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The gargantuul regiment is a series of numbers from E100#100#100#100#100#100#100#100#100 to E1#1#1#1#1#1#1#1#1#10,000 defined using Hyper-E Notation (i.e. beginning from gargantuul and up to myria-endekaxis).[1] The numbers were coined by Sbiis Saibian.

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Ginorgol regiment Googondol regiment

List of numbers of the regiment[]

Name of number Hyper-E Notation (definition) Arrow notation (approximation) Fast-growing hierarchy (approximation)
gargantuul E100#100#100#100#100#100#100#100#100 \(10\uparrow^9 100\) \(f_{10}(100)\)
ginorgolennex E100#100#100#100#100#100#100#100#1#2 \(10\uparrow^9 (10\uparrow^8 100)\) \(f_{10}(f_9(100))\)
ginorgoloctexiennex E100#100#100#100#100#100#100#100#2#2 \(10\uparrow^9 (10\uparrow^8 (10\uparrow^8 100))\) \(f_{10}(f_9^2(100))\)
ginorgolduoctexiennex E100#100#100#100#100#100#100#100#3#2 \(10\uparrow^9 (10\uparrow^8 (10\uparrow^8 (10\uparrow^8 100)))\) \(f_{10}(f_9^3(100))\)
gargantuulennex E100#100#100#100#100#100#100#100#100#2 \(10\uparrow^9 (10\uparrow^9 100)\) \(f_{10}^2(100)\)
ginorgolduennex E100#100#100#100#100#100#100#100#1#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 100))\) \(f_{10}^2(f_9(100))\)
ginorgoloctexiduennex E100#100#100#100#100#100#100#100#2#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 (10\uparrow^8 100)))\) \(f_{10}^2(f_9^2(100))\)
ginorgolduoctexiduennex E100#100#100#100#100#100#100#100#3#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 (10\uparrow^8 (10\uparrow^8 100))))\) \(f_{10}^2(f_9^3(100))\)
gargantuulduennex E100#100#100#100#100#100#100#100#100#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 100))\) \(f_{10}^3(100)\)
gargantuulchime E1000#1000#1000#1000#1000#1000#1000#1000#1000 \(10\uparrow^9 1000\) \(f_{10}(1000)\)
gargantuulennexichime E1000#1000#1000#1000#1000#1000#1000#1000#1000#2 \(10\uparrow^9 (10\uparrow^9 1000)\) \(f_{10}^2(1000)\)
gargantuulennexichime E1000#1000#1000#1000#1000#1000#1000#1000#1000#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 1000))\) \(f_{10}^3(1000)\)
gargantuultoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000

\(10\uparrow^9 10^4\) \(f_{10}(10,000)\)
gargantuulennexitoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000#2

\(10\uparrow^9 (10\uparrow^9 10^4)\) \(f_{10}^2(10,000)\)
gargantuulduennexitoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000#3

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^4))\) \(f_{10}^3(10,000)\)
gargantuulgong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000

\(10\uparrow^9 10^5\) \(f_{10}(100,000)\)
gargantuulennexigong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000#2

\(10\uparrow^9 (10\uparrow^9 10^5)\) \(f_{10}^2(100,000)\)
gargantuulduennexigong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000#3

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^5))\) \(f_{10}^3(100,000)\)
gargantuulbong E100,000,000#100,000,000#100,000,000# ...

...100,000,000#100,000,000#100,000,000 w/9 100,000,000s

\(10\uparrow^9 10^8\) \(f_{10}(10^8)\)
gargantuulennexibong E100,000,000#100,000,000#100,000,000# ...

... #100,000,000#100,000,000#100,000,000#2 w/9 100,000,000s

\(10\uparrow^9 (10\uparrow^9 10^8)\) \(f_{10}^2(10^8)\)
gargantuulduennexibong E100,000,000#100,000,000#100,000,000# ...

... #100,000,000#100,000,000#100,000,000#3 w/9 100,000,000s

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^8))\) \(f_{10}^3(10^8)\)
gargantuulthrong E100,000,000,000#100,000,000,000# ...

...#100,000,000,000#100,000,000,000 w/9 100,000,000,000s

\(10\uparrow^9 10^{11}\) \(f_{10}(10^{11})\)
gargantuulennexithrong E100,000,000,000#100,000,000,000# ...

... #100,000,000,000#100,000,000,000#2 w/9 100,000,000,000s

\(10\uparrow^9 (10\uparrow^9 10^{11})\) \(f_{10}^2(10^{11})\)
gargantuulduennexithrong E100,000,000,000#100,000,000,000# ...

... #100,000,000,000#100,000,000,000#3 w/9 100,000,000,000s

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^{11}))\) \(f_{10}^3(10^{11})\)
googolennex E100#1#1#1#1#1#1#1#1#2 \(10\uparrow^9 10^{100}\) \(f_{10}(f_2(323))\)
grangolennex E100#100#1#1#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^2 100)\) \(f_{10}(f_3(100))\)
greagolennex E100#100#100#1#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^3 100)\) \(f_{10}(f_4(100))\)
gigangolennex E100#100#100#100#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^4 100)\) \(f_{10}(f_5(100))\)
gorgegolennex E100#100#100#100#100#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^5 100)\) \(f_{10}(f_6(100))\)
gulgolennex E100#100#100#100#100#100#1#1#1#2 \(10\uparrow^9 (10 \uparrow^6 100)\) \(f_{10}(f_7(100))\)
gaspgolennex E100#100#100#100#100#100#100#1#1#2 \(10\uparrow^9 (10 \uparrow^7 100)\) \(f_{10}(f_8(100))\)
gargantuulplex E(E100#100#100#100#100#100#100#100#100) \(10\uparrow (10 \uparrow^9 100)\) \(f_2(f_{10}(100))\)
gargantuuldex E100#(E100#100#100#100#100#100#100#100#100) \(10\uparrow^2 (10 \uparrow^9 100)\) \(f_3(f_{10}(100))\)
gargantuulthrex E100#100#

