Greagol regiment

The greagol regiment is a series of numbers from E100#100#100 to E1#1#1#10,000 defined using Hyper-E notation (i.e. beginning from greagol and up to myria-petaxis).Sbiis Saibian, 4.3.2 - Hyper-E Numbers The numbers were coined by Sbiis Saibian.
Previous regiment	Next regiment
Grangol regiment 	Gigangol regiment
== List of numbers of the regiment ==
Name of number 	Hyper-E Notation (definition) 	Scientific notation (exact value) 	Scientific notation (approximation) 	Fast-growing hierarchy (approximation)
Greagol 	E100#100#100 	\(\left.\begin{matrix}\underbrace{10^{...^{10^{100}}}} \\ \underbrace{\quad\;\; \vdots \quad\;\;} \\ \underbrace{10^{...^{10^{100}}}} \\ 100\quad 10's \end{matrix} \right \} \text{100 lower braces}\) 	\(100 \uparrow\uparrow\uparrow 100\) 	\(f_4(100)\)
Googolthrex 	E100#1#1#2 = E100#100#googol 	\(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} 10^{100}\) 	\(100 \uparrow\uparrow\uparrow 10\uparrow 100\) 	\(f_4(f_2(324))\)
Googolplexithrex 	E100#2#1#2 = E100#100#googolplex 	\(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} 10^{10^{100}}\) 	\(100 \uparrow\uparrow\uparrow 10\uparrow 10\uparrow 100\) 	\(f_4(f_2^2(324))\)
Grangolthrex 	E100#100#1#2 = E100#100#grangol 	\(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}\) 	\(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 100\) 	\(f_4(f_3(100))\)
Grangoldexithrex 	E100#100#2#2 = E100#100#grangoldex 	\(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}\) 	\(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) 	\(f_4(f_3^2(100))\)
Grangoldudexithrex 	E100#100#3#2 = E100#100#grangoldudex 	\(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\& & 100\quad 10's \end{matrix} \right \} \text {3 lower braces}\) 	\(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) 	\(f_4(f_3^3(100))\)
Greagolthrex 	E100#100#100#2 = E100#100#(E100#100#100) = E100#100#greagol 	\(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {100 lower braces}\) 	\(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 100\) 	\(f_4^2(100)\)
Grangolduthrex 	E100#100#1#3 = E100#100#grangol#2 	\(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}\) 	\(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 100\) 	\(f_4^2(f_3(100))\)
Grangoldexiduthrex 	E100#100#2#3 = E100#100#grangoldex#2 	\(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}\) 	\(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) 	\(f_4^2(f_3^2(100))\)
Grangoldudexiduthrex	E100#100#3#3 = E100#100#grangoldudex#2 	\(\left. \left.\left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {3 lower braces}\) 	\(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\)	\(f_4^2(f_3^3(100))\)
Greagolduthrex 	E100#100#100#3 = E100#100#(E100#100#100#2) = E100#100#greagolthrex	\(\left. \left.\left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {100 lower braces}\)	\(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow\uparrow 100\) 	\(f_4^3(100)\)
Name of number 	Hyper-E Notation (definition) 	Arrow notation (approximation) 	Fast-growing hierarchy (approximation)
Grangoltrithrex 	E100#100#1#4 = E100#100#grangol#3 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))\) 	\(f_4^3(f_3(100))\)
Grangoldexitrithrex 	E100#100#2#4 = E100#100#grangoldex#3 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))\) 	\(f_4^3(f_3^2(100))\)
Grangoldudexitrithrex 	E100#100#3#4 = E100#100#grangoldudex#3 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))\) 	\(f_4^3(f_3^3(100))\)
Greagoltrithrex 	E100#100#100#4 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))\) 	\(f_4^4(100)\)
