Tritet

The tritet is equal to \( \lbrace 4,4,4 \rbrace = 4 \lbrace4\rbrace 4 = 4\uparrow\uparrow\uparrow\uparrow4\) (4 hexated to 4) in BEAF. The term was coined by Jonathan Bowers. This is the fourth Ackermann number.
Unlike with Tritet Jr., it's impossible to simplify the tritet using the laws of algebra since it's simply way too large.
Googology Wiki user Hyp cos calls this number a trientet, and it's equal to s(4,4,4), s(4,2,5), s(4,4,1,2), s(4,1,1,3), or s(4,1,1,1,2) in strong array notation. Numbers from linear array notation | Steps Toward Infinity!
 coined crahal for this number, and it's equal to \([4,4,4]\) in Graham Array Notation, as well as \(gc(1)\) in the Graham-Conway function.
== Computation ==
Tritet can be computed in the following process:
* \(a_1 = 4\)
* \(a_2 = 4 \uparrow\uparrow 4 = 4 \uparrow\uparrow\uparrow 2\) (this is tritet Jr.)
* \(a_3 = 4 \uparrow\uparrow a_2 = 4 \uparrow\uparrow\uparrow 3\)
* \(a_4 = 4 \uparrow\uparrow a_3 = 4 \uparrow\uparrow\uparrow 4\)
* etc.
* Tritet is equal to \(a_{a_{a_4}}\).
== Etymology ==
The name of this number is based on tri- (three) and tetra- (four), meaning that there are 3 4's in the array.
==Approximations==
==Sources==
==See also==
*Tritet Jr.
* Tritri
*Ackermann Number
ja:トリテット
zh:特利德特
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:Up-arrow notation level
Category:3 entry linear
Category:Greek-based name
Category:BEAF
Category:Powers of 2