## INTRODUCTION

__INTRODUCTION:__

The counting numbers 1, 2, 3, 4…… are called** natural numbers**. The smallest natural number is 1, but the largest natural number does not exist.

The collection ‘0’ and all natural numbers is called **whole numbers**. 0 is the smallest whole number. Negatives of counting numbers, i:e. 1, 2, are called **negative numbers.**

The collection of whole number and negative numbers is called **integers.**

The smallest or the greatest integer does not exist. −1, −2, are called negative integers and 1, 2, 3, 4, …. are called **positive integers.**

**0 is neither positive nor negative.**

**On a number line:**

a) A number to the right of the given number is greater than the given number.

b) An integer and its opposite are equidistant from 0 but in opposite directions.

**WHEN WE**

i) Add a positive integer, we move toward** right.**

ii) Add a negative integer, we move toward** left.**

iii) Subtract a positive integer, we move towards** left.**

iv) Subtract a negative integer we move towards** right.**

__Try these:__** (Page 2)**

**A number line representing integers is given below.**

–3 and –2 are marked by E and F respectively.

**Which integers are marked by B, D, H, J, M and O?**

**Solution: **Let us complete the given number line such that integers marked by various alphabets are shown. Therefore

**The integer marked by B = ****6 The integer marked by D = ****4**

**The integer marked by H = ****0 The integer marked by J = 2**

**The integer marked by M = 5 The integer marked by O = 7 **

**2. ****Arrange 7, −****5, 4, 0 and −****4 in ascending order and then mark them on a number line to check your answer.**

**Solution: **Since (i) every positive integer is greater than 0.

(ii) every negative integer is less than 0.

We get –5 < (–4) < 0 < 4 < 7

**The required ascending order is –5, –4, 0, 4, 7**

Since the integer to the right on a number line is greater than that on the left. And the integer on the left is smaller than that on the right.