Acceptance for Turing Machines is Undecidable, but Recognizable

Here we show that the A_TM problem is undecidable and recognizable, which is asking if there is a decider for whether an arbitrary Turing Machine accepts an arbitrary input. The proof is by contradiction and diagonalization.

What is a Turing Machine? It is a state machine that has a set of states, input, tape alphabet, a start state, exactly one accept state, and exactly one reject state. See https://www.youtube.com/watch?v=j0bIxPqlYLE&ab_channel=EasyTheory for more details.

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