Hughal is equal to G(1,7). It is equal to 3↑↑↑↑↑↑↑3 using arrow notation.[1] The term was coined by Aarex Tiaokhiao.

Definition

  1. Let G(0,y) = y
  2. G(x+1,y) = 3↑↑↑...↑↑↑3 with G(x,y) up-arrows
  3. Hughal is equal to G(1,7) = 3↑↑↑...↑↑↑3 with G(0,7) = 7 up-arrows

Approximations

Notation Approximation
Arrow notation \(3\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow3\) (exact)
BEAF \(\{3,3,7\}\) (exact)
Hyper-E notation \(\textrm E[3]1\#1\#1\#1\#1\#\#3\) (exact)
Chained arrow notation \(3\rightarrow3\rightarrow7\) (exact)
Hyperfactorial array notation \(4!6\)
Strong array notation \(s(3,3,7)\) (exact)
Fast-growing hierarchy \(f_8(2)\)
Hardy hierarchy \(H_{\omega^8}(2)\)
Slow-growing hierarchy \(g_{\varphi(6,0)}(3)\)

Sources

  1. Forcal - Aarex's Large Numbers (archived 2016-04-11)
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