Turing machine halting problem

Question

Hi,

I have a question about turing machines and halting problem.

Suppose that we have Atm = {(M,w) where M is a turing machine and w is an input} and
HALTtm = {(M,w) where M is a turing machine halts with an input w}

I want to prove that HALTtm <=m Atm

I've tried some methods but I think they're far from the solution. Anyone can give some clues ??

Answer 1

Well, observe that for all (M,w) in HALTtm, it must be that (M,w) is in Atm. Then show there exists some (M',w') which is a member of Atm but which does not halt, and so is not in HALTtm.