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Goppatoth is equal to $$10 \uparrow\uparrow 100 \&\ 10$$ using the array of operator.[1] 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)...((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 $$\{10,50 [1 \backslash 2] 2\}$$
Extended Cascading-E notation $$\textrm{E}10\#\text{^^}\#101$$
Hyperfactorial Array Notation $$101![1,1,1,1,2]$$
Dollar Function $$100[[0]_2]$$
Username5243's Array Notation $$10[0\{0,_11\}1]100$$
Fast-growing hierarchy $$f_{\varepsilon_0}(101)$$
Hardy hierarchy $$H_{\varepsilon_0}(102)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega+1})}(100)$$

## Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.