Gag (often used as a prefix) or Knackered Man is a function defined as \(\mathrm{gag}(n) = A(n,n)\), where \(A(x,y)\) stands for the Ackermann function.[1] Due to Ackermann function's relation with Arrow notation , \(\text{Gag-x} = 2\uparrow^{x-2}(x+3)-3\)
Approximations
Notation | Approximation |
---|---|
Arrow notation | \(2\uparrow^{x-2}(x+3)-3\) |
BEAF | \(\{2,(n-2),(n+3)\}\) |
Bird's array notation | \(\{2,(n-2),(n+3)\}\) |
Fast-growing hierarchy | \(f_\omega(n)\) |
Hardy hierarchy | \(H_{\omega^\omega}(n)\) |
Slow-growing hierarchy | \(g_{\varphi(\omega, 0)}(n)\) |