An equivalence relation $a \sim b$ is a binary relation which is symmetric, transitive, and reflexive.
What if I give up on reflexiveness?
I mean, in the set where the binary operation $\sim$ is defined, there's at least one element $a$ such that $a \nsim a$ (and at least one element $b$ for which $b \sim b$, because I'm not talking of an irreflexive relation).
Does such a relation have a name in mathematics?
I'm not asking for examples of such a relation