootrigotrigahlah, E100#^#100#^#100######3
* Hexoogotrigahlah / ectootrigahlah / ectoogotrigahlah, E100#^#100#^#100######100
* Heptoogotrigahlah / zettootrigahlah / zettoogotrigahlah, E100#^#100#^#100#######100
* Ogdoogotrigahlah / yottootrigahlah / yottoogotrigahlah, E100#^#100#^#100########100
* Entoogotrigahlah / ronnootrigahlah / ronnogotrigahlah,, E100#^#100#^#100#^#9
* Dektoogotrigahlah / quettootrigahlah / quettoogotrigahlah,, E100#^#100#^#100#^#10
* Lvapofrtri, <u>1<sup>[(4)[1</sup></u><sub>0</sub>(76)
* Gooquadrol, {10,100 (1) 4}
* Gotergahlah, E100#^#100#^#100#^#100
* Trulinoogol, 10[0{1}3]100
* Giquadrol, {10,100,2 (1) 4}
* Grangotergahlah, E100#^#100#^#100#^#100#100
* Gaquadrol, {10,100,3 (1) 4}
* Greagotergahlah, E100#^#100#^#100#^#100#100#100
* Gigangotergahlah, E100#^#100#^#100#^#100#100#100#100
* Booquadrol, {10,10,100 (1) 4}
* Gugoldgotergahlah, E100#^#100#^#100#^#100##100
* Gugolthragotergahlah, E100#^#100#^#100#^#100##100##100
* Lé Tritri au lait, 3(1, 3)3 / 3 / 3
* Gugolteslagotergahlah, E100#^#100#^#100#^#100##100##100##100
* Throogotergahlah, E100#^#100#^#100#^#100###100
* Tetroogotergahlah, E100#^#100#^#100#^#100####100
* Quadreequadrol, {10,10,10,10,100,4 (1) 4}
* Lvapofrtet, <u>1<sup>[(5)[1</sup></u><sub>0</sub>(76)
* Gooquintol, {10,100 (1) 5}
* Goppegahlah, E100#^#100#^#100#^#100#^#100
* Goosextol, {10,100 (1) 6}
* Gohexgahlah / gohexahlah, E100#^#* #6
* Gooseptol, {10,100 (1) 7}
* Gohepgahlah, E100#^#* #7
* Goo-octol, {10,100(1)8}
* Go-ahtgahlah, E100#^#* #8
* Goo-nonol, {10,100(1)9}
* Go-enngahlah, E100#^#* #9
* Emperal, {10,10 (1) 10}
* Godekahlah, E100#^#* #10
* Kahen, <u>1<sup>[ ] [1]</sup></u><sub>0</sub>(76)
* Gossol, {10,10 (1) 100}
* Godgoldgahlah / gohectgahlah / godgoldahlah, E100#^#* #100
* Kilulinoogol, 10[0{1}0,1]100
* Titaniprimol, #{1:1}((10))*100
* Gwossol, {10,10(1)1000}
* Godgoldgahlahgong, E100,000#^#* #100,000

=== Part 3.20: <math>f_{\omega^{\omega+1}}(f_3(10))</math> ~ <math>f_{\omega^{\omega+2}}(f_3(10))</math> ===

* <nowiki>Emperalplex, {10,10 (1) {10,10 (1) 10}}</nowiki>
* <nowiki>Gossolplex, {10,10 (1) {10,10 (1) 100}}</nowiki>
* Grand godgoldgahlah, E100#^#* #100#2
* Kilulin-Googol, 10[1{1}0,1]100
* Grangol-carta-godgoldgahlah, E100#^#* #100#100
* Greagol-carta-godgoldgahlah, E100#^#* #100#100#100
* Gigangol-carta-godgoldgahlah, E100#^#* #100#100#100#100
* Gugold-carta-godgoldgahlah, E100#^#* #100##100
* Graatagold-carta-godgoldgahlah, E100#^#* #100##100#100
* Gugolthra-carta-godgoldgahlah, E100#^#* #100##100##100
* Throogol-carta-godgoldgahlah, E100#^#* #100###100
* Tetroogol-carta-godgoldgahlah, E100#^#* #100####100
* Pentoogol-carta-godgoldgahlah, E100#^#* #100#####100
* Hexoogol-carta-godgoldgahlah, E100#^#* #100######100
* Kilulin-Linoogol, 10[0{1}1,1]100
* Godgahlah-carta-godgoldgahlah, E100#^#* #100#^#100
* Grandgahlah-carta-godgoldgahlah, E100#^#* #100#^#100#100
