Cardinality

In mathematics, the cardinality of a set means the number of its elements. For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3. The cardinality of a set A can also be represented as ${\displaystyle |A|}$.^[1][2]

Two sets have the same (or equal) cardinality if and only if they have the same number of elements, which is the another way of saying that there is a 1-to-1 correspondence between the two sets.^[3] The cardinality of the set A is less than or equal to the cardinality of set B if and only if there is an injective function from A to B. The cardinality of the set B is greater than or equal to the cardinality of set A if and only if there is an injective function from A to B.

The cardinality of a set is only one way of giving a number to the size of a set. The concept of measure is yet another way.

1. ↑ "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-08-23.
2. ↑ "Cardinality | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-23.
3. ↑ "Infinite Sets and Cardinality". Mathematics LibreTexts. 2019-12-05. Retrieved 2020-08-23.