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

Gaggolplex 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]

## 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 · quintoggol · quintagol · (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