The set of natural numbers

## 1. Summary of theory Tóm

### 1.1. Set N and Set N*

The numbers 0, 1, 2, 3, … are natural numbers. The set of natural numbers denoted N

The set of non-zero natural numbers is denoted by N*.

### 1.2. Order in the set of natural numbers số

1. Of two distinct natural numbers, one is smaller than the other. When the number a is smaller than the number b, we write a < b or b > a

2. Every natural number has a unique successor. Two consecutive natural numbers are less than one unit apart

3. The number 0 is the smallest natural number. There is no greatest natural number.

4. The set of natural numbers has infinitely many elements.

## 2. Illustrated exercise

**Question 1: **Write the natural number immediately after the number 22; thirty first; 49

**Solution guide:**

The next number of a natural number is one more than that number. Therefore:

The next number of 22 is the number: 23

The next number of 31 is the number: 32

The next number of 49 is the number: 50

**Verse 2: **Write the set A of natural numbers by listing the elements:

\(A = \left\{ {x \in N|11 < x < 20} \right\}\)

**Solution guide:**

Set A includes the following elements: 12; 13; 14; 15; 16; 17; 18; 19

**Question 3:** Write the set B of natural numbers that do not exceed 9

**Solution guide:**

Since the set B is a natural number not exceeding 9, so it is the numbers from 1 to 9, we will write it in two ways as follows:

Method 1: \(B = \left\{ {x \in N|0 \le x \le 9} \right\}\)

Method 2: \(B = \left\{ {0;1;2;3;4;5;6;7;8;9} \right\}\)

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Write the natural number immediately after the number 12; 23; 30

**Verse 2:** Write the set A of natural numbers by listing the elements:

\(A = \left\{ {x \in N|3 < x < 11} \right\}\)

**Question 3: **Write the set B of odd natural numbers that do not exceed 15

### 3.2. Multiple choice exercises Bài

**Question 1: **Given the set N = { 2, 4, 6, 8 }, how many elements are there in the set N?

A. 1

B. 2

C. 3

D. 4

**Verse 2: **A is the set of natural numbers less than 5, then A =?

A. A = { 0, 1, 2, 3, 4 }

B. A = { 1, 2, 3, 4 }

C. A = { 0, 1, 2, 3 }

D. A = { 0, 1, 2, 3, 4, 5 }

**Question 3: **Fill in the blanks to get three consecutive natural numbers increasing : 49, …., ….

A. 50;51

B. 51;53

C. 48;47

D. 59;69

**Question 4: **What is the natural number following 29?

A. 29

B. 30

C. 28

D. 31

**Question 5: **B is the set of letters in the word “TAPHOP”, so B =?

A. B = { T, P, H, O, P }

B. B = { T, A, P, H, P }

C. B = { T, A, P, H, O, P }

D. B = { T, A, P, H, O }

**Question 6: **Let the set A be the set of natural numbers less than or equal to 7. Which of the following can represent the set A

A. A = {0; first; 2; 3; 4; 5; 6; 7}

B. A = {0; first; 2; 3; 4; 5; 6}

C. \(A = \left\{ {n \in N|n < 7} \right\}\)

D. \(A = \left\{ {n \in N*|n \le 7} \right\}\)

**Verse 7: **Let the set C be the set of natural numbers greater than 18 and less than 22.

Which of the following is a representation of the set C:

A. C = {18; 19; 20; 21; 22}

B. C = {18;19; 20; 21}

C. C = {n ∈ ℕ | 18 < n < 22}

D. C = {n ∈ ℕ | 18 n ≤ 22}

**Verse 8: **Let E be the set of natural numbers less than 9.

Which of the following can be written to represent the set E:

A. E = { 1; 2; 3; 4; 5; 6; 7; 8; 9}

B. E = {0; first; 2; 3; 4; 5; 6; 7; 8}

C. E = {n ∈ ℕ | n < 9}

D. E = {n ∈ ℕ | n 9}

**Verse 9: **Given the set \(A = \left\{ {n \in N|61 < x < 65} \right\}\)

Choose the correct answer:

A. A = {61, 62, 63, 64}

B. A = {62, 63, 64, 65}

C. A = {62, 63, 64}

D. A = {62, 63, 64; 65}

**Question 10: **Choose the false statements from the following statements

A. \(0 \notin N*\)

B. There exists a number a in N but not in N*

C. There exists a number b that belongs to N* but not to N

D. \(8 \in N\)

## 4. Conclusion

Through this lesson The collection of natural numbers, students need to complete some of the objectives given by the lesson, such as:

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