* Greagahlah-carta-godgoldgahlah, E100#^#* #100#^#100#100#100
* Gugoldgahlah-carta-godgoldgahlah, E100#^#* #100#^#100##100
* Throogahlah-carta-godgoldgahlah, E100#^#* #100#^#100###100
* Tetroogahlah-carta-godgoldgahlah, E100#^#* #100#^#100####100
* Kilulin-Dulinoogol, 10[0{1}2,1]100
* Gotrigahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100
* Grangotrigahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100#100
* Gugoldgotrigahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100##100
* Throogotrigahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100###100
* Gotergahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100#^#100
* Goppegahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100#^#100#^#100
* Gohexgahlah-carta-godgoldgahlah, E100#^#* #100#^#100#^#100#^#100#^#100#^#100
* Grand emperal, {10,10 (1) 10,2}
* Gissol, {10,10 (1) 100,2}
* Dukilulinoogol, 10[0{1}0,2]100
* Gotrigoldgahlah / gotrigoldahlah, E100#^#* ##3
* Gwissol, {10,10(1)1000,2}
* Gissolplex, {10,10 (1) {10,10 (1) 100,2},2}
* Grangol-carta-gotrigoldgahlah, E100#^#* #100#^#* #100#100
* Gugold-carta-gotrigoldgahlah, E100#^#* #100#^#* #100##100
* Throogol-carta-gotrigoldgahlah, E100#^#* #100#^#* #100###100
* Godgahlah-carta-gotrigoldgahlah, E100#^#* #100#^#* #100#^#100
* Gotrigahlah-carta-gotrigoldgahlah, E100#^#* #100#^#* #100#^#100#^#100
* Gotergahlah-carta-gotrigoldgahlah, E100#^#* #100#^#* #100#^#100#^#100#^#100
* Goppegahlah-carta-gotrigoldgahlah, E100#^#* #100#^#* #100#^#100#^#100#^#100#^#100
* Dienlinel, s(3,2,2{2}3,3)
* Dienlintrienel, s(3,3,3{2}3,3)
* Gassol, {10,10 (1) 100,3}
* Gotergoldgahlah / gotergoldahlah, E100#^#* ##4
* Gassolplex, {10,10 (1) {10,10 (1) 100,3},3}
* Gwassol, {10,10(1)1000,3}
* Grangol-carta-gotergoldgahlah, E100#^#* #100#^#* #100#^#* #100#100
* Gugold-carta-gotergoldgahlah, E100#^#* #100#^#* #100#^#* #100##100
* Throogol-carta-gotergoldgahlah, E100#^#* #100#^#* #100#^#* #100###100
* Godgahlah-carta-gotergoldgahlah, E100#^#* #100#^#* #100#^#* #100#^#100
* Geesol, {10,10 (1) 100,4}
* Goppegoldgahlah / goppegoldahlah, E100#^#* ##5
* Geesolplex, {10,10 (1) {10,10 (1) 100,4},4}
* Gussol, {10,10 (1) 100,5}
* Gohexgoldgahlah / gohexgoldahlah, E100#^#* ##6
* Gohepgoldgahlah / gohepgoldahlah, E100#^#* ##7
* Gasol, {10,10(1)100,7}
* Go-ahtgoldgahlah / go-ahtgoldahlah, E100#^#* ##8
* Go-enngoldgahlah / go-enngoldahlah, E100#^#* ##9
* Godekagoldgahlah / godekagoldahlah, E100#^#* ##10
* Hyperal, {10,10 (1) 10,10}
* '''Fish number 3''', <math>\approx f_{(\omega^{\omega+1}) 63+1}(63)</math>
* Godthroogahlah / godthroldahlah, E100#^#* ##100
* Mossol, {10,10 (1) 10,100}
* Megulinoogol, 10[0{1}0,0,1]100
* Mwossol, {10,10(1)10,1000}
* Mossolgong, {10,10(1)10,100000}

=== Part 3.21: <math>f_{\omega^{\omega+2}}(f_3(10))</math> ~ <math>f_{\omega^{\omega 2}}(f_3(10))</math> ===

* <nowiki>Hyperalplex, {10,10 (1) 10,{10,10 (1) 10,10}}</nowiki>
