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Uncountable

Revision as of 05:36, 5 November 2006 by Bubka (talk | contribs) (→‎Proof that <math>\mathbb{R}</math> is uncountable)

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A set $S$ is said to be uncountable if there is no injection $f:S\to\mathbb{Z}$. A well-known example of an uncountable set is the set of real numbers $\mathbb{R}$.

Proof that $\mathbb{R}$ is uncountable

We give an indirect proof here. This is one of the most famous indirect proofs and was given by George Cantor.

Suppose that the set ${x \in \mathbb{R}: 0 < x < 1}$ is countable.

See Also

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