Googoldubang or googolbangbang is equal to \((10^{100}!)!\).[1]

Aarex Tiaokhiao calls it googolbibang and googolbarxi.[2] It is also the tetorial of googol, or 10100!2 in Nested Factorial Notation.[3]

Etymology

The name "googolbangbang" can be separated into 3 parts, "googol" and 2 "-bang"s, where the suffix "-bang" means factorial operation, so 2 "-bang"s means factorial operation applying 2 times.

Approximations

Notation Lower bound Upper bound
Arrow notation \(10 \uparrow 10 \uparrow 10 \uparrow 101\) \(10 \uparrow 10 \uparrow 10 \uparrow 102\)
Chained arrow notation \(10 \rightarrow (10 \rightarrow (10 \rightarrow 101))\) \(10 \rightarrow (10 \rightarrow (10 \rightarrow 102))\)
Hyper-E notation \(E101\#3\) \(E102\#3\)
Hyperfactorial array notation (10100!)!
H* function H(H(H(33)))) H(H(H(34))))
BEAF & Bird's array notation \(\{10,\{10,\{10,101\}\}\}\) \(\{10,\{10,\{10,102\}\}\}\)
Fast-growing hierarchy \(f_2^{3}(332)\) \(f_2^{3}(333)\)
Hardy hierarchy \(H_{\omega^23}(332)\) \(H_{\omega^23}(333)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^{\omega^2}+1}}}(10)\) \(g_{\omega^{\omega^{\omega^{\omega^2}+2}}}(10)\)

Sources

See also

Googol plex bang stack numbers

0-stack series: googol · googolplex · googolbang · googolplexplex · googolplexbang · googolbangplex · googolbangbang · googolplexplexplex · googolplexplexbang · googolplexbangplex · googolplexbangbang · googolbangplexplex · googolbangplexbang · googolbangbangplex · googolbangbangbang
1-stack series: googolstack · googolstackplex · googolstackbang · googolstackplexplex · googolstackplexbang · googolstackbangplex · googolstackbangbang · googolplexstack · googolplexstackplex · googolplexstackbang · googolbangstack · googolbangstackplex · googolbangstackbang · googolplexplexstack · googolplexbangstack · googolbangplexstack · googolbangbangstack
2-stack series: googolstackstack · googolstackstackplex · googolstackstackbang · googolstackplexstack · googolstackbangstack · googolplexstackstack · googolbangstackstack
3-stack series: googolstackstackstack

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