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The supertet is equal to {4,4,4,4}, {4,4(1)2} or {4,2/2} in BEAF.[1]. It can also be written 4{{{{4}}}}4, or 4 & 4, using the array of operator, or 4 bi-rowexponentiated to 4, or 4 bi-rowtetrated to 2. The term was coined by Jonathan Bowers. It is decently close to a well-known combinatorial constant, Harvey Friedman's n(4).

Supertet can be computed in 3-bracket operator notation using the following process:

  • \(t_1 = 4\)
  • \(t_2 = 4 \lbrace4\lbrace4\lbrace4\rbrace^{3}\rbrace^{3}\rbrace^{3} 4\)
  • \(t_3 = 4 \lbrace4\lbrace4\cdots\lbrace4\rbrace^{3}4\rbrace^{3}\cdots\rbrace^{3}4 \) with \(t_2\) 4's from the center out.
  • \(t_4 = 4 \lbrace4\lbrace4\cdots\lbrace4\rbrace^{3}4\rbrace^{3}\cdots\rbrace^{3}4 \) with \(t_3\) 4's from the center out.
  • etc.
  • Supertet is \(t_{t_{t_{\cdots1}}}\), where there are \(t_{t_{t_{\cdots1}}}\) \(t\)s, where there are \(t_{t_{t_{t_1}}}\) \(t\)s.

Supertet is comparable to \(f_{\omega^2}(4)\) in the fast-growing hierarchy.

File:Supertet.jpg


Etymology Edit

The name of this number is based on the words "super" and "tetra-" (four).

Sources Edit

  1. Template:Citation/CS1
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