Here's a demonstration of how the "simple" proof breaks down: http://www.quora.com/Mathematics/Theoretically-speaking-how-can-the-sum-of-all-positive-integers-b

Here's a demonstration of how the "simple" proof breaks down: http://www.quora.com/Mathematics/Theoretically-speaking-how-can-the-sum-of-all-positive-integers-be-1-12 http://www.quora.com/Mathematics/Theoretically-speaking-how-... (via http://kottke.org/14/01/the-sum-of-all-positive-integers http://kottke.org/14/01/the-sum-of-all-positive-integers)