BOCF VS veblen函数

本条目展示BOCF和veblen函数的列表分析。

BOCF	veblen函数
$\psi (0)$	1
$\psi (0)\times 2$	2
$\psi (1)$	$\omega$
$\psi (1)\times 2$	$\omega \times 2$
$\psi (2)$	${\omega }^2$
$\psi (3)$	${\omega }^3$
$\psi (\psi (1))$	${\omega }^{\omega }$
$\psi (\psi (1)+1)$	${\omega }^{\omega +1}$
$\psi (\psi (1)\times 2)$	${\omega }^{\omega \times 2}$
$\psi (\psi (2))$	${\omega }^{{\omega }^2}$
$\psi (\psi (\psi (1)))$	${\omega }^{{\omega }^{\omega }}$
$\psi (\psi (\psi (\psi (1))))$	${\omega }^{{\omega }^{{\omega }^{\omega }}}$
$\psi (\mathrm{\Omega })$	$\phi (1,0)$
$\psi (\mathrm{\Omega })+1$	$\phi (1,0)+1$
$\psi (\mathrm{\Omega })\times 2$	$\phi (1,0)\times 2$
$\psi (\mathrm{\Omega })\times 3$	$\phi (1,0)\times 3$
$\psi (\mathrm{\Omega }+1)$	${\omega }^{\phi (1,0)+1}$
$\psi (\mathrm{\Omega }+\psi (1))$	${\omega }^{\phi (1,0)+\omega }$
$\psi (\mathrm{\Omega }+\psi (\psi (1)))$	${\omega }^{\phi (1,0)+{\omega }^{\omega }}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }))$	${\omega }^{\phi (1,0)\times 2}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })+1)$	${\omega }^{\phi (1,0)\times 2+1}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })+\psi (1))$	${\omega }^{\phi (1,0)\times 2+\omega }$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })\times 2)$	${\omega }^{\phi (1,0)\times 3}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })\times 3)$	${\omega }^{\phi (1,0)\times 4}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+1))$	${\omega }^{{\omega }^{\phi (1,0)+1}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+1)+1)$	${\omega }^{{\omega }^{\phi (1,0)+1}+1}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+1)\times 2)$	${\omega }^{{\omega }^{\phi (1,0)+1}\times 2}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+2))$	${\omega }^{{\omega }^{\phi (1,0)+2}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+3))$	${\omega }^{{\omega }^{\phi (1,0)+3}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (1)))$	${\omega }^{{\omega }^{\phi (1,0)+\omega }}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })))$	${\omega }^{{\omega }^{\phi (1,0)\times 2}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })\times 2))$	${\omega }^{{\omega }^{\phi (1,0)\times 3}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+1)))$	${\omega }^{{\omega }^{{\omega }^{\phi (1,0)+1}}}$
$\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+1))))$	${\omega }^{{\omega }^{{\omega }^{{\omega }^{\phi (1,0)+1}}}}$
$\psi (\mathrm{\Omega }\times 2)$	$\phi (1,1)$
$\psi (\mathrm{\Omega }\times 2+1)$	${\omega }^{\phi (1,1)+1}$
$\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }))$	${\omega }^{\phi (1,1)+\phi (1,0)}$
$\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })))$	${\omega }^{\phi (1,1)+{\omega }^{\phi (1,0)\times 2}}$
$\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }\times 2))$	${\omega }^{\phi (1,1)\times 2}$
$\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }\times 2+1))$	${\omega }^{{\omega }^{\phi (1,1)+1}}$
$\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }\times 2+\psi (\mathrm{\Omega }\times 2)))$	${\omega }^{{\omega }^{\phi (1,1)\times 2}}$
$\psi (\mathrm{\Omega }\times 3)$	$\phi (1,2)$
$\psi (\mathrm{\Omega }\times 4)$	$\phi (1,3)$
$\psi (\mathrm{\Omega }\times \omega )$	$\phi (1,\omega )$
$\psi (\mathrm{\Omega }\times \omega +1)$	${\omega }^{\phi (1,\omega )+1}$
$\psi (\mathrm{\Omega }\times \omega +\psi (\mathrm{\Omega }))$	${\omega }^{\phi (1,\omega )+\phi (1,0)}$
$\psi (\mathrm{\Omega }\times \omega +\psi (\mathrm{\Omega }\times 2))$	${\omega }^{\phi (1,\omega )+\phi (1,1)}$
$\psi (\mathrm{\Omega }\times \omega +\psi (\mathrm{\Omega }\times \omega ))$	${\omega }^{\phi (1,\omega )\times 2}$
$\psi (\mathrm{\Omega }\times \omega +\psi (\mathrm{\Omega }\times \omega +1))$	${\omega }^{{\omega }^{\phi (1,\omega )+1}}$
