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Created short definition of "bijection" with two examples.
A '''Bijection''' is a one to one, onto mapping between two sets. In other words, a bijection between sets A and B is a mapping such that every element in the A is mapped to a distinct element in B, and every element in the B has a distinct element in the A mapped to it. For example, one bijection between the sets {A, B, C} and {1, 2, 3}, maps: A to 1, B to 2, and 3 to C.
If there is a bijection between two sets, then we say that they have the same [[cardinality]], or size.
Bijections between [[infinite]] sets are particularly interesting, as they produce some counterintuitive results. For instance, there is a bijection between the integers and the even integers that maps every integer x to the even integer 2x. Notice that this satisfies the definition of bijection, which then implies that the integers and the even integers have the same size.
[[Category:Set Theory]]
If there is a bijection between two sets, then we say that they have the same [[cardinality]], or size.
Bijections between [[infinite]] sets are particularly interesting, as they produce some counterintuitive results. For instance, there is a bijection between the integers and the even integers that maps every integer x to the even integer 2x. Notice that this satisfies the definition of bijection, which then implies that the integers and the even integers have the same size.
[[Category:Set Theory]]