How can one prove

1. Feb 28, 2006

dextercioby

that the number of elements of $\mathbb{R}$ (seen as a set, obviously) is bigger than the number of elements of $\mathbb{N}$ ...?

Daniel.

2. Feb 28, 2006

George Jones

Staff Emeritus
Two sets have the same cardinality iff there exists a bijection between the sets. Cantor showed that there is no bijection between $\mathbb{R}$ and $\mathbb{N}$. A cool proof of this involves a very simple idea - simple once one has seen it, but not until then.

Regards,
George

3. Mar 1, 2006

Daniel.

4. Mar 1, 2006

Palindrom

Very nice. I've never seen that proof before.

5. Mar 1, 2006

Mafer

Wow...that's good!