An easily understood proof of Cantor’s Theorem: http://www.mathacademy.com/pr/prime/articles/cantor_theorem/...

"Take a minute to ponder what this means. Cantor’s Theorem shows that given any set, there is another set which is 'larger' in the special sense of being a bigger kind of infinity. Hence, there can be no 'largest infinity' either! The kinds of infinity are therefore 'infinite!"