Proving R is Bigger Than N Set Elements

  • Context: Graduate 
  • Thread starter Thread starter dextercioby
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
4 replies · 3K views
Messages
13,416
Reaction score
4,226
that the number of elements of [itex]\mathbb{R}[/itex] (seen as a set, obviously) is bigger than the number of elements of [itex]\mathbb{N}[/itex] ...? :bugeye:

Daniel.
 
Physics news on Phys.org
Two sets have the same cardinality iff there exists a bijection between the sets. Cantor showed that there is no bijection between [itex]\mathbb{R}[/itex] and [itex]\mathbb{N}[/itex]. A "[URL 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:
Very nice. I've never seen that proof before.