Is it possible to make in injection

X*X --> P(X)

(*= carthesian product, P(X) is the powerset of X, that is, the set of all subsets from X)

without the choice-axiom?

I tried to construct such an injection but it seems somewhat hard

there's ofcourse an injection X--> P(X) given by x -> {x}

But X*X--> P(X) doesn't work with <x,y> -> {x,y}

U need a way to distuinguish between <x,y> and <y,x> somehow.