Googology Wiki
Advertisement
Googology Wiki

View full site to see MathJax equation

Not to be confused with Joycian tetratri.

Joyce's tetratri is equal to \(\text g(2,1,1,4,3,3)\) in Joyce's More Generalized Exponential Notation.[1][2] The value was created by Andre Joyce as a failed attempt to define the Bowersism tetratri, which is much larger. In arrow notation, it is equal to 3^^^^(3^^^3-1 ^'s)^^^^^3. This number is closer to tritriplex.

Approximations[]

Notation Approximation
Bowers' Exploding Array Function {3,3,{3,3,3}-1} (exact)
Hyper-E notation E3##3#2
X-Sequence Hyper-Exponential Notation 3{X}(3{X}3-1)
Fast-growing hierarchy \(f_{\omega}(f_4(3))\)
Hardy hierarchy \(H_{\omega^{\omega}+\omega^4}(3)\)
Slow-growing hierarchy \(g_{\varphi(\zeta_0,0)}(3)\)

Sources[]

Advertisement