1. 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.

2. Ordinal number is one of the basic concepts of set theory, and it is a generalization of the first and second numbers used to express order in daily life. The concept of ordinal number is based on the concept of well-ordered set, which is a special case of partial ordered set and totally ordered set.

Extended data:

In informal usage, cardinality is what is usually called counting. They are the same as natural numbers starting from 0 (that is, 0, 1, 2, ...). The most important thing is what can be formally defined as a finite radix. Infinite cardinality exists only in advanced mathematics and logic.

More formally, nonzero numbers have two purposes: to describe the size of a set or to describe the position of an element in a sequence. For finite sets and sequences, we can easily see that these two concepts are consistent, because we can construct a set with exact size for all numbers describing a position in a sequence.

For example, 3 describes the "c" in the sequence.

The intuition behind the formal definition of cardinality is to construct the concept of relative size of a set without mentioning which members it has. This is easy for finite sets; You can simply calculate the number of members of a set. In order to compare the sizes of larger sets, more subtle concepts must be used.

References:

Baidu encyclopedia base

References:

Baidu encyclopedia ordinal number