* <nowiki>Mossolplex, {10,10 (1) 10,{10,10 (1) 10,100}}</nowiki>
* Megulin-Kilulinoogol, 10[0{1}0,1,1]100
* Grangol-carta-godthroogahlah, E100#^#* ##100#100
* Greagol-carta-godthroogahlah, E100#^#* ##100#100#100
* Gugold-carta-godthroogahlah, E100#^#* ##100##100
* Throogol-carta-godthroogahlah, E100#^#* ##100###100
* Godgahlah-carta-godthroogahlah, E100#^#* ##100#^#100
* Gotrigahlah-carta-godthroogahlah, E100#^#* ##100#^#100#^#100
* Gotergahlah-carta-godthroogahlah, E100#^#* ##100#^#100#^#100#^#100
* Godgoldgahlah-carta-godthroogahlah, E100#^#* ##100#^#* #100
* Gotrigoldgahlah-carta-godthroogahlah, E100#^#* ##100#^#* #100#^#* #100
* Gotergoldgahlah-carta-godthroogahlah, E100#^#* ##100#^#* #100#^#* #100#^#* #100
* Gotrithroogahlah, E100#^#* ##100#^#* ##100
* Missol, {10,10 (1) 10,100,2}
* Dumegulinoogol, 10[0{1}0,0,2]100
* Mwissol, {10,10(1)10,1000,2}
* Trienlinel, s(3,2,2{2}3,3,3)
* Goterthroogahlah, E100#^#* ##100#^#* ##100#^#* ##100
* Massol, {10,10 (1) 10,100,3}
* Mwassol, {10,10(1)10,1000,3}
* Deux tritri, {3,3,3(1)3,3,3}
* Goppethroogahlah, E100#^#* ##100#^#* ##100#^#* ##100#^#* ##100
* Meesol, {10,10 (1) 10,100,4}
* Gohexthroogahlah, E100#^#* ##100#^#* ##100#^#* ##100#^#* ##100#^#* ##100
* Mussol, {10,10 (1) 10,100,5}
* Gohepthroogahlah, E100#^#* ###7
* Moosol, {10,10(1)10,100,6}
* Go-ahthroogahlah, E100#^#* ###8
* Masol, {10,10(1)10,100,7}
* Go-ennthroogahlah, E100#^#* ###9
* Godekathroogahlah, E100#^#* ###10
* Trideca-hyperal, {10,10(1)10,10,10}
* Godtetroogahlah / godteroogahlah / godteroldahlah, E100#^#* ###100
* Bossol, {10,10 (1) 10,10,100}
* Gigulinoogol, 10[0{1}0,0,0,1]100
* Titanitrol, #{3:1}((10))*100
* Bwossol, {10,10(1)10,10,1000}
* <nowiki>Bossolplex, {10,10 (1) 10,10,{10,10 (1) 10,10,100}}</nowiki>
* Grangol-carta-godtetroogahlah, E100#^#* ###100#100
* Gugold-carta-godtetroogahlah, E100#^#* ###100##100
* Godgahlah-carta-godtetroogahlah, E100#^#* ###100#^#100
* Godgoldgahlah-carta-godtetroogahlah, E100#^#* ###100#^#* #100
* Godthroogahlah-carta-godtetroogahlah, E100#^#* ###100#^#* ##100
* Gotritetroogahlah, E100#^#* ###100#^#* ###100
* Bissol, {10,10 (1) 10,10,100,2}
* Tetenlinel, s(3,2,2{2}3,3,3,3)
* Gotertetroogahlah, E100#^#* ###100#^#* ###100#^#* ###100
* Bassol, {10,10 (1) 10,10,100,3}
* Gopentetroogahlah|Goppetetroogahlah, E100#^#* ####5
* Beesol, {10,10 (1) 10,10,100,4}
* Deux supertet, {4,4,4,4(1)4,4,4,4}
* Gohextetroogahlah, E100#^#* ####6
* Deux superpent, {5,5,5,5,5(1)5,5,5,5,5}
* Bussol, {10,10 (1) 10,10,100,5}
* Goheptetroogahlah, E100#^#* ####7
* Go-ahtetroogahlah, E100#^#* ####8
* Go-enntetroogahlah, E100#^#* ####9
* Godekatetroogahlah, E100#^#* ####10
* Godpentoogahlah / godpetoogahlah / godpetoldahlah, E100#^#* ####100
* Trossol, {10,10 (1) 10,10,10,100}
* Terulinoogol, 10[0{1}0,0,0,0,1]100
* Titaniterol, #{4:1}((10))*100
* Trwossol, {10,10(1)10,10,10,1000}
* <nowiki>Trossolplex, {10,10 (1) 10,10,10,{10,10 (1) 10,10,10,100}}</nowiki>
