http://www.brainpickings.org/index.php/2012/08/07/how-big-is-infinity-ted-ed/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+brainpickings%2Frss+%28Brain+Pickings%29
or
http://www.youtube.com/watch?feature=player_embedded&v=UPA3bwVVzGI
Wonderful animation showing how Cantor proved that the infinity of irrational numbers is bigger than the infinity of rational numbers, how you cannot list every fraction, and the description of his Continuum Hypothesis: are there infinities of different sizes between the infinite set of whole numbers and the (larger) infinite set of decimal numbers (this is probably horribly wrong. One of those videos where you think "I understand!" while watching, yet as soon as you try to explain...)
And the most amazing thing:
Gödel proved that you cannot prove that the Continuum Hypothesis is false.
