Nit picking, but floating point is commutative either.
1 + NaN == NaN
Nan + 1 == NaN
Nan != Nan
(NaN is defined as not being equal to itself) 1 + NaN == NaN
Nan + 1 == NaN
Nan != Nan
(NaN is defined as not being equal to itself)NaN is a strange thing anyways, for example you cannot invert it so that NaN+(-NaN)=0