The definition of natural number is a very simple concept, but it has very important properties. Next, we will introduce the definition, properties and operation of natural numbers.
Definition of natural number
A natural number is an integer starting from 1, which is represented by the symbol 1, 2, 3, 4. Natural numbers can be used for counting, sorting, comparing sizes, etc.
The definition of natural numbers can be proved by induction. First, 1 is a natural number, that is,1∈ n. Secondly, if n is a natural number, then n+ 1 is also a natural number, that is, n+1∈ n. Therefore, the set n of natural numbers is constructed as follows:
N={ 1，2，3，4，}
Properties of natural numbers
Natural numbers have the following properties:
1. Natural numbers are infinite. Even if we take any natural number, there is always another natural number behind it.
2. Natural numbers are unique. For any two natural numbers m and n, if m=n, then m and n are exactly the same.
3. Natural numbers are comparable. For any two natural numbers m and n, we can compare their sizes, that is, mn.
4. The addition and multiplication of natural numbers are closed. That is to say, for any two natural numbers m and n, their sum m+n and product mn are also natural numbers.
Natural number operation
The operations of natural numbers include addition, subtraction, multiplication and division. Among them, addition and multiplication are closed, that is, for any two natural numbers m and n, their sum m+n and product mn are also natural numbers. The law of addition, subtraction, multiplication and division is not necessarily closed, because addition, subtraction, multiplication and division may produce negative numbers or fractions.
1. Addition of natural numbers
The addition of natural numbers refers to the operation of adding two natural numbers. For example:
2+3=5
4+7= 1 1
The addition of natural numbers has the properties of exchange law, association law and distribution law.
2. Multiplication of natural numbers
Natural number multiplication refers to the operation of multiplying two natural numbers. For example:
2×3=6
4×7=28
The multiplication of natural numbers has the properties of commutative law, associative law and distributive law.
3. Natural number subtraction
The subtraction of natural numbers refers to the operation of subtracting another natural number from one natural number. For example:
5-2=3
7-4=3
The subtraction of natural numbers has no properties such as commutative law and associative law.
4. Division of natural numbers
Division of natural numbers refers to the operation of dividing one natural number by another. For example:
6÷2=3
28÷7=4
The division of natural numbers does not have the properties of commutative law and associative law.