Talk:Transfinity

Why it's classified as uncomputable? TBPO 19:25, 12 May 2025 (UTC)

For some Collatz function $f$, it should be possible to construct a function $I_{f}$ such that $I_{f}\left(x,y\right)={\begin{cases}x,&y=0\\I_{f}\left(f\left(x\right),y-1\right),&y\neq 0\end{cases}}$
Assuming that's true, $H_{f}\left(x\right)=\beta \left(I_{f},x\right)$ acts as a sort of halting oracle for iterated $f$ (where halting is defined by reaching 0). $H_{f}$ returns a natural number if iterating eventually halts, and returns $\omega$ otherwise.
I'll have to try constructing Collatz functions and $I_{f}$ later, but I don't see what would stop them from being constructible.–PkmnQ (talk) 23:29, 12 May 2025 (UTC)