I would like to propose an entire function for googology wiki. Please let me know if it is okay to add it to the "other notations approximation" charts on the number pages. Thanks!

Hyper-Log notation or Hyper-L notation is an extension of the Log function that itself is a fast growing function, but not fast enough. Hyper-L notation is as follows. The standard notation is L(n) to indicate it is a hyper-L function.

First order Hyper-L function:

Representation: L(n)

Rule: L(n)= log(n)


L(5)= 100,000

L(33)= decillion

L(100)= googol

L(googol)= googolplex

Second Order Hyper-L Function:

Representation: L((n))

Rule: L((n))= 10^(log(n))^(log(n))^...^(log(n)); where ... equals log(n)


L((5))= 10^100,000^100,000^...^100,000 (... = 100,000)

L((33))= 10^decillion^decillion^...^decillion (... = decillion)

L((100))= 10^googol^googol^googol^...^googol (... = googol)

L((googol))= 10^googolplex^googolplex^...^googolplex (... = googolplex)

Third Order Hyper-L Function:

Representation: L(((n)))

Rule: \(10 \uparrow\uparrow...\uparrow\uparrow(N)\) with log(n) up arrows


L(((5)))= \(10 \uparrow\uparrow...\uparrow\uparrow(100,000)\) with 100,000 up arrows

L(((33)))= \(10 \uparrow\uparrow...\uparrow\uparrow(decillion)\) with decillion up arrows

L(((100)))= \(10 \uparrow\uparrow...\uparrow\uparrow(googol)\) with googol up arrows

L(((googol)))= \(10 \uparrow\uparrow...\uparrow\uparrow(googolplex)\) with googolplex up arrows

Beyond 3rd Order Hyper-L

Continues with same expansion rate seen before:

Representation: L(...(n)...) with any amount of parenthesis

Rule: depends on # of parenthesis


L((((((((((googol))))))))))= Dekalogogoogol

L(...(googol)...) when ... is L((((((((((googol)))))))))) = Duodekalogogoogol

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