Cardinal number:

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.

Ordinal number:

One of the basic concepts of set theory is the generalization of first-order and second-order used 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.

The difference between cardinal number and ordinal number

1, cardinality and ordinal number are written differently: cardinality is 1, 2, 3, 4 ... ordinal numbers are first, second, third, fourth, etc.

2. 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. Ordinal numbers add another meaning to cardinality.

3. Cardinality and ordinal number have different uses: cardinality can be compared in size and can be operated. For example, let |A|=a and |B|=β, and define a+β = | {(a, 0):A∈A} ∨{(B, 1): b ∈ b} |.

In addition, the product of a and β is defined as |AxB|, and A×B is the cartesian product of A and B; Ordinal number, there are many ways to express ordinal number in Chinese. Usually add "first" before integers, such as: first and second. There are also those that only use cardinality. Such as: five elements: water, fire, wood, gold and earth.