Googondol regiment

The googondol regiment is a series of numbers from E100#100#100#100#100#100#100#100#100#100 to E100##10#2 defined using Hyper-E Notation (i.e. beginning from googondol and up to great googondol).Sbiis Saibian, 4.3.2 - Hyper-E Numbers The numbers were coined by Sbiis Saibian.
Previous regiment 	Next regiment
Gargantuul regiment	Gugold regiment
== List of numbers of the regiment ==
Name of number 	Hyper-E Notation (definition) 	Arrow notation (approximation) 	Fast-growing hierarchy (approximation)
googondol 	E100#100#100#100#100#100#100#100#100#100 	\(10\uparrow^{10}100\) 	\(f_{11}(100)\)
gargantuuldecex 	E100#100#100#100#100#100#100#100#100#1#2 	\(10\uparrow^{10}(10\uparrow^{9}100)\) 	\(f_{11}(f_{10}(100))\)
gargantuulennexidecex 	E100#100#100#100#100#100#100#100#100#2#2 	\(10\uparrow^{10}(10\uparrow^{9}(10\uparrow^{9}100))\) 	\(f_{11}(f_{10}^2(100))\)
gargantuulduennexidecex 	E100#100#100#100#100#100#100#100#100#3#2 	\(10\uparrow^{10}(10\uparrow^{9}(10\uparrow^{9}(10\uparrow^{9}100)))\) 	\(f_{11}(f_{10}^3(100))\)
googondoldecex 	E100#100#100#100#100#100#100#100#100#100#2	\(10\uparrow^{10}(10\uparrow^{10}100)\) 	\(f_{11}^2(100)\)
gargantuuldudecex 	E100#100#100#100#100#100#100#100#100#1#3 	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{9}100))\) 	\(f_{11}^2(f_{10}(100))\)
gargantuulennexidudecex 	E100#100#100#100#100#100#100#100#100#2#3 	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{9}(10\uparrow^{9}100)))\) 	\(f_{11}^2(f_{10}^2(100))\)
gargantuulduennexidudecex	E100#100#100#100#100#100#100#100#100#3#3 	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{9}(10\uparrow^{9}(10\uparrow^{9}100))))\) 	\(f_{11}^2(f_{10}^3(100))\)
googondoldudecex 	E100#100#100#100#100#100#100#100#100#100#3	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}100))\) 	\(f_{11}^3(100)\)
googondolchime 	E1000#1000#1000#1000#1000#1000#
1000#1000#1000#1000	\(10\uparrow^{10}1000\) 	\(f_{11}(1000)\)
googondoldecexichime 	E1000#1000#1000#1000#1000#1000#
1000#1000#1000#1000#2	\(10\uparrow^{10}(10\uparrow^{10}1000)\) 	\(f_{11}^2(1000)\)
googondoldudecexichime 	E1000#1000#1000#1000#1000#1000#
1000#1000#1000#1000#3	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}1000))\) 	\(f_{11}^3(1000)\)
googondoltoll 	E10,000#10,000#10,000#10,000#10,000#
10,000#10,000#10,000#10,000#10,000	\(10\uparrow^{10}10^4\) 	\(f_{11}(10,000)\)
googondoldecexitoll 	E10,000#10,000#10,000#10,000#10,000#
10,000#10,000#10,000#10,000#10,000#2	\(10\uparrow^{10}(10\uparrow^{10}10^4)\) 	\(f_{11}^2(10,000)\)
googondoldudecexitoll 	E10,000#10,000#10,000#10,000#10,000#
10,000#10,000#10,000#10,000#10,000#3	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}10^4))\) 	\(f_{11}^3(10,000)\)
googondolgong 	E100,000#100,000#100,000#100,000#
100,000#100,000#100,000#100,000#100,000#100,000	\(10\uparrow^{10}10^5\) 	\(f_{11}(100,000)\)
googondoldecexigong 	E100,000#100,000#100,000#100,000#100,000#
100,000#100,000#100,000#100,000#100,000#2	\(10\uparrow^{10}(10\uparrow^{10}10^5)\) 	\(f_{11}^2(100,000)\)
googondoldudecexigong 	E100,000#100,000#100,000#100,000#100,000#
100,000#100,000#100,000#100,000#100,000#3	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}10^5))\) 	\(f_{11}^3(100,000)\)
googondolbong 	E100,000,000#100,000,000# ...
... #100,000,000#100,000,000
w/10 100,000,000s	\(10\uparrow^{10}10^8\) 	\(f_{11}(10^8)\)
googondoldecexibong 	E100,000,000#100,000,000# ...
