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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 $$\text{s}(100,100\{12\}1\{12\}1\{12\}1\{12\}1\{1`2\}2)$$
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

1. Using particular notation $$\{a,b (X \uparrow\uparrow X)(X \uparrow\uparrow X)\cdots(X \uparrow\uparrow X) c \#\}$$ for $$\{X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X)\cdots X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) c-1 \#\}$$