NaN is a float

Note that NaN is a float:

?- X is nan, float(X).
X = 1.5NaN.

But it incomparable, i.e. not anywhere on the (pseudo) real line:

?- X is nan, float(X), \+ (X < 0), \+ (X > 0), \+ (X =:= 0).
X = 1.5NaN.

Arithmetic comparison between NaN also fails, but unification succeeds

?- X is nan, Y is nan, X = Y.
X = Y, Y = 1.5NaN.

?- X is nan, Y is nan, X =:= Y.
false.