Mathematically, cardinality is a concept describing the size of any set in set theory. Two sets that can establish a one-to-one correspondence between elements are called reciprocal sets. For example, a set of three people and a set of three horses can establish a one-to-one correspondence, which is two equal sets.

According to the equivalence relation, the sets are classified, and all mutually equivalent sets are classified into the same category. In this way, each set is classified into a certain category. Any class to which set A belongs is called the cardinality of set A, and it is denoted as |A| (or cardA). Thus, when A and B belong to the same class, the cardinality of A and B is the same, that is |A|=|B|. When A and B belong to different classes, their cardinality is also different.

Extended data:

Cardinality can compare sizes.

Let the cardinality of A and B be a and β respectively, that is |A|=a and |B|=β. If subsets of A and B are equivalent, the cardinal number of A is not greater than B, and it is marked as a≤β or β≥ A. If A is less than or equal to β, but A is not equal to β (that is, A is not equal to B), it is marked as A < β, or β >. Answer.

In the case of admitting axiom of choice, we can prove the disambiguation theorem of cardinality-the cardinality of any two sets can be compared, that is, there are no sets A and B, so that A cannot be equal to any subset of B, and B cannot be equal to any subset of A. ..