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Tritetrep is equal to \(f_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}(10)\) using the fast-growing hierarchy.[1] The term was coined by wiki user Denis Maksudov.

It is equal to \(f_{\omega^{\omega^{\omega^{\varepsilon_02}}}}(10)=f_{\varphi_0(\varphi_0(\varphi_0(\varphi_1(0)+\varphi_1(0))))}(10)\) using Veblen function \(\varphi_\alpha(\beta)\).

Etymology Edit

The 3 parts of the name, "tri", "tetr" and "ep", mean 3, tetration and \(\varepsilon_0\) respectively, which form \(\varepsilon_0\uparrow\uparrow3=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}\) when concatenated backwards. So the full name indicates the ordinal index of the number.

Approximations in other notations Edit

Notation Approximation
BEAF \(\{10,10((X \uparrow\uparrow X)^3) 2\}\)[2]
Extended Cascading-E Notation \(E10(\#\text{^^}\#)\text{^}(\#\text{^^}\#)\text{^}(\#\text{^^}\#)10\)
Hardy hierarchy \(H_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}(10)\)
Slow-growing hierarchy \(g_{\vartheta(\varepsilon_{\Omega 2}^{\varepsilon_{\Omega + 1}^{\varepsilon_{\Omega + 1}}})}(10)\)

Sources Edit

  1. My system of number names (FGS) - Traveling To The Infinity
  2. Using particular notation \(\{a,b (A) 2\} = A\ \&\ a\) with prime b.
Numbers by Denis Maksudov
Epsilon series
Epsilon(0)-addition series: Zeraddep · Unaddep · Baddep · Traddep · Quadraddep · Quintaddep · Sextaddep · Septaddep · Octaddep · Nonaddep · Dekaddep · Hektaddep · Kiladdep · Megaddep · Gigaddep · Teraddep · Petaddep · Exaddep · Zettaddep · Yottaddep
Epsilon(0)-multiplication series: Bultep · Trultep · Quadrultep · Quintultep · Sextultep · Septultep · Octultep · Nonultep · Dekultep · Hektultep · Kilultep · Megultep · Gigultep · Terultep · Petultep · Exultep · Zettultep · Yottultep
Epsilon(0)-exponentiation series: Bexep · Trexep · Quadrexep · Quintexep · Sextexep · Septexep · Octexep · Nonexep · Dekexep · Hektexep · Kilexep · Megexep · Gigexep · Terexep · Petexep · Exexep · Zettexep · Yottexep
Epsilon(0)-tetration series: Bitetrep · Tritetrep · Quadritetrep · Quintitetrep · Sextitetrep · Septitetrep · Octitetrep · Nonitetrep · Dekotetrep · Hektotetrep · Kilotetrep · Megotetrep · Gigotetrep · Terotetrep · Petotetrep · Exotetrep · Zettotetrep · Yottotetrep
Epsilon(1)-addition series: Unaddunep · Baddunep · Traddunep · Quadraddunep · Quintaddunep · Sextaddunep · Septaddunep · Octaddunep · Nonaddunep · Dekaddunep · Hektaddunep · Kiladdunep · Megaddunep · Gigaddunep · Teraddunep · Petaddunep · Exaddunep · Zettaddunep · Yottaddunep
Inserted epsilon series: Uninep · Binep · Trinep · Quadrinep · Quintinep · Sextinep · Septinep · Octinep · Noninep · Dekinep · Hektinep · Kilinep · Meginep · Giginep · Terinep · Petinep · Exinep · Zettinep · Yottinep
Inserted eta series
Phi series
Tar series

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