Supertet

Supertet is equal to {4,4,4,4}, {4,4(1)2} or {4,2/2} in BEAF.. It can also be written 4{{{{4}}}}4, or 4 & 4, using the array of operator. The term was coined by Jonathan Bowers. It is decently close to a well-known combinatorial constant, Harvey Friedman's n(4). It is comparable to Sbiis Saibian's grinningoltesla-tetrexitetris.
Supertet can be computed in 3-bracket operator notation using the following process:
* \(t_1 = 4\)
* \(t_2 = 4\{\{\{4\{\{\{4\{\{\{4\}\}\}4\}\}\}4\}\}\}4\)
* \(t_3 = 4\{\{\{4\{\{\{4\cdots\{\{\{4\}\}\}4\}\}\}\cdots\}\}\}4 \) with \(t_2\) 4's from the center out.
* \(t_4 = 4\{\{\{4\{\{\{4\cdots\{\{\{4\}\}\}4\}\}\}\cdots\}\}\}4 \) 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.
== Etymology ==
The name of this number is based on the words "super" and "tetra-" (four).
== Approximations ==
== Sources ==
== See also ==
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:4 entry linear
Category:Greek-based name
Category:BEAF
Category:Powers of 2
Category:Linear omega level