Recent content by patfan7452

If a function f: N-->X is surjective , is f^-1(X) (its inverse image) also surjective? If so, why?

Thanks for the replies. Shredder, Why does "f f-1({x}) is the set of natural numbers s.t f(n)=x" clearly partition N? Also, why is the map from X to some subset of N bijective?

Hey all, Can anyone prove this theorem? Let N (natural numbers) ---> X be an onto function. Then X is countable. I've been staring at it for 3 hours and really can't come up with anything. Any help?