Is < binary relation a strict partial order on IEEE doubles?

To me it looks that it is:

• irreflexivity: NaN < NaN == false
• transitivity: if a < b and b < c then a < c (the antecedent is never true for NaNs)
• asymmetry: if a < b then not b < a (again, the antecedent is never true for NaNs)

However, it cannot be extended to non-strict partial ordering <= because there's no (reflexive) equality for doubles (NaN != NaN).

It can be extended, but <= as defined by IEEE isn't that extension.