>>16692642
One way of “understanding” the theorem and some of its proofs is:
>A Turing machines cannot solve the Halting Problem.
>There is a nice way of encoding Turing machines into [math]\mathbb N[/math]
>The Halting problem becomes a yes-or-no question about [math]\mathbb N[/math]
>Therefore a Turing machine cannot always answer these questions
The basic statement about complete and consistent axiom systems falls out of this. The only problem is the proof is longer when you expand all the steps formally, but conceptually I think it’s useful