1. ## equivalence relations

How to describe all the functions which are also equivalence relations

2. Originally Posted by koukou8617
How to describe all the functions which are also equivalence relations

What does that even mean?

3. Originally Posted by koukou8617
How to describe all the functions which are also equivalence relations
4. I guess he's thinking of a function as this: $(f,X,X) \subset X\times X$ such that for every $x\in X$ there exists a unique $y\in X$ such that $(x,y)\in (f,X,X)$ from which it follows immediately that if $(f,X,X)$ is to be an equivalence relation then $f\equiv id_X$ (because of reflexivity) ie. $(f,X,X)=\{ (x,x)\in X\times X \}$