Grangolquadrithrex 	E100#100#1#5 = E100#100#grangol#4 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101)))))\) 	\(f_4^4(f_3(100))\)
Grangoldexiquadrithrex 	E100#100#2#5 = E100#100#grangoldex#4 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3))))\) 	\(f_4^4(f_3^2(100))\)
Grangoldudexiquadrithrex	E100#100#3#5 = E100#100#grangoldudex#4 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4))))\) 	\(f_4^4(f_3^3(100))\)
Greagolquadrithrex 	E100#100#100#5 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101))))\) 	\(f_4^5(100)\)
Grangolquintithrex 	E100#100#1#6 = E100#100#grangol#5 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))))\) 	\(f_4^5(f_3(100))\)
Grangoldexiquintithrex 	E100#100#2#6 = E100#100#grangoldex#5 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))))\) 	\(f_4^5(f_3^2(100))\)
Grangoldudexiquintithrex	E100#100#3#6 = E100#100#grangoldudex#5 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))))\) 	\(f_4^5(f_3^3(100))\)
Greagolquintithrex 	E100#100#100#6 	\(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))))\) 	\(f_4^6(100)\)
Greagolsextithrex 	E100#100#100#7 	\(10\uparrow^4 8\) 	\(f_4^7(100)\)
Greagolseptithrex 	E100#100#100#8 	\(10\uparrow^4 9\) 	\(f_4^8(100)\)
Greagoloctithrex 	E100#100#100#9 	\(10\uparrow^4 10\) 	\(f_4^9(100)\)
Greagolnonithrex 	E100#100#100#10 	\(10\uparrow^4 11\) 	\(f_4^{10}(100)\)
Greagoldecithrex 	E100#100#100#11 	\(10\uparrow^4 12\) 	\(f_4^{11}(100)\)
Greagolthrexichime 	E1000#1000#1000#2 	\(10\uparrow^3 (10\uparrow^3 (1001))\) 	\(f_4^2(1000)\)
Greagolduthrexichime 	E1000#1000#1000#3 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))\) 	\(f_4^2(f_3(1000))\)
Greagoltrithrexichime 	E1000#1000#1000#4 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))\) 	\(f_4^3(f_3(1000))\)
Greagolquadrithrexichime	E1000#1000#1000#5 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))))\) 	\(f_4^4(f_3(1000))\)
Greagolquintithrexichime	E1000#1000#1000#6 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))))\)	\(f_4^5(f_3(1000))\)
Greagoltoll 	E10,000#10,000#10,000 	\(10\uparrow^3 (10^4)\) 	\(f_4(10,000)\)
Greagolthrexitoll 	E10,000#10,000#10,000#2 	\(10\uparrow^3 (10\uparrow^3 (10^4))\) 	\(f_4(f_3(10,000))\)
Greagolduthrexitoll 	E10,000#10,000#10,000#3 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\) 	\(f_4^2(f_3(10,000))\)
Greagoltrithrexitoll 	E10,000#10,000#10,000#4 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\) 	\(f_4^3(f_3(10,000))\)
Greagolquadrithrexitoll 	E10,000#10,000#10,000#5 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4))))\) 	\(f_4^4(f_3(10,000))\)
Greagolquintithrexitoll 	E10,000#10,000#10,000#6 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))))\) 	\(f_4^5(f_3(10,000))\)
Greagolgong 	E100,000#100,000#100,000 	\(10\uparrow^3 (10^5)\) 	\(f_4(100,000)\)
Greagolthrexigong 	E100,000#100,000#100,000#2 	\(10\uparrow^3 (10\uparrow^3 (10^5))\) 	\(f_4(f_3(100,000))\)
Greagolduthrexigong 	E100,000#100,000#100,000#3 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))\) 	\(f_4^2(f_3(100,000))\)
Greagoltrithrexigong 	E100,000#100,000#100,000#4 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))\) 	\(f_4^3(f_3(100,000))\)
Greagolquadrithrexigong 	E100,000#100,000#100,000#5 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))))\) 	\(f_4^4(f_3(100,000))\)
Greagolquintithrexigong 	E100,000#100,000#100,000#6 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))))\)	\(f_4^5(f_3(100,000))\)
