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The tethraduli-thraelgathor is equal to E100(#^^#)^(#^^#*#^###)100 in Extended Cascading-E Notation.[1] The term was coined by Sbiis Saibian.

Etymology

The name of this number is based on the number "tethrathraelgathor" and the Latin prefix "duo-", meaning 2.

Approximations in other notations

Notation Approximation
BEAF $$\{100,100((X \uparrow\uparrow X)^2*X^{X^3}) 2\}$$[2]
Bird's array notation $$\{100,100 [1,1,1,2[1 \backslash 2]2 \backslash 2] 2\}$$
Hyperfactorial array notation $$100![1,[1,[1,1,4],2,1,2],[1],1,2]$$
Fast-growing hierarchy $$f_{\varepsilon_0^{\varepsilon_0\omega^{\omega^3}}}(100)$$
Hardy hierarchy $$H_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0\omega^{\omega^3}}}}(100)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega2}^{\varepsilon_{\Omega 2}\Omega^{\Omega^2\omega}})}(100)$$

Sources

1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2016-02-23.
2. Using particular notation $$\{a,b (A) 2\} = A\ \&\ a$$ with prime b.