# What Have We Discussed ?

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1.The numbers 1, 2, 3,... which we use for counting are known as

2. If you **add 1** to a natural number, we get its **subtract 1** from a natural number, you get its

3. Every natural number has a **except 1** has a

4. If we **add the number zero** to the collection of **natural numbers,** we get the collection of

5. Every whole number has a **except zero** has a

6. All natural numbers are

7. We take a line, mark a point on it and label it 0. We then mark out points to the right of 0, at equal intervals. Label them as 1, 2, 3,.... Thus, we have a number line with the whole numbers represented on it. We can easily perform the number operations of **addition,** **subtraction** and **multiplication** on the **number line.**

8. Addition corresponds to moving to the right on the number line, whereas subtraction corresponds to moving to the left. **Multiplication** corresponds to **making jumps of equal distance** **starting from zero.**

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## Properties of Whole numbers

Property | Operations | |||
---|---|---|---|---|

Name | Addition | Subtraction | Multiplication | Division |

Closure | a+εb w | a-b∈/w | axbεw | a÷b∈/w |

Commutative | a+b =b+a | a-b≠ b-a | axb=bxa | a÷b≠b÷a |

Assosiative | a+(b+c)=(a+b)+c | (a-b)-c≠a-(b-c) | (axb)xc=axbxc | (a÷b)÷c≠a÷(b÷c) |

Distributive | ax(b+c)=ab+ac | ax(b-c)=ab-ac | Not applicable | Not applicable |

Identity | a+0=a | a-0=a | ax1=a | a÷1=a |