The Pigeonhole Principle

The Pigeonhole Principle is a counting argument method of mathematical proof.  It says that if you have more items to distribute than pigeonholes to put them into then at least one of the pigeonholes must contain more than one item.  This simple principle becomes interesting when you extend it to countably infinite sets, e.g. the natural numbers.  See: http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel