| − | A '''bijection''' is a [[injectivity|one-to-one]], [[surjectivity|onto]] [[mapping]] between two [[set]]s. 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. | + | A '''bijection''' is a [[injectivity|one-to-one]], [[surjectivity|onto]] [[mapping]] between two [[set]]s. In other words, a bijection between sets A and B is a mapping such that every element in set A is mapped to a distinct element in set B, and every element in set B has a distinct element in the set 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. | | If there is a bijection between two sets, then we say that they have the same [[cardinality]], or size. |