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This is an article which refers to a personal web site as the first source of the notion in the title. Please be careful as a personal web site is not usually a peer-reviewed source unlike academic journals, and hence might include wrong information. For more details, see this document.

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This array is from rombito’s googolisms.^[1] If needed, please read for the shorter explanation.

Definitions[]

{]0[} = 100
{]x[} = 10^{]x-1[}
{]x,0[} = {]x[}
{]x,y[} = {]{]x,y-1[}[}
{]x,y,0[} = {]x,y[}
{]x,y,z[} = {]{]x,y,z-1[},{]x,y,z-1[}[}
{]x,y,z,α[} = {]{]x,y,z,α-1[},{]x,y,z,α-1[},{]x,y,z,α-1[}[}
{]a₀...a_z-1, a_z[} = {]{]a₀...a_z-1, a_z-1[}...{]₀...a_z-1, a_z-1[},0[}
{1]x[} = {]x,x,x,x,x,x,x,x...[} (x copies of x) = {1]x,y[}
{1]x,y[} ={1]{1]x,y-1[}[}
{1]x,y,z[} = {1]{1]x,y,z-1[},{1]x,y,z-1[}[}
…
{Λ]x[} = {Λ-1]x,x,x,x,x,x,x,x...[} (x copies of x)
{Λ]x,y[} ={Λ]{Λ]x,y-1[}[}
{Λ]x,y,z[} ={Λ]{Λ]x,y,z-1[},{Λ]x,y,z-1[}[}
…

Examples and translations[]

{]x[} = $(10\uparrow \uparrow x)^{100}$
{]x,1[} = $(10\uparrow \uparrow ((10\uparrow \uparrow x)^{100}))^{100}$
{]x,y[} = $(10\uparrow \uparrow (\{]x,y-1[\})^{100}$

sources[]

↑ rombito’s googolisms/notations (site.google.com)00:24 Dec 22 2024

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