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
3. Natural Numbers, N
The natural numbers are the positive integers. We denote the set of natural
numbers by N; hence N = {1,2,3…..}
The natural numbers were the first number system developed and were used
primarily, at one time, for counting. Notice the following relationship between
the above numbers systems:
NZQR
The natural numbers are closed only under the operation of addition and multiplication. The difference and quotient of two natural numbers needed not be a natural number.
The prime numbers are those natural numbers p, excluding 1, which are only divisible 1 and p itself. We list the first few prime numbers:
2,3,5,7,11,13,17,19…