Petinphi

Petinphi is equal to \(f_{\beta[10^{15}]}(10)\) using the fast-growing hierarchy,My system of number names (FGS) - Traveling To The Infinity where \(\beta[n]\) is defined as:
*\(\beta[0] = 0\)
*\(\beta[\alpha + 1] = \varphi(\beta[\alpha],0)\)
The term was coined by wiki user Denis Maksudov.
== Etymology ==
The 3 parts of the name, "peto", "in" and "phi", mean \(10^{15}\), the "in-" operation and \(\varphi\) function respectively, which form \(\beta[10^{15}]\) (i.e. \(10^{15}\) more insertions of \(\varphi\)) when concatenated backwards. So the full name indicates the ordinal index of the FGH.
== Sources ==
Category:Numbers
Category:Numbers by Denis Maksudov
Category:10-based FGH numbers
Category:Bachmann's collapsing level
Category:-phi