Ordering Of Integers

 

An integer on a number line is always greater than every integer on its left. Thus, 5 is greater than 4. 

5>4, 4>3, 3>2, 2 > 1, 1 > 0, 0 > -1, -1 > -2 and so on.

Similarly, an integer on a number line is always lesser than every integer on its right. Thus, -5 is less than -4

-5<-4,-4<-3,-3<-2, -2 < -1, -1 < 0, 0 < 1, 1 < 2 and so on.

Every positive integer is greater than every negative integer.

Zero is less than every positive integer and is greater than every negative integer.

The greater the number, the lesser is its opposite. For example, 9 is greater than 5, but -9 is less than -5; similarly, -9 > -15 or, 9 < 15 and so on

The lesser the number, the greater is its opposite.  For example, 6 is less than 7, but -6 is greater than -7; similarly, -8 < -5 or 8 > 5 and so on.

 

Demonstration:

Arrange the integers from greater to lesser:

(i) 8, -2, 3, 0, -6, -7, 7, -1

(ii) -12, 17, -2, 3, -6, -15, 0, 1

(iii) 11, -21, -18, 13, -5, -1, 1, 10

Solution:

(i) 8, 7, 3, 0, -1, -2, -6, -7

(ii) 17, 3, 1, 0, -2, -6, -12, -15

(iii) 13, 11, 10, 1, -1, -5, -18, -21