ペンテーション
a ↑ 3 n = a ↑ 2 a ↑ 2 ⋯ ↑ 2 a ↑ 2 a ⏟ n = a ↑ 2 ( a ↑ 2 ( ⋯ a ↑ 2 ( a ↑ 2 a ) ) ) = a ↑ 2 a ↑ 2 a ↑ 2 ⋯ ↑ 2 a ↑ 2 a ⏟ n − 1 = a ↑ 2 a ↑ 3 ( n − 1 ) a ↑ 3 n = a a ⋅ ⋅ ⋅ a a ⏟ 高 さ n = ( ( ( a a ) ⋅ ⋅ ⋅ ) a ) a {\displaystyle {\begin{aligned}a\uparrow ^{3}n&=\underbrace {a\uparrow ^{2}a\uparrow ^{2}\cdots \uparrow ^{2}a\uparrow ^{2}a} _{n}=a\uparrow ^{2}{\biggl (}a\uparrow ^{2}{\Bigl (}\cdots a\uparrow ^{2}{\bigl (}a\uparrow ^{2}a{\bigr )}{\Bigr )}{\biggr )}\\&=a\uparrow ^{2}\underbrace {a\uparrow ^{2}a\uparrow ^{2}\cdots \uparrow ^{2}a\uparrow ^{2}a} _{n-1}=a\uparrow ^{2}a\uparrow ^{3}\left(n-1\right)\\a\uparrow ^{3}n&=\underbrace {^{^{^{^{^{^{a}a}\cdot }\cdot }\cdot }a}a} _{{\text{高 さ }}n}={^{\left({^{\left({^{^{^{\left({^{a}a}\right)}\cdot }\cdot }\cdot }\right)}a}\right)}a}\end{aligned}}}
ペンテーションを表すにはいくつか等価な表記がある。