Trimentri

Trimentri is equal to \(\{3,3 ((1) 1) 2\} = \{3,3 (0,0,0,1) 2\} = \{3,3 (0,0,3) 2\} = \{3,3 (0,3,2) 2\}\) in BEAF. The term was coined by Jonathan Bowers. It can be thought as:
*3-superdimensional array of 3's
*1-trimensional array of 3's
*"3 tetrated to 3" array of 3's
*"3 pentated to 2" array of 3's.
**This signifies that trimentri is the smallest pentational array that is not degenerate, as trimentri is an X^^X-sized array of 3's, which decomposes into this tetrational array. This is because an X^^X-sized array of 2's degenerate into 4. However, you'll see that most pentational arrays cannot be decomposed into simple tetrational arrays, as the pentational arrays grow so fast so that:
***Consider the array {3, 3, 3([1]1)2}:
****Let an be a function so that:
*****a1 = 3
*****a2 = {3, 3((1)1)2}
*****a3 = {3, trimentri((1)1)2}
*****...
****This array will be equal to aa₃.
**Therefore, the true limit of well-defined BEAF is slightly higher than the a^^b & a-sized arrays.
The array of trimentri is the array which defines trilatri, but with all entries replaced with the entire array twice. So, it has (39)3 = 327 = 7,625,597,484,987 entries.
== Approximations ==
Notation 	Approximation
Bird's Array Notation 	\(\{3,3[1,1,1,2]2\}\)
Cascading-E notation 	\(\textrm E[3]3\#\text{^}\#\text{^}\#\text{^}\#3\)
Fast-growing hierarchy (using CNF's fundamental sequences)	\(f_{\omega^{\omega^{\omega^{\omega}}}}(3)\)
Hardy hierarchy 	\(H_{\omega^{\omega^{\omega^{\omega^{\omega}}}}}(3)\)
Slow-growing hierarchy 	\(g_{\vartheta(\Omega^{\Omega^{\Omega^2\omega}})}(3)\)
== Sources ==
== See also ==
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:Higher array notation
Category:Greek-based name
Category:BEAF
Category:Powers of 3
Category:Double exponentiated polynomial omega level