Greagolbong 	E100,000,000#100,000,000#100,000,000 	\(10\uparrow^3 (10^8)\) 	\(f_4(10^8)\)
Greagolthrexibong 	E100,000,000#100,000,000#100,000,000#2 	\(10\uparrow^3 (10\uparrow^3 (10^8))\) 	\(f_4(f_3(10^8))\)
Greagolduthrexibong 	E100,000,000#100,000,000#100,000,000#3 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^8)))\) 	\(f_4^2(f_3(10^8))\)
Greagolthrong 	E100,000,000,000#100,000,000,000#100,000,000,000 	\(10\uparrow^3 (10^{11})\) 	\(f_4(10^{11})\)
Greagolthrexithrong 	E100,000,000,000#100,000,000,000#100,000,000,000#2	\(10\uparrow^3 (10\uparrow^3 (10^{11}))\) 	\(f_4(f_3(10^{11}))\)
Greagolduthrexithrong 	E100,000,000,000#100,000,000,000#100,000,000,000#3	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{11})))\) 	\(f_4^2(f_3(10^{11}))\)
Gaggolchime 	E1#1#1000 	\(10\uparrow^3 1000\) 	\(f_4(1000)\)
Gaggoltoll 	E1#1#10,000 	\(10\uparrow^3 10000\) 	\(f_4(10,000)\)
Gaggolgong 	E1#1#100,000 	\(10\uparrow^3 100000\) 	\(f_4(100,000)\)
Gaggolbong 	E1#1#100,000,000 	\(10\uparrow^3 10^8\) 	\(f_4(10^8)\)
Gaggolthrong 	E1#1#100,000,000,000 	\(10\uparrow^3 10^{11}\) 	\(f_4(10^{11})\)
Googolthrex 	E100#1#1#2 = E100#1#googol 	\(10\uparrow^3 10^{100}\) 	\(f_4(f_2(324))\)
Googolplexithrex 	E100#2#1#2 = E100#2#googolplex 	\(10\uparrow^3 10^{10^{10^{100}}}\) 	\(f_4(f_2^2(324))\)
Googoldexithrex 	E100#1#2#2 = E100#1#(E100#1#2) 	\(10\uparrow^3 (10\uparrow^2 (10^{100}))\) 	\(f_4(f_3(f_2(324)))\)
Greagolplex 	E(E100#100#100) 	\(10\uparrow (10\uparrow^3 (101))\) 	\(f_2(f_4(100))\)
Greagoldex 	E100#(E100#100#100) = E100#100#101 	\(10\uparrow^2 (10\uparrow^3 (101))\) 	\(f_4(101)\)
Ecetonthrex 	E303#1#1#2 = E303#1#(E303) = E303#1#centillion 	\(10\uparrow^3 (10^{303})\) 	\(f_4(996)\)
Ecetonduthrex 	E303#1#1#3 = E303#1#ecetonthrex 	\(10\uparrow^3 (10\uparrow^3 (10^{303}))\) 	\(f_4^2(996)\)
Ecetontrithrex 	E303#1#1#4 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))\) 	\(f_4^3(996)\)
Ecetonquadrithrex 	E303#1#1#5 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303}))))\) 	\(f_4^4(996)\)
Ecetonquintithrex 	E303#1#1#6 	\(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))))\) 	\(f_4^5(996)\)
Tria-petaxis 	E1#1#1#3 = E1#1#deka-taxis 	\(10\uparrow^4 3\) 	\(f_4^2(10)\)
Tetra-petaxis 	E1#1#1#4 = E1#1#tria-petaxis 	\(10\uparrow^4 4\) 	\(f_4^3(10)\)
Penta-petaxis 	E1#1#1#5 = E1#1#tetra-petaxis 	\(10\uparrow^4 5\) 	\(f_4^4(10)\)
Hexa-petaxis 	E1#1#1#6 = E1#1#penta-petaxis 	\(10\uparrow^4 6\) 	\(f_4^5(10)\)
Hepta-petaxis 	E1#1#1#7 = E1#1#hexa-petaxis 	\(10\uparrow^4 7\) 	\(f_4^6(10)\)
Octa-petaxis 	E1#1#1#8 = E1#1#hepta-petaxis 	\(10\uparrow^4 8\) 	\(f_4^7(10)\)
Enna-petaxis 	E1#1#1#9 = E1#1#octa-petaxis 	\(10\uparrow^4 9\) 	\(f_4^8(10)\)
Deka-petaxis 	E1#1#1#10 = E1#1#enna-petaxis 	\(10\uparrow^4 10\) 	\(f_4^9(10)\)
Hecta-petaxis 	E1#1#1#100 	\(10\uparrow^4 100\) 	\(f_5(99)\)
Chilia-petaxis 	E1#1#1#1000 	\(10\uparrow^4 1000\) 	\(f_5(999)\)
Myria-petaxis 	E1#1#1#10,000 	\(10\uparrow^4 10000\) 	\(f_5(9999)\)
== Etymology ==
Parts of names	Meaning
tria 	3
tetra 	4
penta 	5
hexa 	6
hepta 	7
octa 	8
enna 	9
deka 	10
hecta 	100
chilia 	1000
myria 	10000
ding 	multiply the base value by 5
chime 	multiply the base value by 10
bell 	multiply the base value by 50
toll 	multiply the base value by 100
gong 	multiply the base value by 1000
bong 	multiply the base value by \(10^6\)
throng 	multiply the base value by \(10^9\)
gandingan 	multiply the base value by \(10^{12}\)
== Sources ==
Category:Saibian's regiments
Category:Series
Category:Numbers by Sbiis Saibian
Category:Numbers
Category:Up-arrow notation level
Category:Googol series