* Grangol-carta-godpentoogahlah, E100#^#* ####100#100
* Godgahlah-carta-godpentoogahlah, E100#^#* ####100#^#100
* Godgoldgahlah-carta-godpentoogahlah, E100#^#* ####100#^#* #100
* Godthroogahlah-carta-godpentoogahlah, E100#^#* ####100#^#* ##100
* Godtetroogahlah-carta-godpentoogahlah, E100#^#* ####100#^#* ###100
* Gotripentoogahlah, E100#^#* ####100#^#* ####100
* Trissol, {10,10 (1) 10,10,10,100,2}
* Pentenlinel, s(3,2,2{2}3,3,3,3,3)
* Trassol, {10,10 (1) 10,10,10,100,3}
* Treesol, {10,10 (1) 10,10,10,100,4}
* Trussol, {10,10 (1) 10,10,10,100,5}
* Godhexoogahlah / go-ectoogahlah / go-ectolgahlah, E100#^#* #####100
* Quadrossol, {10,10 (1) 10,10,10,10,100}
* Petulinoogol, 10[0{1}0,0,0,0,0,1]100
* Quadrissol, {10,10 (1) 10,10,10,10,100,2}
* Quadrassol, {10,10 (1) 10,10,10,10,100,3}
* Quadreesol, {10,10 (1) 10,10,10,10,100,4}
* Quadrussol, {10,10 (1) 10,10,10,10,100,5}
* Deux superhex, {6,6,6,6,6,6(1)6,6,6,6,6,6}
* Godheptoogahlah / godzettoogahlah / godzettolgahlah, E100#^#* ######100
* Quintossol, {10,10 (1) 10,10,10,10,10,100}
* Ectulinoogol, 10[0{1}0,0,0,0,0,0,1]100
* Quintissol, {10,10 (1) 10,10,10,10,10,100,2}
* Quintassol, {10,10 (1) 10,10,10,10,10,100,3}
* Quinteesol, {10,10 (1) 10,10,10,10,10,100,4}
* Quintussol, {10,10 (1) 10,10,10,10,10,100,5}
* Deux superhept, {7,7,7,7,7,7,7(1)7,7,7,7,7,7,7}
* Godogdoogahlah / godyottoogahlah / godyottolgahlah, E100#^#* #######100
* Sextossol, {10,10 (1) 10,10,10,10,10,10,100}
* Zettulinoogol, 10[0{1}0,0,0,0,0,0,0,1]100
* Deux superogd, {8,8,8,8,8,8,8,8(1)8,8,8,8,8,8,8,8}
* Godentoogahlah, E100#^#* ########100
* Septossol, {10,10 (1) 10,10,10,10,10,10,10,100}
* Yottulinoogol, 10[0{1}0,0,0,0,0,0,0,0,1]100
* Deux superenn, {9,9,9,9,9,9,9,9,9(1)9,9,9,9,9,9,9,9,9}
* Octossol, {10,10(1)10,10,10,10,10,10,10,10,100}
* Goddektoogahlah, E100#^#* #########100
* Xennulinoogol, 10[0{1}0,0,0,0,0,0,0,0,0,1]100
* Diteral, {10,10 (1)(1) 2}
* Wekulinoogol, 10[0{1}0,0,0,0,0,0,0,0,0,0,1]100
* Dozenal-diteral, {12,12(1)(1)2}
* Hexadecimal-diteral, {16,16(1)(1)2}
* Niftimal-diteral, {36,36(1)2}
* Never gonna give you up, {69, 69 [2] 1 [2] 2}
* Dubol, {10,100 (1)(1) 2}
* Deutero-godgahlah, E100#^#* #^#100
* Gratuitous Golden Googol (DeepLineMadom), {16777216,100 (1)(1) 2}
* Behemicol, #{0:2}((10))*100
* Dubolgong, {10,100000(1)(1)2}
* Deutero-godgahlahgong, E100,000#^#* #^#100,000

=== Part 3.22: <math>f_{\omega^{\omega 2}}(f_3(10))</math> ~ <math>f_{\omega^{\omega 3}}(f_3(10))</math> ===

* Linbel, s(3,2,2{2}1{2}2)
* Diteralplex, {10,3,2 (1)(1) 2}
* Grand deutero-godgahlah, E100#^#* #^#100#2
* Grangol-carta-deutero-godgahlah, E100#^#* #^#100#100
* Lintrienbel, s(3,3,3{2}1{2}2)
* Greagol-carta-deutero-godgahlah, E100#^#* #^#100#100#100
* Gugold-carta-deutero-godgahlah, E100#^#* #^#100##100
* Throogol-carta-deutero-godgahlah, E100#^#* #^#100###100
* Linblinel, s(3,2,2{2}2{2}2)
* Godgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#100
* Grandgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#100#100
* Linbdulinel, s(3,2,2{2}3{2}2)
* Gugoldgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#100##100
* Gotrigahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#100#^#100
* Gotergahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#100#^#100#^#100
* Goppegahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* #5
* Godgoldgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* #100
* Gotrigoldgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* #100#^#* #100
* Linbdienlinel, s(3,2,2{2}3,3{2}2)
* Gotergoldgahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* #100#^#* #100#^#* #100
* Godthroogahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* ##100
* Godtetroogahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* ###100
* Godpentoogahlah-carta-deutero-godgahlah, E100#^#* #^#100#^#* ####100
* Dutrol, {10,100 (1)(1) 3}
* Deutero-gotrigahlah, E100#^#* #^#100#^#* #^#100
* Dutrolplex, {10,{10,100(1)(1)3}(1)(1)3}
* Dulinbel, s(3,2,2{2}1{2}3)
* Duquadrol, {10,100 (1)(1) 4}
* Deutero-gotergahlah, E100#^#* #^#100#^#* #^#100#^#* #^#100
* Duquintol, {10,100 (1)(1) 5}
* Deutero-goppegahlah, E100#^#* #^#100#^#* #^#100#^#* #^#100#^#* #^#100
* Deutero-gohexgahlah, E100#^#* #^#* #6
* Deutero-gohepgahlah, E100#^#* #^#* #7
* Deutero-go-ahtgahlah, E100#^#* #^#* #8
* Deutero-go-enngahlah, E100#^#* #^#* #9
* Admiral, {10,10 (1)(1) 10}
* Deutero-godekahlah, E100#^#* #^#* #10
* Dossol, {10,10 (1)(1) 100}
* Deutero-godgoldgahlah / deutero-godgoldahlah, E100#^#* #^#* #100
* Dwossol, {10,10(1)(1)1000}
* <nowiki>Dossolplex, {10,10 (1)(1) {10,10 (1)(1) 100}}</nowiki>
* Grand deutero-godgoldgahlah, E100#^#* #^#* #100#2
* Grangol-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#100
* Gugold-carta-deutero-godgoldgahlah, E100#^#* #^#* #100##100
* Godgahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#100
* Gotrigahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#100#^#100
* Godgoldgahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#* #100
* Godthroogahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#* ##100
* Cyperal, {65,googolplex(1)1000,googol(1)7* quadragintaquingentillion,42}
* Deutero-godgahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#* #^#100
* Dienlinbel, s(3,2,2{2}1{2}3,3)
* Deutero-gotrigahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#* #^#100#^#* #^#100
* Deutero-gotergahlah-carta-deutero-godgoldgahlah, E100#^#* #^#* #100#^#* #^#100#^#* #^#100#^#* #^#100
* Deutero-gotrigoldgahlah, E100#^#* #^#* #100#^#* #^#* #100
* Deutero-gotergoldgahlah, E100#^#* #^#* #100#^#* #^#* #100#^#* #^#* #100
* Deutero-goppegoldgahlah, E100#^#* #^#* ##5
* Deutero-gohexgoldgahlah, E100#^#* #^#* ##6
* Deutero-gohepgoldgahlah, E100#^#* #^#* ##7
* Deutero-go-ahtgoldgahlah, E100#^#* #^#* ##8
* Deutero-go-enngoldgahlah, E100#^#* #^#* ##9
