Real Number System

• All positive and negative numbers including zero are called integers. It is usually denoted by I or Z.

I or Z = { ... –3, –2, –1, 0, 1, 2, 3 …}

Here, –1, –2, –3 … are called negative integers whereas 1, 2, 3 … are called positive integers and 0 is taken as neutral.

• The absolute value of an integer is its numerical value regardless of its sign. The absolute value of an integer n is denoted as |n|.

          Therefore, |−10| = 10, |−2| = 2, |0| = 0, |7| = 7 etc.

• The opposite of an integer is the integer with its sign reversed. The opposite of integer a is −a and the opposite of integer −b is +b or b.

          Thus, opposite of 5 is −5, opposite of −8 is 8.

• Integers can be represented on a number line. For this, a line has to be drawn and a point, 0, has to be marked on it. Towards the right of zero, the points, 1, 2, 3 …, are marked at equal gaps. Similar…