(E100#100#100#100#100#100#100#100#100)

\(10\uparrow^3 (10 \uparrow^9 100)\) \(f_4(f_{10}(100))\)
gargantuultetrex E100#100#100#

(E100#100#100#100#100#100#100#100#100)

\(10\uparrow^4 (10 \uparrow^9 100)\) \(f_5(f_{10}(100))\)
gargantuulpentex E100#100#100#100#

(E100#100#100#100#100#100#100#100#100)

\(10\uparrow^5 (10 \uparrow^9 100)\) \(f_6(f_{10}(100))\)
gargantuulhex E100#100#100#100#100#

(E100#100#100#100#100#100#100#100#100)

\(10\uparrow^6 (10 \uparrow^9 100)\) \(f_7(f_{10}(100))\)
gargantuulheptex E100#100#100#100#100#100#

(E100#100#100#100#100#100#100#100#100)

\(10\uparrow^7 (10 \uparrow^9 100)\) \(f_8(f_{10}(100))\)
gargantuuloctex E100#100#100#100#100#100#100#

(E100#100#100#100#100#100#100#100#100) = E100#100#100#100#100#100#100#100#101

\(10\uparrow^8 (10 \uparrow^9 100)\) \(f_9(f_{10}(100))\)
ecetonennex E303#1#1#1#1#1#1#1#1#2 \(10 \uparrow^9 10^{303}\) \(f_{10}(f_2(996))\)
ecetonduennex E303#1#1#1#1#1#1#1#1#3 \(10 \uparrow^9 (10 \uparrow^9 10^{303})\) \(f_{10}^2(f_2(996))\)
tria-endekaxis E1#1#1#1#1#1#1#1#1#3 \(10 \uparrow^{10} 3\) \(f_{10}^2(100)\)
tetra-endekaxis E1#1#1#1#1#1#1#1#1#4 \(10 \uparrow^{10} 4\) \(f_{10}^3(100)\)
deka-endekaxis E1#1#1#1#1#1#1#1#1#10 \(10 \uparrow^{10} 10\) \(f_{11}(9)\)
hecta-endekaxis E1#1#1#1#1#1#1#1#1#100 \(10 \uparrow^{10} 100\) \(f_{11}(99)\)
chilia-endekaxis E1#1#1#1#1#1#1#1#1#1000 \(10 \uparrow^{10} 1000\) \(f_{11}(999)\)
myria-endekaxis E1#1#1#1#1#1#1#1#1#10,000 \(10 \uparrow^{10} 10000\) \(f_{11}(9999)\)

Sources[]

  1. Sbiis Saibian, 4.3.2 - Hyper-E Numbers
Saibian's regiments

Hyper-E regiments: Guppy regiment · Grangol regiment · Greagol regiment · Gigangol regiment · Gorgegol regiment · Gulgol regiment · Gaspgol regiment · Ginorgol regiment · Gargantuul regiment · Googondol regiment
Extended Hyper-E regiments: Gugold regiment · Graatagold regiment · Greegold regiment · Grinningold regiment · Golaagold regiment · Gruelohgold regiment · Gaspgold regiment · Ginorgold regiment · Gargantuuld regiment · Googondold regiment · Gugolthra regiment · Throogol regiment · Tetroogol regiment · Pentoogol regiment · Hexoogol regiment · Heptoogol regiment · Ogdoogol regiment · Entoogol regiment · Dektoogol regiment
Cascading-E regiments: Godgahlah regiment · Gridgahlah regiment · Kubikahlah regiment · Quarticahlah regiment · Quinticahlah regiment · Sexticahlah regiment · Septicahlah regiment · Octicahlah regiment · Nonicahlah regiment · Decicahlah regiment · Godgathor regiment · Gralgathor regiment · Thraelgathor regiment · Terinngathor regiment · Pentaelgathor regiment · Hexaelgathor regiment · Heptaelgathor regiment · Octaelgathor regiment · Ennaelgathor regiment · Dekaelgathor regiment · Godtothol regiment · Godtertol regiment · Godtopol regiment · Godhathor regiment · Godheptol regiment · Godoctol regiment · Godentol regiment · Goddekathol regiment
Extended Cascading-E regiments: Tethrathoth regiment · Monster-Giant regiment · Tethriterator regiment · Tethracross regiment · Tethracubor regiment · Tethrateron regiment · Tethrapeton regiment · Tethrahexon regiment · Tethrahepton regiment · Tethra-ogdon regiment · Tethrennon regiment · Tethradekon regiment · Tethratope regiment · Pentacthulhum regiment · Pentacthulcross regiment · Pentacthulcubor regiment · Pentacthulteron regiment · Pentacthulpeton regiment · Pentacthulhexon regiment · Pentacthulhepton regiment · Pentacthul-ogdon regiment · Pentacthulennon regiment · Pentacthuldekon regiment · Pentacthultope regiment · Hexacthulhum super regiment · Heptacthulhum super regiment · Ogdacthulhum super regiment · Ennacthulhum super regiment · Dekacthulhum super regiment
Beyond...: Blasphemorgulus regiment
Redstonepillager's extensions: Extended Gridgahlah regiment · Tethratopothoth regiment · Godsgodgulus regiment · Blasphemorgulus regiment · Blasphemordeugulus regiment · Ominongulus regiment

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