What is a natural number?

Natural number refers to the number used to measure the number of things or to indicate the order of things. That is, the number 0, 1, 2, 3, 4 represents the number. Natural numbers start from 0, one by one, forming an infinite group. Natural numbers are ordered and infinite.

Usually you can see all natural numbers everywhere, so how to distinguish the range of natural numbers, including which numbers? Today, let's talk about what is a natural number.

The number 0 1 representing the number of objects is called a natural number. Natural numbers start from 0, 0, 1, 2, 3, 4, ... one after another, forming an infinite group. Natural numbers are ordered and infinite, and can be divided into even and odd numbers, composite numbers and prime numbers.

Natural numbers are used to measure the number of things or to indicate the order of things, that is, the numbers represented by 0, 1, 2, 3 and 4. ...

Natural number set is a set of all non-negative integers, usually represented by n, and there are infinitely many natural numbers. (Note: Integers include natural numbers, so natural numbers must be integers and non-negative integers. )

There are addition and multiplication operations in the natural number set. The result of addition or multiplication of two natural numbers is still a natural number, and subtraction or division is also possible, but the result of subtraction and division is not necessarily a natural number, so subtraction and phase Divison are not always effective in the set of natural numbers. Natural numbers are the most basic of all numbers that people know. In order to make the number system have a strict logical basis, mathematicians in the19th century established two equivalent theories of natural numbers: ordinal number theory and cardinal number theory, which made the concept, operation and related properties of natural numbers strictly discussed.

Natural number set n is a set that satisfies the following conditions.

① There is an element in n, which is recorded as 1.

② Every element in n can find an element in n as its successor.

③ 1 is the successor of 0. ④0 is not the successor of any element.

⑤ Different elements have different successors.

⑥ (inductive axiom) Any subset m of n, if 1∈M, and as long as X is in M, it can be deduced that the successor of X is also in M, then M = N. ..

Cardinality theory defines natural numbers as the cardinality of finite sets. This theory puts forward that two finite sets that can establish one-to-one correspondence between elements have the same quantitative characteristics, which are called cardinality. In this way, all the single element sets {x}, {y}, {a}, {b} and so on have the same cardinality, which is recorded as 1. Similarly, whenever two fingers can establish a one-to-one set, their cardinality is the same, recorded as 2, and so on. The addition and multiplication of natural numbers can be defined by ordinal number or cardinal number theory, and the operations under the two theories are consistent.

Natural numbers play a great role in daily life, and people use them widely. Natural numbers are the earliest numbers in human history, which are widely used in counting and measurement. People often use natural numbers to mark or sort things, such as bus routes, house numbers, postal codes, etc.

Natural numbers are integers (including positive integers and zeros), but not all integers are natural numbers. For example,-1 -2 -3 ... is an integer rather than a natural number. Natural numbers are infinite.

The set of all nonnegative integers is called the nonnegative integer set, that is, the natural number set.

When counting objects, the number of 1.2.3.4.5.6.7.8.9 is called a natural number. Natural numbers have two meanings: quantity and order, which are divided into cardinal number and ordinal number.

Basic unit: Counting unit: one, ten, one hundred, one thousand, ten thousand, one hundred thousand. ......

In short, a natural number is an integer greater than or equal to 0. Of course, negative numbers, decimals and fractions are not included.

05 natural number classification

According to whether it is even, it can be divided into odd and even numbers.

1, odd number: Numbers that are not divisible by 2 are called odd numbers.

2. Even number: The number divisible by 2 is called even number. That is to say, except odd numbers, they are all even numbers.

Note: 0 is an even number. In 2002, the International Mathematical Association stipulated that zero is an even number. In 2004, China also stipulated that zero is an even number. Even numbers can be divisible by 2, and so can 0, but numbers are still 0.

According to the number of factors, it can be divided into prime number, composite number, 1 and 0.

1, prime number: only 1 and its own natural number are called prime numbers. Also known as prime numbers.

2. Composite number: a natural number with other factors besides 1, which is itself called a composite number.

3. 1 only 1 factor. It is neither a prime number nor a composite number.

4, of course, 0 can't calculate the factor, just like 1, which is neither a prime number nor a composite number.

Note: This is a factor, not a divisor.