> Classically, id(x) != id(x) is logically inconsistent.

Equality is domain dependent. For example ∞!=∞ could be justified, as can (0/0)!=(0/0). In the domain of real numbers, equality can be an undecideable problem[1]. I guess the designers of these languages had to choose between tolerable defaults or throwing exceptions. I'm happy with JS doing this:

    % node
    > 1.0/-0
    -Infinity
    > 1.0/0
    Infinity
    > 0/0
    NaN
    > 0/NaN
    NaN
    > 1+NaN
    NaN

[1] https://math.stackexchange.com/questions/143727/determining-...