Difference between revisions of "Cardinality"
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| − | Cardinality is a measure of the size of a set. For finite sets, its cardinality is simply the number of elements in it. | + | Cardinality is a measure of the size of a [[set theory|set]]. For [[finite]] sets, its cardinality is simply the number of elements in it. In general, two sets have the same cardinality if there is a [[bijection]] between them. That is, the elements of one set can be put into one-to-one correspondence with those of the other. |
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| + | For example, the set of even numbers, and the set of all multiples of 3 is the same, as they can be put into one-to-one correspondence as follows: | ||
| + | 2:3,4:6,6:9,8:12,10:15,..2n:3n... | ||
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| + | Both sets are [[countable]], as they have the same cardinality as the set of [[natural number]]s (0,1,2...). | ||
[[category: set theory]] | [[category: set theory]] | ||
Revision as of 00:01, August 19, 2007
Cardinality is a measure of the size of a set. For finite sets, its cardinality is simply the number of elements in it. In general, two sets have the same cardinality if there is a bijection between them. That is, the elements of one set can be put into one-to-one correspondence with those of the other.
For example, the set of even numbers, and the set of all multiples of 3 is the same, as they can be put into one-to-one correspondence as follows: 2:3,4:6,6:9,8:12,10:15,..2n:3n...
Both sets are countable, as they have the same cardinality as the set of natural numbers (0,1,2...).