[gallopingcomp]

1. I would object to the “similarly”, because they are not similar types of statements. And yes, the tautology aspect is the whole point of the axiomatic method (which has limitations that cannot be directly blamed on that premise).

2. You didn’t do the first two. But the symbols now mean different things than their conventional interpretations in number theory.

3. > It's derived from initial assumptions, which is how all math works

It’s exactly how _logic_ works, and is how all math works, but that would only qualify it as (il)logic, and not inherently math. Necessary but not sufficient condition.

(Sorry ;)