Quadritetrep

Quadritetrep is equal to \(f_{\varepsilon_0\uparrow\uparrow4}(10)\) using the fast-growing hierarchy.My system of number names (FGS) - Traveling To The Infinity The term was coined by wiki user Denis Maksudov.
It is equal to \(f_{\omega^{\omega^{\omega^{\omega^{\varepsilon_02}}}}}(10)=f_{\varphi_0(\varphi_0(\varphi_0(\varphi_0(\varphi_1(0)+\varphi_1(0)))))}(10)\) using Veblen function \(\varphi_\alpha(\beta)\).
== Etymology ==
The 3 parts of the name, "quadri", "tetr" and "ep", mean 4, tetration and \(\varepsilon_0\) respectively, which form \(\varepsilon_0\uparrow\uparrow4\) when concatenated backwards. So the full name indicates the ordinal index of the FGH.
== Approximations in other notations ==
Notation 	Approximation
BEAF 	\(\{10,10((X \uparrow\uparrow X)^4) 2\}\)Using particular notation \(\{a,b (A) 2\} = A\ \&\ a\) with prime b.
Extended Cascading-E Notation	\(E10(\#\text{^^}\#)\text{^}(\#\text{^^}\#)\text{^}(\#\text{^^}\#)\text{^}(\#\text{^^}\#)10\)
Hardy hierarchy 	\(H_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}(10)\)
Slow-growing hierarchy 	\(g_{\vartheta(\varepsilon_{\Omega 2}^{\varepsilon_{\Omega + 1}^{\varepsilon_{\Omega + 1}^{\varepsilon_{\Omega + 1}}}})}(10)\)
== Sources ==
Category:Numbers
Category:Numbers by Denis Maksudov
Category:10-based FGH numbers
Category:Epsilon level
Category:-ep