FANDOM


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)