>[...] Thus (a-b) is not the same as -(b-a) for IEEE floats!
Nor is x*0 equal to 0 for every x; nor does x == y imply f(x) == f(y) for every x, y, f; nor is addition or multiplication associative. There aren't many identities that do hold of floating point numbers.
Yes, but they DO hold for Rational (I believe). The argument against NaN = 0 :% 0, Inf = 1 :% 0, etc. is that the otherwise valid identies for _Rational_ are disturbed.
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