Difference between revisions of "Uncountable"
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=== Proof that <math>\mathbb{R}</math> is uncountable === | === Proof that <math>\mathbb{R}</math> is uncountable === | ||
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| + | We give an indirect proof here. This is one of the most famous indirect proofs and was given by George Cantor. | ||
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| + | Suppose that the set <math>{x \in \mathbb{R}: 0 < x < 1}</math> is countable. | ||
==See Also== | ==See Also== | ||
Revision as of 05:36, 5 November 2006
This article is a stub. Help us out by expanding it.
A set 
is said to be uncountable if there is no injection 
. A well-known example of an uncountable set is the set of real numbers 
.
Proof that 
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 
is countable.
