I like this justifiation of NaN != NaN; it emphasizes that NaN has representional intent, more than just some bit pattern.

We take for granted that (except for things like x86 extended precision registers) floating point basically works the same everywhere, which was the huge victory of IEEE 754. It easy to lose sight of that huge win, and to be ungrateful, when one's first introduction to IEEE 754 are details like NaN!=NaN.