Proof

[Napoleon42]

1. The problem statement, all variables and given/known data

"A is a countable set and f: A --> B is A onto B, proove B is countable.


help anyone? :-)

[jhicks]

Consider what you are given in words. If the mapping f: A->B is onto, this implies that every element b of B has a corresponding a such that f(a)=b, so f(A) completely spans B. What does this imply about the size of A relative to B?

[Dick]

A can be put into 1-1 correspondence with the natural numbers, N. So every element of B can be assigned to a natural number via f. So B can be put into 1-1 correspondence with a subset of N. Is a subset of N countable?