# 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 "[URL [Broken] proof[/URL] of this involves a very simple idea - simple once one has seen it, but not until then.

Regards,
George

Last edited by a moderator: May 2, 2017
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!