How to describe all the functions which are also equivalence relations
I guess he's thinking of a function as this: $\displaystyle (f,X,X) \subset X\times X$ such that for every $\displaystyle x\in X$ there exists a unique $\displaystyle y\in X$ such that $\displaystyle (x,y)\in (f,X,X)$ from which it follows immediately that if $\displaystyle (f,X,X)$ is to be an equivalence relation then $\displaystyle f\equiv id_X$ (because of reflexivity) ie. $\displaystyle (f,X,X)=\{ (x,x)\in X\times X \}$