$\psi (\mathrm{\Omega }\times \omega +\mathrm{\Omega })$	$\phi (1,\omega +1)$
$\psi (\mathrm{\Omega }\times \omega \times 2)$	$\phi (1,\omega \times 2)$
$\psi (\mathrm{\Omega }\times {\omega }^2)$	$\phi (1,{\omega }^2)$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }))$	$\phi (1,\phi (1,0))$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega })\times 2)$	$\phi (1,\phi (1,0)\times 2)$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }+1))$	$\phi (1,{\omega }^{\phi (1,0)+1})$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }+\psi (\mathrm{\Omega })))$	$\phi (1,{\omega }^{\phi (1,0)\times 2})$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }+\psi (\mathrm{\Omega }))))$	$\phi (1,{\omega }^{{\omega }^{\phi (1,0)+1}})$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times 2))$	$\phi (1,\phi (1,1))$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times 3))$	$\phi (1,\phi (1,2))$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times \omega ))$	$\phi (1,\phi (1,\omega ))$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega })))$	$\phi (1,\phi (1,\phi (1,0)))$
$\psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega }))))$	$\phi (1,\phi (1,\phi (1,\phi (1,0))))$
$\psi ({\mathrm{\Omega }}^2)$	$\phi (2,0)$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega })$	$\phi (1,\phi (2,0)+1)$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \omega )$	$\phi (1,\phi (2,0)+\omega )$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi (\mathrm{\Omega }))$	$\phi (1,\phi (2,0)+\phi (1,0))$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi (\mathrm{\Omega }\times \psi (\mathrm{\Omega })))$	$\phi (1,\phi (2,0)+\phi (1,\phi (1,0)))$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2))$	$\phi (1,\phi (2,0)\times 2)$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2)\times 2)$	$\phi (1,\phi (2,0)\times 3)$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2+1))$	$\phi (1,{\omega }^{\phi (2,0)+1})$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2+\psi ({\mathrm{\Omega }}^2)))$	$\phi (1,{\omega }^{\phi (2,0)\times 2})$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }))$	$\phi (1,\phi (1,\phi (2,0)+1))$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \omega ))$	$\phi (1,\phi (1,\phi (2,0)+\omega ))$
$\psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2)))$	$\phi (1,\phi (1,\phi (2,0)\times 2))$
$\psi ({\mathrm{\Omega }}^2\times 2)$	$\phi (2,1)$
$\psi ({\mathrm{\Omega }}^2\times 2+\mathrm{\Omega })$	$\phi (1,\phi (2,1)+1)$
$\psi ({\mathrm{\Omega }}^2\times 2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2\times 2))$	$\phi (1,\phi (2,1)\times 2)$
$\psi ({\mathrm{\Omega }}^2\times 2+\mathrm{\Omega }\times \psi ({\mathrm{\Omega }}^2\times 2+\mathrm{\Omega }))$	$\phi (1,\phi (1,\phi (2,1)+1))$
$\psi ({\mathrm{\Omega }}^2\times 3)$	$\phi (2,2)$
$\psi ({\mathrm{\Omega }}^2\times 4)$	$\phi (2,3)$
$\psi ({\mathrm{\Omega }}^2\times \omega )$	$\phi (2,\omega )$
$\psi ({\mathrm{\Omega }}^2\times \psi (\mathrm{\Omega }))$	$\phi (2,\phi (1,0))$
$\psi ({\mathrm{\Omega }}^2\times \psi ({\mathrm{\Omega }}^2))$	$\phi (2,\phi (2,0))$
$\psi ({\mathrm{\Omega }}^2\times \psi ({\mathrm{\Omega }}^2\times \psi ({\mathrm{\Omega }}^2)))$	$\phi (2,\phi (2,\phi (2,0)))$
$\psi ({\mathrm{\Omega }}^3)$	$\phi (3,0)$
$\psi ({\mathrm{\Omega }}^3+{\mathrm{\Omega }}^2)$	$\phi (2,\phi (3,0)+1)$
$\psi ({\mathrm{\Omega }}^3+{\mathrm{\Omega }}^2\times \psi ({\mathrm{\Omega }}^3))$	$\phi (2,\phi (3,0)\times 2)$
$\psi ({\mathrm{\Omega }}^3\times 2)$	$\phi (3,1)$
$\psi ({\mathrm{\Omega }}^3\times 3)$	$\phi (3,2)$
$\psi ({\mathrm{\Omega }}^3\times \omega )$	$\phi (3,\omega )$
$\psi ({\mathrm{\Omega }}^3\times \psi ({\mathrm{\Omega }}^3))$	$\phi (3,\phi (3,0))$
$\psi ({\mathrm{\Omega }}^4)$	$\phi (4,0)$
$\psi ({\mathrm{\Omega }}^5)$	$\phi (5,0)$
$\psi ({\mathrm{\Omega }}^{\omega })$	$\phi (\omega ,0)$