# Halting problem confusion

Does the non-solvability of the halting problem mean that no program can tell if an arbitrary program halts, or only that if such a program exists then there is no computable proof that it works?

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Didn't know you were into computers, Jesus... –  The Chaz 2.0 May 31 '12 at 14:33
The first. There is no program such that $\dots$ –  André Nicolas May 31 '12 at 14:33

It means the former: there is no program $e$ that computes the characteristic function of the set $K = \{ i : \text{program } i \text{ halts on input } i\}$. Undecidablity has nothing to do with provable computability, it it just about actual computability.