... #100,000,000#100,000,000#2
w/10 100,000,000s	\(10\uparrow^{10}(10\uparrow^{10}10^8)\) 	\(f_{11}^2(10^8)\)
googondoldudecexibong 	E100,000,000#100,000,000# ...
... #100,000,000#100,000,000#3
w/10 100,000,000s	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}10^8))\) 	\(f_{11}^3(10^8)\)
googondolthrong 	E100,000,000,000#100,000,000,000# ...
...#100,000,000,000#100,000,000,000
w/10 100,000,000,000s	\(10\uparrow^{10}10^{11}\) 	\(f_{11}(10^{11})\)
googondoldecexithrong 	E100,000,000,000#100,000,000,000# ...
...#100,000,000,000#100,000,000,000#2
w/10 100,000,000,000s	\(10\uparrow^{10}(10\uparrow^{10}10^{11})\) 	\(f_{11}^2(10^{11})\)
googondoldudecexithrong 	E100,000,000,000#100,000,000,000# ...
...#100,000,000,000#100,000,000,000#3
w/10 100,000,000,000s	\(10\uparrow^{10}(10\uparrow^{10}(10\uparrow^{10}10^{11}))\) 	\(f_{11}^3(10^{11})\)
googoldecex 	E100#1#1#1#1#1#1#1#1#1#2 	\(10\uparrow^{10}10^{100}\) 	\(f_{11}(f_2(323))\)
grangoldecex 	E100#100#1#1#1#1#1#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{2}100)\) 	\(f_{11}(f_3(100))\)
greagoldecex 	E100#100#100#1#1#1#1#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{3}100)\) 	\(f_{11}(f_4(100))\)
gigangoldecex 	E100#100#100#100#1#1#1#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{4}100)\) 	\(f_{11}(f_5(100))\)
gorgegoldecex 	E100#100#100#100#100#1#1#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{5}100)\) 	\(f_{11}(f_6(100))\)
gulgoldecex 	E100#100#100#100#100#100#1#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{6}100)\) 	\(f_{11}(f_7(100))\)
gaspgoldecex 	E100#100#100#100#100#100#100#1#1#1#2 	\(10\uparrow^{10}(10\uparrow^{7}100)\) 	\(f_{11}(f_8(100))\)
ginorgoldecex 	E100#100#100#100#100#100#100#100#1#1#2 	\(10\uparrow^{10}(10\uparrow^{8}100)\) 	\(f_{11}(f_9(100))\)
googondolplex 	E(E100##10) 	\(10\uparrow(10\uparrow^{10}100)\) 	\(f_2(f_{11}(100))\)
googondoldex 	E100#(E100##10) 	\(10\uparrow^2 (10\uparrow^{10}100)\) 	\(f_3(f_{11}(100))\)
googondolthrex 	E100#100#(E100##10) 	\(10\uparrow^3 (10\uparrow^{10}100)\) 	\(f_4(f_{11}(100))\)
googondoltetrex 	E100#100#100#(E100##10) 	\(10\uparrow^4 (10\uparrow^{10}100)\) 	\(f_5(f_{11}(100))\)
googondolpentex 	E100#100#100#100#(E100##10) 	\(10\uparrow^5 (10\uparrow^{10}100)\) 	\(f_6(f_{11}(100))\)
googondolhex 	E100#100#100#100#100#(E100##10) 	\(10\uparrow^6 (10\uparrow^{10}100)\) 	\(f_7(f_{11}(100))\)
googondolheptex 	E100#100#100#100#100#100#(E100##10) 	\(10\uparrow^7 (10\uparrow^{10}100)\) 	\(f_8(f_{11}(100))\)
googondoloctex 	E100#100#100#100#100#100#100#(E100##10) 	\(10\uparrow^8 (10\uparrow^{10}100)\) 	\(f_9(f_{11}(100))\)
googondolennex 	E100#100#100#100#100#100#100#100#(E100##10)
= E100#100#100#100#100#100#100#100#100#101	\(10\uparrow^9 (10\uparrow^{10}100)\) 	\(f_{10}(f_{11}(100))\)
ecetondecex 	E303#1#1#1#1#1#1#1#1#1#2 	\(10\uparrow^{10} (10^{303})\) 	\(f_{11}(f_2(996))\)
ecetondudecex 	E303#1#1#1#1#1#1#1#1#1#3 	\(10\uparrow^{10} (10\uparrow^{10} (10^{303}))\) 	\(f_{11}^2(f_2(996))\)
tria-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#3 	\(10\uparrow^{11} 3\) 	\(f_{11}^2(100)\)
tetra-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#4 	\(10\uparrow^{11} 4\) 	\(f_{11}^3(100)\)
deka-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#10 	\(10\uparrow^{11} 10\) 	\(f_{12}(9)\)
