What Is a Whole Number?

An integer is a collection of positive, zero, and negative integers.

We divide the integers into three categories with 0 as the limit:

1. A positive integer, that is, an integer greater than 0, such as 1, 2, 3 ...

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2. Zero, which is neither a positive nor a negative integer, is a number between positive and negative integers.

3.

A number that is divisible by 2 in an integer is called

The following table shows the basic properties of integer addition and multiplication. (Ie holds for any integers a, b and c)

nature	addition	multiplication
Closed	Is an integer	Is an integer
Binding law
Exchange law
Existence unit
Existence inverse		In the integer set, only 1 or -1 has integer inverses for multiplication
Distribution law

1 is the divisor of any number, ie for any integer , There is always 1 |

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0 is a multiple of any non-zero number,

, Is an integer, then

| 0.

1. If the last digit of a number is a single even number, the number is divisible by 2.

2. If the sum of a number is divisible by 3, the integer is divisible by 3.

3. If the last two digits of a number are divisible by 4, then the number is divisible by 4.

4. If the last digit of a number is 0 or 5, the number is divisible by 5.

5. If a number is divisible by 2 and 3, then the number is divisible by 6.

6. If the single digit of a number is truncated, then subtract the double digit from the remaining digits. If the difference is a multiple of 7, the original number can be divided by 7. If the difference is too large or it is not easy to see whether the multiple of 7 is in the mental arithmetic, you need to continue the process of "censoring, double, subtraction, and difference checking" until you can clearly judge. For example, the process of determining whether 133 is a multiple of 7 is as follows:

, So 133 is a multiple of 7; for example, the process of determining whether 6139 is a multiple of 7 is as follows:

,

, So 6139 is a multiple of 7, and so on.

7. If the unfinished three digits of a number are divisible by 8, then the number is divisible by 8.

8. If the sum of a number is divisible by 9, then the integer is divisible by 9.

9. If the last digit of a number is 0, the number is divisible by 10.

10. If the difference between the sum of the odd digits and the sum of the even digits of a number is divisible by 11, then the number is divisible by 11. The multiple test of 11 can also be used in the above inspection 7

1.

Why use

What about an integer set? This involves the contribution of a German female mathematician to ring theory, her name is Knott.

In 1920, she had introduced the concepts of "left mold" and "right mold". The Ideal Theory of the Whole Ring, written in 1921, is a milestone in the development of exchange algebra. Among them, when Knott introduced the concept of the integer ring (the integer set itself is also a number ring), she was German, and the integer in German was called Zahlen, so she remembered the integer ring as Z. use

Indicated.