Hello everyone!

Recently I've noticed that reflexivity was removed from the semantic requirements' note of std::equality_comparable:
This got me wondering whether reflexivity is a semantic requirement of std::equality_comparable or not?

As far as I understand, the intention behind the std::equality_comparable concept is to represent types,
which provide operator == implementing mathematical equality, which is, by definition,
reflexive, symmetric and transitive, so I would say that transitivity should be one of the semantic requirements.

However, when I look at the wording of [concept.equalitycomparable]/2, I'm not so sure:
Let a and b be objects of type T.
T models equality_comparable only if bool(a == b) is true when a is equal to b, and false otherwise. 

Is it valid for a type modelling std::equality_comparable to return false from operator == when a does equal to b,
as long as, that operator == never returns true when a does not equal to b?
In order words, does std::equality_comparable concept permits non-comparable values, such as NaN?

The phrase "(...) and false otherwise." might suggest that. The description, available on cppreference.com,
of semantic requirements of the std::equality_comparable concept explicitly permits non-comparable values:
std::equality_comparable<T> is modeled only if, 
given objects a and b of type T, bool(a == b) is true if and only if a and b are equal.
Together with the requirement that a == b is equality-preserving, 
this implies that == is symmetric and transitive, 
and further that == is reflexive for all objects a that are equal to at least one other object.

Does the wording of the normative rule [concept.equalitycomparable]/2 intentionally permits non-comparable values,
in order to allow floating-point types, such as float and double, to model the std::equality_comparable concept?

Thank you, Mateusz Zych