uncountable
Definition A set is uncountable if it is not countable^{}. In other words, a set $S$ is uncountable, if there is no subset of $\mathbb{N}$ (the set of natural numbers) with the same cardinality as $S$.
 1.

2.
The real numbers form an uncountable set. The famous proof of this result is based on Cantor’s diagonal argument.
Title  uncountable 

Canonical name  Uncountable 
Date of creation  20130322 11:59:08 
Last modified on  20130322 11:59:08 
Owner  yark (2760) 
Last modified by  yark (2760) 
Numerical id  9 
Author  yark (2760) 
Entry type  Definition 
Classification  msc 03E10 
Synonym  uncountable set 
Related topic  CardinalityOfTheContinuum 