To me equality is whatever an = sign represents. shrug
But this reminds me of something amusing. I will never forget how hard it was for me to understand the distinction between isomorphic and naturally isomorphic. You see I thought of "isomorphic" as meaning "the same as". But then how could these two vector spaces be more the same than those two vector spaces? After all they're the same, right?
In C++, = is the operation that invokes the copy constructor. Is that equality? In C++ , == is equality, insofar as equality has meaning in a mutable language.
But this reminds me of something amusing. I will never forget how hard it was for me to understand the distinction between isomorphic and naturally isomorphic. You see I thought of "isomorphic" as meaning "the same as". But then how could these two vector spaces be more the same than those two vector spaces? After all they're the same, right?