# equivalence relations

• January 12th 2010, 08:20 AM
koukou8617
equivalence relations
How to describe all the functions which are also equivalence relations

(Happy)
• January 12th 2010, 08:28 AM
Drexel28
Quote:

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

(Happy)

What does that even mean?
• January 12th 2010, 08:30 AM
Plato
Quote:

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

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. $(f,X,X)=\{ (x,x)\in X\times X \}$