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Mathematics - Algebraic Number Theory - Pigeonhole Principle

1a. If X and Y are infinite sets with the same number of elements, show that the following conditions are equivelent for a function f: X-->Y:

(i). f is injective
(ii). f is bijective
(iii) f is surjective

1b. Suppose there are 11 pigeons sitting in some pigeonhole. If there are only 10 pigeonholes prove that there is a hole containing more than one pigeon.

I just dont know where to begin with the proof and how to show this.

Solution Summary

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