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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.

See also

Jonathan Bowers' array of series

Higher tetration level: Gotriplexulus · Goppatoth · Goppatothplex
Pentation level: Triakulus · Kungulus · Kungulusplex
Higher operation group: Quadrunculus · Tridecatrix · Humongulus
Lineational group: Tetdecatrix · Pendecatrix · Hexdecatrix · Hepdecatrix · Ocdecatrix · Endecatrix · Lineatrix · Lineatrixplex
Golapulus group: Golapulus · Golapulusplex · Dekulus
Cookie Fonster's extensions: Second Goppatoth · Gippatoth · Gappatoth · Geepatoth · Boppatoth · Troppatoth · Quadroppatoth · Humongulusplex · Tridecatrax · Tridecatreex · Tridecatrowx · Tridecatrux · Gonguldeus · Humingulus · Gongultreus · Humangulus · Gongulquadeus · Possible interpretation of tetrakulus · Humeengulus · Generatrix · Incredulus · Incridulus · Incradulus · Increedulus · Tercredulus · Tercridulus · Tercradulus · Tercreedulus · Pencredulus · Excredulus · Epcredulus · Ogcredulus · Goobawamba · Gibbawamba · Gabbawamba · Boobawamba · Troobawamba · Goobawantra · Emperatrix · Gossablossla · Hyperlatrix · Goobaduamba · Goobatriombia · Goobaquardimbia · Goobaquindingia · Goobasesixtia · Goobasebiptia · Goobagogdiktia · Goobanogdiktia · Xaplorgulus · Goobadektimtia · Goxxablorg · Gooxadworg · Goxxathrorg · Goxxaquorg · Cosslorgulus · Tesslorgulus · Pesslorgulus · Hesslorgulus · Zesslorgulus · Yosslorgulus · Brosslorgulus · Gosslorgulus · Mosslorgulus · Hasslorgulus · Kysslorgulus · Pisslorgulus · Sasslorgulus · Pexxlorgulus · Nisslorgulus · Zozzlorgulus · Ginglapulus · Ganglapulus · Geenglapulus · Bolapulus · Trolapulus · Goplapulus · Goduplapulus · Gotriplapulus · Hypertriakulus · Tetrakulus · Pentakulus · Hexakulus · Heptakulus · Oktakulus · Ennakulus · Big Mac · The Whopper

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