Pepto-tethrinoogol is equal to \(\{100,100[1\backslash2]1[1\backslash2]1[1\backslash2]1[1\backslash2]1[1\backslash2]2\}\) in Bird's array notation, using the modified Hierarchial Hyper-Nested Array Notation.[1] The term was coined by googology user HaydenTheGoogologist2009.
Approximations[]
| Notation | Approximation |
|---|---|
| Bowers' Exploding Array Function | \(\{100,100 (X \uparrow\uparrow X)(X \uparrow\uparrow X)(X \uparrow\uparrow X)(X \uparrow\uparrow X)(X \uparrow\uparrow X) 2\}\)[note 1] |
| DeepLineMadom's Array Notation | \(100[1\{1/2\}1\{1/2\}1\{1/2\}1\{1/2\}1\{1/2\}2]100\) |
| Extended Cascading-E Notation | \(\text{E}100(\#\text{^^}\#)\text{^}\#5\) |
| Strong array notation | \(\text{s}(100,100\{1`2\}1\{1`2\}1\{1`2\}1\{1`2\}1\{1`2\}2)\) |
| X-Sequence Hyper-Exponential Notation | \(100\{(X\uparrow\uparrow X)^5\}99\) |
| Fast-growing hierarchy | \(f_{\varepsilon_0^5}(100)\) |
| Hardy hierarchy | \(H_{\varepsilon_0^{\varepsilon_0^4} }(100)\) |
| Slow-growing hierarchy | \(g_{\psi_0(\varepsilon_{\Omega2}^4\varepsilon_{\Omega+1})}(100)\) |
Footnotes[]
- ↑ Using particular notation \(\{a,b (X \uparrow\uparrow X)(X \uparrow\uparrow X)\cdots(X \uparrow\uparrow X) c \#\}\) for \(\{X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X)\cdots X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) c-1 \#\}\)
Sources[]
- ↑ Hayden's Big Numbers - My BAN and SAN numbers Retrieved 2023-03-18.