When was the theory of binary relations developed?

Question

I'm interested in the history of mathematics and can't find anything in my books about when binary relations, equivalence relations and equivalence classes were formulated. Was it at the turn 20th century when the foundations and the logical basis of mathematics were the focus of attention? Am I right that they came after functions?

Answer 1

At least a decade before Russell-Whitehead, the notion of an equivalence relation was introduced (either by Dedekind, Peano, or one of their contemporaries, I will have to check my sources). This development made it possible to reformulate Cantor's construction of the reals as "equivalence classes of Cauchy sequences of rationals". Cantor himself did not formulate it this way since he did not have the notion of a "binary relation that's reflexive, symmetric, and transitive".