FANDOM


a$b = a+b

a$[0] = a*2

a$[0][0] = a*2^2

a$[1] = a*2^a ~ a^a has arrow-level \(\uparrow\)

a$[1][1] ~ (a^a)^(a^a) = a^a^{a+1}

a$[2] has arrow-level \(\uparrow\uparrow\)

Dollar Function without $ Arrow Level
[1] \(\uparrow\)
[n] \(\uparrow^n\)
[[0]] \(\uparrow_1\)
[n[0]] \(\uparrow_1\uparrow^n\)
[[0][0]] \(\uparrow_1\uparrow_1\)
[[1]] \(\uparrow_2\)
[[[0]]] \(\uparrow_{\uparrow_1}\)
[[0]_2] \(\uparrow_{,\uparrow}\)
[[1]_2] \(\uparrow_{\uparrow,\uparrow}\)
[[[0]_2]_2] \(\uparrow_{\uparrow_{,\uparrow},\uparrow}\)
[[0]_3] \(\uparrow_{,\uparrow\uparrow}\)
[[0]_[0]_2] \(\uparrow_{,\uparrow_{,\uparrow}}\)
[[[0],1]] \(\uparrow_{,,\uparrow}\)
[[[1],1]] \(\uparrow_{\uparrow_{,,\uparrow},,\uparrow}\)
[[[1],1]] \(\uparrow_{\uparrow_1,,\uparrow}\)
[[[[0],1],1]] \(\uparrow_{\uparrow_{,\uparrow_{,,\uparrow}},,\uparrow}\)
[[[0,1]_2,1]] \(\uparrow_{\uparrow_{,,\uparrow},,\uparrow}\)
[[[0,1]_3,1]] \(\uparrow_{,\uparrow,\uparrow}\)
[[[0],2]] \(\uparrow_{,,\uparrow\uparrow}\)
[[0,[[0],1]]] \(\uparrow_{,,\uparrow_{,\uparrow_{,,\uparrow}}}\)
[[0,[0,1]_2]] \(\uparrow_{,,,\uparrow}\)

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