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Gaggolplex is equal to {10,gaggol,3} in BEAF, or 10 pentated to gaggol.[1] The term was coined by Jonathan Bowers.

This number is also called hectataxia-taxis by Sbiis Saibian, and it's equal to E1#1#gaggol = E1#1#100#2 in Hyper-E notation.[2] It's also called gaggolthrex by Aarex Tiaokhiao.[3]

Username5243 calls this number toogolplex or toogoltrex, and it's equal to 10[3]10[3]100 in Username5243's Array Notation.[4]

DeepLineMadom calls this number quidoogolplex, and it's equal to 10[5]10[5]100 using DeepLineMadom's Array Notation.[5]

## Computation

The number can be computed as follows:

1. Let N1 be 10.
2. Let N2 be 1010...1010 where there are N1 tens.
3. Let N3 be 1010...1010 where there are N2 tens.
4. Continue in this fashion.
5. Gaggolplex is N(N(100)).

## Etymology

The name of the number is based on suffix -plex and the number gaggol.

## Approximations

Notation Approximation
Up-arrow notation $$10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 100$$ (exact)
Hyper-E notation $$\textrm E1\#1\#100\#2$$ (exact)
Chained arrow notation $$10 \rightarrow (10 \rightarrow 100 \rightarrow 3) \rightarrow 3$$ (exact)
Hyperfactorial array notation $$(102!2)!2$$
Taro's multivariable Ackermann function A(5,A(5,99))
Fast-growing hierarchy $$f_4(f_4(100))$$
Hardy hierarchy $$H_{(\omega^4) 2}(100)$$
Slow-growing hierarchy $$g_{\zeta_{\zeta_0}}(100)$$

## Sources

Jonathan Bowers' googol series

Googol series: googol(plex/duplex/triplex/quadraplex/quinplex) · giggol(plex/duplex) · gaggol(plex/duplex) · geegol(plex) · gigol(plex) · goggol(plex) · gagol(plex)
Boogol series: boogol(plex/duplex/triplex) · biggol(plex/duplex) · baggol(plex) · beegol(plex) · bigol · boggol · bagol
Troogol series: troogol(plex/duplex) · triggol(plex/duplex) · traggol(plex/duplex) · treegol · trigol · troggol · tragol
Quintoogol series: quintoogol(plex) · quintiggol · quintaggol · quinteegol · quintigol · quintagol
Sextoogol series: sextoogol · septoogol · octoogol
Goobol series: goobol(plex) · gibbol · gabbol · geebol · gibol · gobbol · gabol
Boobol series: boobol · bibbol · babbol · beebol · bibol · bobbol · babol
Troobol series: troobol · tribbol · trabbol
Gootrol series: gootrol · gitrol · gatrol · geetrol · gietrol · gotrol · gaitrol
Bootrol series: bootrol · trootrol · quadrootrol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = $$a \uparrow^c b$$ in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.