Trexep

Trexep is equal to \(f_{\varepsilon_0^3}(10)\) 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 \(f_{\omega^{\varepsilon_03}}(10)=f_{\varphi_0(\varphi_1(0)\cdot 3)}(10)\) using the Veblen function \(\varphi_\alpha(\beta)\).
== Etymology ==
The 3 parts of the name, "tri", "ex" and "ep", mean 3, exponentiation and \(\varepsilon_0\) respectively, which form \(\varepsilon_0^3\) when concatenated backwards. So the full name indicates the ordinal index of the FGH.
== Approximations in other notations ==
Notation 	Approximation
BEAF 	\(\{10,10 (X \uparrow\uparrow X)(X \uparrow\uparrow X)(X \uparrow\uparrow X) 2\}\)Using particular notation \(\{a,b (X \uparrow\uparrow X)(X \uparrow\uparrow X)\cdots(X \uparrow\uparrow X) c \#\}\) for \(\{X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X)\cdots X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) c-1 \#\}\)
Bird's array notation 	\(\{10,10 [1 \backslash 2] 1 [1 \backslash 2] 1 [1 \backslash 2] 2\}\)
Hyperfactorial array notation	\(10![1,1,3,1,2]\)
Extended Cascading-E Notation	\(E10 \# \text{^^} \#*\#\text{^^}\#*\#\text{^^}\#10\)
Hardy hierarchy 	\(H_{\varepsilon_0^{\varepsilon_0^2}}(10)\)
Slow-growing hierarchy 	\(g_{\vartheta(\varepsilon_{\Omega2}^2\varepsilon_{\Omega+1})}(10)\)
== Sources ==
Category:Numbers
Category:Numbers by Denis Maksudov
Category:10-based FGH numbers
Category:Epsilon level
Category:-ep