And here's a great book that explains it to children: http://www.amazon.com/The-Cat-Numberland-Ivar-Ekeland/dp/081...

If you're looking for math books for kids, I highly recommend "The Cat in Numberland". It's an illustrated story that touches upon the different kinds of infinities, and even describes Cantor's diagonalization argument in a very friendly, intuitive way. Most adults would also benefit from reading this book.

It's out of print, but might be found at your local library or bought used on Amazon (http://www.amazon.com/The-Cat-Numberland-Ivar-Ekeland/dp/081...).