Exactly. So your claim that: > So you can remove the ones that do not halt by inspecting them one by one and developing a specific algorithm for each one that

Exactly. So your claim that: > So you can remove the ones that do not halt by inspecting them one by one and developing a specific algorithm for each one that determines if it halts or not. Is impossible. You can’t, in general, inspect Turing machines one-by-one to determine if they halt.