Goppatoth

Goppatoth is equal to \(10 \uparrow\uparrow 100\ \&\ 10\) using the array of operator. It has giggol entries, which fill 100-dimensional tetrational hypercube. The term was coined by Jonathan Bowers. The number is comparable to Saibian's tethrathoth.
It can also be written as \(\lbrace10,10(((...(((0,1)1)1)...)1)1)2\rbrace\) with 50 pairs of parentheses.
The array expansion of the first few entries and levels of separators is:
{10,10,...,10,10(1)...(1)10,10,...,10,10(2)...(1)...(2)...(3)...(4)...(0,1)...(1,1)...(2,1)...(0,2)...(0,3)...(0,0,1)...(0,0,2)...(0,0,0,1)...(0,0,0,0,1)...((1)1)...(1(1)1)...(0,1(1)1)...((1)2)...((1)0,1)...((1)(1)1)...((2)1)...((3)1)...((0,1)1)...((0,0,1)1)...(((1)1)1)...(((0,1)1)1)...((((((((((((((((((((((((((((((((((((((((((((((((((0,1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)1)...(((0,1)1)1)...(((1)1)1)...((0,0,1)1)...((0,1)1)...((3)1)...((2)1)...((1)(1)1)...((1)0,1)...((1)2)...(0,1(1)1)...(1(1)1)...((1)1)...(0,0,0,0,1)...(0,0,0,1)...(0,0,2)...(0,0,1)...(0,3)...(0,2)...(2,1)...(1,1)...(0,1)...(4)...(3)...(2)...(1)...(2)10,10,...,10,10(1)...(1)10,10,...,10,10}
== Approximations ==
Notation 	Approximation
Bird's array notation 	\(\{10,51 [1 \backslash 2] 2\}\)
Extended Cascading-E notation	\(\textrm{E}10\#\text{^^}\#101\)
Hyperfactorial Array Notation	\(101![1,1,1,1,2]\)
Fast-growing hierarchy 	\(f_{\varepsilon_0}(101)\)
Hardy hierarchy 	\(H_{\varepsilon_0}(102)\)
Slow-growing hierarchy (using this system
of fundamental sequences)	\(g\)\(_{\psi_0(\varepsilon_{\Omega+1})}\)\((100)\)\(= g_{\psi_0(\Omega_2)}(100)\)
== Sources ==
== See also ==
ja:ゴッパトス
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:Iterated Cantor normal form level
Category:Higher array notation
Category:BEAF