ノート:クヌースの矢印表記

${\displaystyle {\begin{aligned}a\uparrow ^{n}b=&a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)\right\}=a\uparrow ^{n-1}a\uparrow ^{n}\left(b-1\right)\\=&\underbrace {a\uparrow ^{n-2}a\uparrow ^{n-2}\cdots \uparrow ^{n-2}a\uparrow ^{n-2}a} _{a\uparrow ^{n}\left(b-1\right)}=a\uparrow ^{n-2}\underbrace {a\uparrow ^{n-2}a\uparrow ^{n-2}\cdots \uparrow ^{n-2}a\uparrow ^{n-2}a} _{a\uparrow ^{n}\left(b-1\right)-1}=a\uparrow ^{n-2}\left[a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)-1\right\}\right]=a\uparrow ^{n-2}a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)-1\right\}\\=&\underbrace {a\uparrow ^{n-3}a\uparrow ^{n-3}\cdots \uparrow ^{n-3}a\uparrow ^{n-3}a} _{a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)-1\right\}}=a\uparrow ^{n-3}\underbrace {a\uparrow ^{n-3}a\uparrow ^{n-3}\cdots \uparrow ^{n-3}a\uparrow ^{n-3}a} _{a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)-1\right\}-1}=a\uparrow ^{n-3}a\uparrow ^{n-2}\left[a\uparrow ^{n-1}\left\{a\uparrow ^{n}\left(b-1\right)-1\right\}-1\right]\\=&a\uparrow ^{2}a\uparrow ^{3}\left(a\uparrow ^{4}\cdots \left(a\uparrow ^{n-2}\left(a\uparrow ^{n-1}\left(a\uparrow ^{n}\left(b-1\right)-1\right)-1\right)-1\right)\cdots -1\right)\\=&a\uparrow a\uparrow ^{2}\left(a\uparrow ^{3}\cdots \left(a\uparrow ^{n-2}\left(a\uparrow ^{n-1}\left(a\uparrow ^{n}\left(b-1\right)-1\right)-1\right)-1\right)\cdots -1\right)=a^{a\uparrow ^{2}\left(a\uparrow ^{3}\left(a\uparrow ^{4}\cdots \left(a\uparrow ^{n-2}\left(a\uparrow ^{n-1}\left(a\uparrow ^{n}\left(b-1\right)-1\right)-1\right)-1\right)\cdots -1\right)-1\right)}\end{aligned}}}$--beautiful icosagon 2020年4月15日 (水) 14:32 (UTC)

↑を^に置き換えて、2↑↑6であれば、2^^6と表現する場合があるようです。2021年3月27日 (土) 01:14 (UTC)