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 | \(g_{\varphi(\omega, 0)}(n)\) |
