BOCF VS veblen函数：修订间差异

2025年7月7日 (一) 10:09的版本

本条目展示BOCF和veblen函数的列表分析。


BOCF	veblen函数
$ψ (0)$	1
$ψ (0) \times 2$	2
$ψ (1)$	$ω$
$ψ (1) \times 2$	$ω \times 2$
$ψ (2)$	$ω^{2}$
$ψ (3)$	$ω^{3}$
$ψ (ψ (1))$	$ω^{ω}$
$ψ (ψ (1) + 1)$	$ω^{ω + 1}$
$ψ (ψ (1) \times 2)$	$ω^{ω \times 2}$
$ψ (ψ (2))$	$ω^{ω^{2}}$
$ψ (ψ (ψ (1)))$	$ω^{ω^{ω}}$
$ψ (ψ (ψ (ψ (1))))$	$ω^{ω^{ω^{ω}}}$
$ψ (Ω)$	$φ (1, 0)$
$ψ (Ω) + 1$	$φ (1, 0) + 1$
$ψ (Ω) \times 2$	$φ (1, 0) \times 2$
$ψ (Ω) \times 3$	$φ (1, 0) \times 3$
$ψ (Ω + 1)$	$ω^{φ (1, 0) + 1}$
$ψ (Ω + ψ (1))$	$ω^{φ (1, 0) + ω}$
$ψ (Ω + ψ (ψ (1)))$	$ω^{φ (1, 0) + ω^{ω}}$
$ψ (Ω + ψ (Ω))$	$ω^{φ (1, 0) \times 2}$
$ψ (Ω + ψ (Ω) + 1)$	$ω^{φ (1, 0) \times 2 + 1}$
$ψ (Ω + ψ (Ω) + ψ (1))$	$ω^{φ (1, 0) \times 2 + ω}$
$ψ (Ω + ψ (Ω) \times 2)$	$ω^{φ (1, 0) \times 3}$
$ψ (Ω + ψ (Ω) \times 3)$	$ω^{φ (1, 0) \times 4}$
$ψ (Ω + ψ (Ω + 1))$	$ω^{ω^{φ (1, 0) + 1}}$
$ψ (Ω + ψ (Ω + 1) + 1)$	$ω^{ω^{φ (1, 0) + 1} + 1}$
$ψ (Ω + ψ (Ω + 1) \times 2)$	$ω^{ω^{φ (1, 0) + 1} \times 2}$
$ψ (Ω + ψ (Ω + 2))$	$ω^{ω^{φ (1, 0) + 2}}$
$ψ (Ω + ψ (Ω + 3))$	$ω^{ω^{φ (1, 0) + 3}}$
$ψ (Ω + ψ (Ω + ψ (1)))$	$ω^{ω^{φ (1, 0) + ω}}$
$ψ (Ω + ψ (Ω + ψ (Ω)))$	$ω^{ω^{φ (1, 0) \times 2}}$
$ψ (Ω + ψ (Ω + ψ (Ω) \times 2))$	$ω^{ω^{φ (1, 0) \times 3}}$
$ψ (Ω + ψ (Ω + ψ (Ω + 1)))$	$ω^{ω^{ω^{φ (1, 0) + 1}}}$
$ψ (Ω + ψ (Ω + ψ (Ω + ψ (Ω + 1))))$	$ω^{ω^{ω^{ω^{φ (1, 0) + 1}}}}$
$ψ (Ω \times 2)$	$φ (1, 1)$
$ψ (Ω \times 2 + 1)$	$ω^{φ (1, 1) + 1}$
$ψ (Ω \times 2 + ψ (Ω))$	$ω^{φ (1, 1) + φ (1, 0)}$
$ψ (Ω \times 2 + ψ (Ω + ψ (Ω)))$	$ω^{φ (1, 1) + ω^{φ (1, 0) \times 2}}$
$ψ (Ω \times 2 + ψ (Ω \times 2))$	$ω^{φ (1, 1) \times 2}$
$ψ (Ω \times 2 + ψ (Ω \times 2 + 1))$	$ω^{ω^{φ (1, 1) + 1}}$
$ψ (Ω \times 2 + ψ (Ω \times 2 + ψ (Ω \times 2)))$	$ω^{ω^{φ (1, 1) \times 2}}$
$ψ (Ω \times 3)$	$φ (1, 2)$
$ψ (Ω \times 4)$	$φ (1, 3)$
$ψ (Ω \times ω)$	$φ (1, ω)$
$ψ (Ω \times ω + 1)$	$ω^{φ (1, ω) + 1}$
$ψ (Ω \times ω + ψ (Ω))$	$ω^{φ (1, ω) + φ (1, 0)}$
$ψ (Ω \times ω + ψ (Ω \times 2))$	$ω^{φ (1, ω) + φ (1, 1)}$
$ψ (Ω \times ω + ψ (Ω \times ω))$	$ω^{φ (1, ω) \times 2}$
$ψ (Ω \times ω + ψ (Ω \times ω + 1))$	$ω^{ω^{φ (1, ω) + 1}}$
$ψ (Ω \times ω + Ω)$	$φ (1, ω + 1)$
$ψ (Ω \times ω \times 2)$	$φ (1, ω \times 2)$
$ψ (Ω \times ω^{2})$	$φ (1, ω^{2})$
$ψ (Ω \times ψ (Ω))$	$φ (1, φ (1, 0))$
$ψ (Ω \times ψ (Ω) \times 2)$	$φ (1, φ (1, 0) \times 2)$
$ψ (Ω \times ψ (Ω + 1))$	$φ (1, ω^{φ (1, 0) + 1})$
$ψ (Ω \times ψ (Ω + ψ (Ω)))$	$φ (1, ω^{φ (1, 0) \times 2})$
$ψ (Ω \times ψ (Ω + ψ (Ω + ψ (Ω))))$	$φ (1, ω^{ω^{φ (1, 0) + 1}})$
$ψ (Ω \times ψ (Ω \times 2))$	$φ (1, φ (1, 1))$
$ψ (Ω \times ψ (Ω \times 3))$	$φ (1, φ (1, 2))$
$ψ (Ω \times ψ (Ω \times ω))$	$φ (1, φ (1, ω))$
$ψ (Ω \times ψ (Ω \times ψ (Ω)))$	$φ (1, φ (1, φ (1, 0)))$
$ψ (Ω \times ψ (Ω \times ψ (Ω \times ψ (Ω))))$	$φ (1, φ (1, φ (1, φ (1, 0))))$
$ψ (Ω^{2})$	$φ (2, 0)$

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 |<math>\psi(\Omega^2)</math>
-|<math>\varphi(1,1)</math>
+|<math>\varphi(2,0)</math>
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