REAL NUMBERS, R
One of the most important properties of the real numbers is that points on a straight line that can represent them. As in Fig 3.1, we choose a point, called the origin, to represent 0 and another point, usually to the right, to represent 1.
Then there is a natural way to pair off the points on the line and the real numbers, that is, each point will represent a unique real number and each real number will be represented by a unique point. We refer to this line as the real line. Accordingly, we can use the words point and number interchangeably.
Those numbers to the right of 0, i.e. on the same side as 1, are called the positive numbers and those numbers to the left of 0 are called the negative numbers. The number 0 itself is neither positive nor negative
11. SUMMARY
In this unit, you have been introduced to the sets of numbers. The set of real numbers, R, contains the set of integers, Z, Rational numbers, Q, Natural numbers, N, and Irrational numbers, Q’.
Intervals on the real line are open, closed, open-closed or closed-open depending on the nature of the endpoints.