I understand the point perfectly. However, if I have a NaN which is captured in a lexical variable (perhaps the result of a division by zero, as you note) then in fact I do have a particular infinity: whatever object is inside that darned variable! If I do another division by zero, then sure, hit me with a different NaN which doesn't compare equal to the first one I got. But don't make my variable not equal to itself.
Normal division by zero gives you Infinity. To get NaN, you have to do something as numerically confounding as divide zero by zero, which isn't any infinity, because the numerator is zero, and which isn't zero or any finite number, because the denominator is zero.
