29 Jun
2014
29 Jun
'14
7:05 p.m.
Is x == x being false really any more surprising than x + 1 == x being true?
Yes, a lot more. Equality is a symmetric relation. So "x equals x" is true for every x. A logic/language in which that is not true is unsound. x + 1 == x is just an equation. Coming up with a theory where it holds is straightforward. For example, addition followed by the "fractional part" operation, on the set [0,1].