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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).[1] The numbers were coined by Sbiis Saibian.

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Grangol regiment Gigangol regiment

List of numbers of the regiment Edit

Name of number Hyper-E Notation (exact equality) Scientific notation (exact equality)
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}
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}
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}}
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}
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}
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}
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}}
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}
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}
Name of number Hyper-E Notation (exact equality) Arrow notation (approximation)
grangoltrithrex E100#100#1#4 = E100#100#grangol#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))\)
grangoldexitrithrex E100#100#2#4 = E100#100#grangoldex#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))\)
grangoldudexitrithrex E100#100#3#4 = E100#100#grangoldudex#3 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))\)
greagoltrithrex E100#100#100#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))\)
grangolquadrithrex E100#100#1#5 = E100#100#grangol#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101)))))\)
grangoldexiquadrithrex E100#100#2#5 = E100#100#grangoldex#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3))))\)
grangoldudexiquadrithrex E100#100#3#5 = E100#100#grangoldudex#4 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4))))\)
greagolquadrithrex E100#100#100#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101))))\)
grangolquintithrex E100#100#1#6 = E100#100#grangol#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))))\)
grangoldexiquintithrex E100#100#2#6 = E100#100#grangoldex#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))))\)
grangoldudexiquintithrex E100#100#3#6 = E100#100#grangoldudex#5 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))))\)
greagolquintithrex E100#100#100#6 \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))))\)
greagolsextithrex E100#100#100#7 \(10\uparrow^4 8\)
greagolseptithrex E100#100#100#8 \(10\uparrow^4 9\)
greagoloctithrex E100#100#100#9 \(10\uparrow^4 10\)
greagolnonithrex E100#100#100#10 \(10\uparrow^4 11\)
greagoldecithrex E100#100#100#11 \(10\uparrow^4 12\)
greagolthrexichime E1000#1000#1000#2 \(10\uparrow^3 (10\uparrow^3 (1001))\)
greagolduthrexichime E1000#1000#1000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))\)
greagoltrithrexichime E1000#1000#1000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))\)
greagolquadrithrexichime E1000#1000#1000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))))\)
greagolquintithrexichime E1000#1000#1000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))))\)
greagoltoll E10,000#10,000#10,000 \(10\uparrow^3 (10^4)\)
greagolthrexitoll E10,000#10,000#10,000#2 \(10\uparrow^3 (10\uparrow^3 (10^4))\)
greagolduthrexitoll E10,000#10,000#10,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\)
greagoltrithrexitoll E10,000#10,000#10,000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\)
greagolquadrithrexitoll E10,000#10,000#10,000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4))))\)
greagolquintithrexitoll E10,000#10,000#10,000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))))\)
greagolgong E100,000#100,000#100,000 \(10\uparrow^3 (10^5)\)
greagolthrexigong E100,000#100,000#100,000#2 \(10\uparrow^3 (10\uparrow^3 (10^5))\)
greagolduthrexigong E100,000#100,000#100,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))\)
greagoltrithrexigong E100,000#100,000#100,000#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))\)
greagolquadrithrexigong E100,000#100,000#100,000#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))))\)
greagolquintithrexigong E100,000#100,000#100,000#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))))\)
greagolbong E100,000,000#100,000,000#100,000,000 \(10\uparrow^3 (10^8)\)
greagolthrexibong E100,000,000#100,000,000#100,000,000#2 \(10\uparrow^3 (10\uparrow^3 (10^8))\)
greagolduthrexibong E100,000,000#100,000,000#100,000,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^8)))\)
greagolthrong E100,000,000,000#100,000,000,000#100,000,000,000 \(10\uparrow^3 (10^{11})\)
greagolthrexithrong E100,000,000,000#100,000,000,000#100,000,000,000#2 \(10\uparrow^3 (10\uparrow^3 (10^{11}))\)
greagolduthrexithrong E100,000,000,000#100,000,000,000#100,000,000,000#3 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{11})))\)
gaggolchime E1#1#1000 \(10\uparrow^3 1000\)
gaggoltoll E1#1#10,000 \(10\uparrow^3 10000\)
gaggolgong E1#1#100,000 \(10\uparrow^3 100000\)
gaggolbong E1#1#100,000,000 \(10\uparrow^3 10^8\)
gaggolthrong E1#1#100,000,000,000 \(10\uparrow^3 10^{11}\)
googolthrex E100#1#1#2 = E100#1#googol \(10\uparrow^3 10^{100}\)
googolplexithrex E100#2#1#2 = E100#2#googolplex \(10\uparrow^3 10^{10^{10^{100}}}\)
googoldexithrex E100#1#2#2 = E100#1#(E100#1#2) \(10\uparrow^3 (10\uparrow^2 (10^{100}))\)
greagolplex E(E100#100#100) \(10\uparrow (10\uparrow^3 (101))\)
greagoldex E100#(E100#100#100) = E100#100#101 \(10\uparrow^2 (10\uparrow^3 (101))\)
ecetonthrex E303#1#1#2 = E303#1#(E303) = E303#1#centillion \(10\uparrow^3 (10^{303})\)
ecetonduthrex E303#1#1#3 = E303#1#ecetonthrex \(10\uparrow^3 (10\uparrow^3 (10^{303}))\)
ecetontrithrex E303#1#1#4 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))\)
ecetonquadrithrex E303#1#1#5 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303}))))\)
ecetonquintithrex E303#1#1#6 \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))))\)
tria-petaxis E1#1#1#3 = E1#1#deka-taxis \(10\uparrow^4 3\)
tetra-petaxis E1#1#1#4 = E1#1#tria-petaxis \(10\uparrow^4 4\)
penta-petaxis E1#1#1#5 = E1#1#tetra-petaxis \(10\uparrow^4 5\)
hexa-petaxis E1#1#1#6 = E1#1#penta-petaxis \(10\uparrow^4 6\)
hepta-petaxis E1#1#1#7 = E1#1#hexa-petaxis \(10\uparrow^4 7\)
octa-petaxis E1#1#1#8 = E1#1#hepta-petaxis \(10\uparrow^4 8\)
enna-petaxis E1#1#1#9 = E1#1#octa-petaxis \(10\uparrow^4 9\)
deka-petaxis E1#1#1#10 = E1#1#enna-petaxis \(10\uparrow^4 10\)
hecta-petaxis E1#1#1#100 \(10\uparrow^4 100\)
chilia-petaxis E1#1#1#1000 \(10\uparrow^4 1000\)
myria-petaxis E1#1#1#10,000 \(10\uparrow^4 10000\)


Etymology Edit

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 Edit

  1. Sbiis Saibian, 4.3.2 - Hyper-E Numbers

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