## FANDOM

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So there are several numbers to define:

Googolplexian is $10^{10^{10^{100}}}$

Googoldupleplexian (a) is $Googolplexian \uparrow \uparrow Googolplexian$

Googoltrupleplexian (b) is $a \rightarrow a \rightarrow 3$

Googolquadrupleplexian (c) is $b \rightarrow b \rightarrow 4$

Googolpentrupleplexian is $c \rightarrow c \rightarrow 5$

This could be extended to a function

Googolplexian is stage 1

$Dupleplex(x) = \text{if }x = 1 \text{ then return Googolplexian else } $$Dupleplex(x-1) \rightarrow Dupleplex(x-1) \rightarrow x Approximation: (((10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow$$ (10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow3)\rightarrow $$((10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow$$ (10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow3)\rightarrow4)\rightarrow $$((10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow$$ (10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow3)\rightarrow $$((10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow$$ (10^{10^{10^{100}}}\uparrow\uparrow10^{10^{10^{100}}})\rightarrow3)\rightarrow4)$$\rightarrow5$

Pseudocode:

// Upper hyper operators
function hyper(a, b, n):
if n = 1:
return a + b
result := a
repeat b - 1 times:
result := hyper(a, result, n - 1)
return result

// Lower hyper operators
function hyper_lower(a, b, n):
if n = 1:
return a + b
result := a
repeat b - 1 times:
result := hyper_lower(result, a, n - 1)
return result

function dupleplex(a):

if a = 1:

return 10^10^10^100

return dupleplex(a - 1)