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Throogol-ex-grand tethrathoth is equal to E100#^^#100#(1+E100###100) using Extended Cascading-E Notation.[1] The term was coined by Sbiis Saibian. This number belongs to the tethrathoth regiment.

Approximations[]

Notation Approximation
BEAF \(\{100,\text{throogol}+1,2 (X \uparrow\uparrow X) 2\}\)[2]
Bird's array notation \(\{100,\text{throogol}+1,2 [1 \backslash 2] 2\}\)
\( \approx \{100,\{100,100,100,99\},2 [1 \backslash 2] 2\}\)
Fast-growing hierarchy \(f_{\varepsilon_{0}+1}(\text{throogol})\)
\( \approx f_{\varepsilon_{0}+1}(f_{\omega^2}(100))\)
Hardy hierarchy \(H_{\varepsilon_{0}2}(\text{throogol})\)

Sources[]

  1. Saibian, Sbiis. 4.3.7 Extended Cascading-E Numbers Part IOne to Infinity. Retrieved 2017-01-02.
  2. Using particular notation \(\{a,b (A) 2\} = A\ \&\ a\) with prime b.
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