Explodotetration

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Explodotetration refers to the binary function \(a\ \{\{\{4\}\}\}\ b = \{a,b,4,3\} = \underbrace{a \{\{\{3\}\}\} a \{\{\{3\}\}\} \ldots \{\{\{3\}\}\} a \{\{\{3\}\}\} a}_{\text{b a's}}\), using BEAF.

In the fast-growing hierarchy, \(f_{\omega2+4}(n)\) approximately corresponds to explodotetrational growth rate.

See also

Hyper operators

Main article: hyper operator

Hyper-operators: successor · addition · multiplication · exponentiation · tetration · pentation · hexation · heptation · octation · enneation · decation (un/doe/tre) · vigintation (doe) · trigintation · centation (tri) · docentation · myriation · circulation
Bowers' extensions: expansion · multiexpansion · powerexpansion · expandotetration · explosion (multi/power/tetra) · detonation · pentonation
Saibian's extensions: hexonation · heptonation · octonation · ennonation · deconation
Tiaokhiao's extensions: megotion (multi/power/tetra) · megoexpansion (multi/power/tetra) · megoexplosion · megodetonation · gigotion (expand/explod/deto) · terotion · more...