Difference between revisions of "Uncountable"
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A set <math>S</math> is said to be '''uncountable''' if there is no [[injection]] <math>f:S\to\mathbb{Z}</math>. A well-known example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. | A set <math>S</math> is said to be '''uncountable''' if there is no [[injection]] <math>f:S\to\mathbb{Z}</math>. A well-known example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. | ||
| − | + | === Proof that <math>\mathbb{R}</math> is uncountable === | |
==See Also== | ==See Also== | ||
Revision as of 05:22, 5 November 2006
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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 
.
