Most definitions of floating-point
max are badly flawed; this note explains what axioms these functions should have, illustrates the problems with existing definitions, and explores the options for fixing the situation.
max should be symmetric, so it suffices to restrict our attention to one of them. For most of the rest of this document, I'll explain everything using
min. The appropriate modifications to get
max should generally be pretty clear.
The first two axioms capture the meaning of minimum; they will likely seem completely obvious (possible the point of absurdity).