Mathematically, radix is also called radix, which refers to a concept in set theory and describes the number of elements contained in any set. 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 corresponding relationship, 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. The class to which any set A belongs is called the cardinality of set A, and it is recorded as (or | 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. If the cardinality of a single element set is recorded as 1, the cardinality of a set of two elements is recorded as 2, and so on, then the cardinality of any finite set is consistent with the natural number in the usual sense. The cardinality of an empty set is also recorded as σ. Therefore, the cardinality of a finite set is also a "number" under the traditional concept. But for infinite sets, the traditional concept has no number, and according to the cardinality concept, infinite sets also have cardinality. For example, any countable set (also called countable set) has the same cardinality as the natural number set n, that is, all countable sets are equal cardinality sets. Not only that, but also it can be proved that the cardinality of real number set R is different from countable set. So the cardinality of a set is a generalization of the concept of number. Cardinality can compare sizes. Let the cardinality of A and B be a and β respectively, that is | A | = A and | B |B|=β. If subsets of A and B are equivalent, then the cardinal number of A is not greater than that of 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), then the cardinal number of A is smaller than that of B, and it is marked as A A. In the case of admitting zermelo and axiom of choice, we can prove the cardinal number triad theorem-the cardinality of any two sets can be. So that A can't be equal to any subset of B, and B can't be equal to any subset of A, and the cardinality can be calculated as | a | = a, | A | = β, and A∩B is an empty set, which is defined as the sum of A and β = a+β. Let | a | = a, | b |B|=β, A×B is the product set of a and b, defined as the product of a and β, and recorded as = =a β.