Content deleted Content added
No edit summary Tag: Reverted |
No edit summary Tag: Reverted |
||
Line 8:
For [[finite set]]s, Cantor's theorem can be seen to be true by simple [[enumeration]] of the number of subsets. Counting the [[empty set]] as a subset, a set with <math>n</math> elements has a total of <math>2^n</math> subsets, and the theorem holds because <math>2^n > n</math> for all [[non-negative integers]].
<b> 2^n can be seen with (n choose 0) + (n choose 1) ... or just turning each thing on and off <b>
Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for [[infinite set|infinite]] sets also. As a consequence, the cardinality of the [[real number]]s, which is the same as that of the power set of the [[integer]]s, is strictly larger than the cardinality of the integers; see [[Cardinality of the continuum]] for details.
| |||