Question

why this is the empty set?

Answer 1

The idea is everything is always equal to itself. That is, for any object `x` it is always true that `x = x`. We say equality is reflexive.

So that set is empty because if some 'x` were in it then we would have x both equal and not equal itself, which is a contradiction.

Answer 2

There are no *x* such that *x* ≠ *x*, so the set of all such *x*'s is empty