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The gwgoogol is equal to k\(\cdot\)googol using hypermathematics, where k is equal to \(10^{198}\) using normal mathemathics.[1] It can also be defined as \(\underbrace{\text{ggg...ggg}}_{100}\text{oogol}\). In normal mathematics, it is exactly \(\sum^{10^{198}-1}_{i=0}10^{100+101i}=10^{100}\left(\frac{10^{101\cdot10^{198}}-1}{10^{101}-1}\right)\). It is therefore somewhat bigger than \(10^{101\cdot10^{198}-1}\) using normal mathematics.

Approximations

Notation Lower bound Upper bound
Arrow notation \(755\uparrow709\uparrow70\) \((10\uparrow101)\uparrow(10\uparrow198)\)
Down-arrow notation \(148\downarrow\downarrow93\) \(15\downarrow\downarrow171\)
Steinhaus-Moser Notation 99[3][3] 100[3][3]
Copy notation \(10^{100}[10^{198}]\)
H* function H(33H(65)) H(34H(65))
Taro's multivariable Ackermann function A(3,A(3,663)) A(3,A(3,664))
Pound-Star Notation #*((1))*((42))*7 #*((1))*((43))*7
BEAF {755,{709,70}} {{10,101},{10,198}}
Hyper-E notation E[148]92#2 E[15]170#2
Bashicu matrix system (0)(1)[661] (0)(1)[662]
Hyperfactorial array notation (119!)! (120!)!
Fast-growing hierarchy \(f_2(f_2(656))\) \(f_2(f_2(657))\)
Hardy hierarchy \(H_{\omega^22}(656)\) \(H_{\omega^22}(657)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^22}}}(10)\) \(g_{\omega^{\omega^{\omega^22}2}}(10)\)

Sources

  1. A googol is a tiny dot

See also

Numbers from A googol is a tiny dot

Hypermathematics: bigoogol · trigoogol · quadrigoogol · ggoogol · biggoogol · gggoogol · gwgoogol · coogol(plex)
Hyperlicious: wakoogol(plex) · wakamoogol(plex) · wonkapoogol(plex) · ultron
Numbers with a W: woogol · wiggol · waggol · weegol · wigol · woggol · wagol · bwoogol · bwiggol · bwaggol · bweegol · bwigol · bwoggol · bwagol
Primes: Gooprol · Booprol · Trooprol · Quadrooprol
Other: Bentley's Number · Pigol · Egol · Phigol · gongol(plex) · kaboodol(plex) · gaz(illion)