Proving R is Bigger Than N Set Elements

[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.

 

[George Jones]

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

Regards,
George

 

[dextercioby]

Thankyou for the reply.

Daniel.

 

[Palindrom]

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

 

[Mafer]

Wow...that's good!