What is the difference between equivalence and equality?

Question

What is the difference between equivalence and equality in C++?

There is a very similar question here. However, this question is tagged with math, while I am interested in the meaning in C++ context.

To see the terms in context: Scott Meyers uses them in an example in this video.

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The video is not available anymore. Probably, this is a video of the same talk. – Swink

Answer 1

On cppreference.com i found the following quote:

For the types that are both EqualityComparable and LessThanComparable, the C++ standard library makes a distinction between equality, which is the value of the expression a == b and equivalence, which is the value of the expression !(a < b) && !(b < a).

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More generally, for each Compare comp you can synthesise an equivalence !comp(a, b) && !comp(b, a). There is only one "equality", but there can be any number of "equivalences" – Extern