* Deutero-godekagoldgahlah, E100#^#* #^#* ##10
* Deutero-godthroogahlah / deutero-godthrolgahlah, E100#^#* #^#* ##100
* Modossol, {10,10(1)(1)10,100}
* Modwossol, {10,10(1)(1)10,1000}
* Deutero-gotrithroogahlah, E100#^#* #^#* ##100#^#* #^#* ##100
* Trienlinbel, s(3,2,2{2}1{2}3,3,3)
* Dimensol, s(3,3{1,2}2)
* Dutritri, {3,3,3 (1) 3,3,3 (1) 3,3,3}
* Deutero-goterthroogahlah, E100#^#* #^#* ##100#^#* #^#* ##100#^#* #^#* ##100
* Deutero-gopethroogahlah|Deutero-goppethroogahlah, E100#^#* #^#* ###5
* Deutero-gohexthroogahlah, E100#^#* #^#* ###6
* Dutridecal, {10,10,10 (1) 10,10,10 (1) 10,10,10}
* Hayden's Dutritri, 3(2, 3)3
* Deutero-godtetroogahlah / deutero-godteroogahlah / deutero-godterolgahlah, E100#^#* #^#* ###100
* Bodossol, {10,10(1)(1)10,10,100}
* Lower dusupertet, {4,4,4,4(1)4,4,4,4(1)4,4,4,4}
* Deutero-godpentoogahlah / deutero-godpetoogahlah / deutero-godpetolgahlah, E100#^#* #^#* ####100
* Deutero-godhexoogahlah / deutero-go-ectoogahlah / deutero-go-ectolgahlah, E100#^#* #^#* #####100
* Deutero-godheptoogahlah / deutero-godzettoogahlah / deutero-gozettolgahlah, E100#^#* #^#* ######100
* Deutero-godogdoogahlah / deutero-godyottoogahlah / deutero-goyottolgahlah, E100#^#* #^#* #######100
* Triteral, {10,10(1)(1)(1)2}
* Triubol, {10,100(1)(1)(1)2}
* Dutetradecal, {10,4(2)2}
* Trito-godgahlah, E100#^#* #^#* #^#100
* Leviathol, #{0:3}((10))*100

=== Part 3.23: <math>f_{\omega^{\omega 3}}(f_3(10))</math> ~ <math>f_{\omega^{\omega^2}}(f_3(10))</math> ===

* Lintrel, s(3,2,2{2}1{2}1{2}2)
* Trito-gotrigahlah, E100#^#* #^#* #^#100#^#* #^#* #^#100
* Trito-gotergahlah, E100#^#* #^#* #^#* #4
* Trito-goppegahlah, E100#^#* #^#* #^#* #5
* Trito-godgoldgahlah, E100#^#* #^#* #^#* #100
* Trito-gotrigoldgahlah, E100#^#* #^#* #^#* ##3
* Trito-godthroogahlah, E100#^#* #^#* #^#* ##100
* Trito-godtetroogahlah, E100#^#* #^#* #^#* ###100
* Trito-godpentoogahlah, E100#^#* #^#* #^#* ####100
* Quadriteral, {10,10(1)(1)(1)(1)2}
* Tetrubol, {10,100 (1)(1)(1)(1) 2}
* Teterto-godgahlah, E100#^#* #^#* #^#* #^#100
* Lintetel, s(3,2,2{2}1{2}1{2}1{2}2)
* Dupentadecal, {10,5(2)2}
* Quintiteral, {10,10(1)(1)(1)(1)(1)2}
* Pepto-godgahlah, E100#^##5
* Linpenel, s(3,2,2{2}1{2}1{2}1{2}1{2}2)
* Exto-godgahlah, E100#^##6
* Linhexel, s(3,2,2{2}1{2}1{2}1{2}1{2}1{2}2)
* Duhexadecal, {10,6(2)2}
* Epto-godgahlah, E100#^##7
* Duheptadecal, {10,7(2)2}
* Ogdo-godgahlah, E100#^##8
* Duoctadecal, {10,8(2)2}
* Ento-godgahlah, E100#^##9
* Duennadecal, {10,9(2)2}
* Xappol, {10,10 (2) 2}
* Dekato-godgahlah, E100#^##10
* Isosto-godgahlah, E100#^##20
* Planel, s(3,2,2{3}2)
* Trianto-godgahlah, E100#^##30
* Saranto-godgahlah, E100#^##40
* Goxxol, {10,100 (2) 2}
* Triabiogodgahlah, E100+<sub>##</sub>100
* Gridgahlah, E100#^##100
* Hyper-grid-hyperon, 100{X<sup>X<sup>2</sup></sup>}100
* Empiriol, #{0:0:1}((10))*100
* Hugebollaxul, 200$[1]

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[[分类:经典大数]]