hecta-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#100 	\(10\uparrow^{11} 100\) 	\(f_{12}(99)\)
chilia-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#1000 	\(10\uparrow^{11} 1000\) 	\(f_{12}(999)\)
myria-dodekaxis 	E1#1#1#1#1#1#1#1#1#1#10,000 	\(10\uparrow^{11} 10000\) 	\(f_{12}(9999)\)
googoadol 	E100##11 	\(10\uparrow^{11} 100\) 	\(f_{12}(100)\)
goograndol 	E100##12 	\(10\uparrow^{12} 100\) 	\(f_{\omega}(13)\)
googreadol 	E100##13 	\(10\uparrow^{13} 100\) 	\(f_{\omega}(14)\)
googigandol 	E100##14 	\(10\uparrow^{14} 100\) 	\(f_{\omega}(15)\)
googorgedol 	E100##15 	\(10\uparrow^{15} 100\) 	\(f_{\omega}(16)\)
googuldol 	E100##16 	\(10\uparrow^{16} 100\) 	\(f_{\omega}(17)\)
googaspdol 	E100##17 	\(10\uparrow^{17} 100\) 	\(f_{\omega}(18)\)
googinordol 	E100##18 	\(10\uparrow^{18} 100\) 	\(f_{\omega}(19)\)
googarganduul 	E100##19 	\(10\uparrow^{19} 100\) 	\(f_{\omega}(20)\)
googonkosol 	E100##20 	\(10\uparrow^{20} 100\) 	\(f_{\omega}(21)\)
googontritol 	E100##30 	\(10\uparrow^{30} 100\) 	\(f_{\omega}(31)\)
googonsartol 	E100##40 	\(10\uparrow^{40} 100\) 	\(f_{\omega}(41)\)
googonpetol 	E100##50 	\(10\uparrow^{50} 100\) 	\(f_{\omega}(51)\)
googonextol 	E100##60 	\(10\uparrow^{60} 100\) 	\(f_{\omega}(61)\)
googoneptol 	E100##70 	\(10\uparrow^{70} 100\) 	\(f_{\omega}(71)\)
googonogdol 	E100##80 	\(10\uparrow^{80} 100\) 	\(f_{\omega}(81)\)
googonentol 	E100##90 	\(10\uparrow^{90} 100\) 	\(f_{\omega}(91)\)
googonhectol 	E100##100 	\(10\uparrow^{100} 100\) 	\(f_{\omega}(101)\)
great googol 	E100##1#2 = E100##(E100##1#1) =
= E100##(E100) = E100##(googol)
= E100#100#100#100# ...
... #100#100#100#100
w/googol 100s	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10^{100}\quad \uparrow 's}100\)	\(f_{\omega}(f_2(323))\)
great grangol 	E100##2#2
= E100##(E100#100) 	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^2 100}100\) 	\(f_{\omega}(f_3(100))\)
great greagol 	E100##3#2
= E100##(E100#100#100) 	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^3 100}100\) 	\(f_{\omega}(f_4(100))\)
great gigangol 	E100##4#2
= E100##(E100#100#100#100) 	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^4 100}100\) 	\(f_{\omega}(f_5(100))\)
great gorgegol 	E100##5#2
= E100##(E100#100#100#100#100) 	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^5 100}100\) 	\(f_{\omega}(f_6(100))\)
great gulgol 	E100##6#2
= E100##(E100#100#100#100#100#100)	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^6 100}100\) 	\(f_{\omega}(f_7(100))\)
great gaspgol 	E100##7#2
= E100##(E100#100#100#100#100#100#100)	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^7 100}100\) 	\(f_{\omega}(f_8(100))\)
great ginorgol 	E100##8#2
= E100##(E100#100#100#100#100#100#100#100)	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^8 100}100\) 	\(f_{\omega}(f_9(100))\)
great gargantuul 	E100##9#2
= E100##(E100#100#100#100#100#100#100#100#100)	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^9 100}100\) 	\(f_{\omega}(f_{10}(100))\)
great googondol 	E100##10#2
= E100##(E100##10) = E100##(googondol) 
= E100#100#100#100#100# ...
... #100#100#100#100#100
w/googondol 100s	\(10\underbrace{\uparrow\uparrow\cdots \uparrow\uparrow}_{10\uparrow^{10} 100}100\) 	\(f_{\omega}(f_{11}(100))\)
== Sources ==
Category:Saibian's regiments
Category:Numbers by Sbiis Saibian
Category:Numbers
Category:Series
Category:Up-arrow notation level