Those are all excellent points. And since you ask, I do have another riddle that goes directly to the point you just made. This one is in the form of a proof.

Given that a = b (e.g. 1/2 = 2/4);

1) a^2 = ab
2) a^2 - b^2 = ab - b^2
3) (a + b)(a - b) = b(a - b)
4) (a + b) = b
5) (b + b) = b
6) 2b = b
7) 2 = 1
8) QED?