Sure, but it makes sense, doesn't it? Even `inf-inf == NaN` and `inf/inf == NaN`, which is true in calculus: limits like these are undefined, unless you use l'Hôpital's rule or something. (I know NaN isn't equal to itself, it's just for illustration purposes) But then again, you usually don't want these popping up in your code.

In practice, though, I can't recall any HPC codes that want to use IEEE-754 infinities as valid data.

A significant chunk of floating point bitspace is dedicated to NaNs to represent explicitly invalid data (mostly I suppose to reduce the need for branches and tests in HPC) and NaNs even break the reflexivity of equality in many languages compared to them negative 0 and positive/negative infinity are perfectly valid