カテゴリー: 巨大数

\[ I_{n+1}\left(a,b\right)=I_{n+1}\left(a,b-1\right)^{\left(n\right)}a \]

\[ a^{\left(n\right)}\left(b^{\left(n\right)}c\right)\ne\left(a^{\left(n\right)}b\right)^{\left(n\right)}c \]

\[ H_{n}\left(a,b\right)=a\uparrow^{n-2}b\;,\;n\in\mathbb{Z} \]

\[ H_{n}\left(0,a\right)=\begin{cases} a+1 & n=0\\ a & n=1\\ 0 & n=2\\ \delta_{0a} & n=3\\ \delta_{0,\mod\left(a,2\right)} & n=4,5,\cdots \end{cases} \]

\[ H_{n}\left(a,b\right):=\begin{cases} b+1 & n=0\\ a+b & n=1\\ \underbrace{a^{\left(n-1\right)}a^{\left(n-1\right)}\cdots a^{\left(n-1\right)}a}_{b\;copies\;of\;a} & n=2,3,\cdots \end{cases} \]

\[ a\uparrow^{n}b:=\begin{cases} ab & n=0\\ 1 & n\geq1\;\land\;b=0\\ \underbrace{a\uparrow^{n-1}a\uparrow^{n-1}\cdots\uparrow^{n-1}a}_{b\;copies\;of\;a} & otherwise \end{cases} \]