TYPES OF NUMBERS AND DEFINITION

What is natural number ?

Recall that the counting numbers 1,2,3, ... constitute the system of natural numbers. These are the numbers which we use in our day-to-day life.

There is no greatest natural number, for if 1 is added to any natural number, we get the next higher natural number, called its successor.

What is whole number ?

When a natural number is subtracted from itself we can not say what is the left out number. To remove this difficulty, the natural numbers were extended by the number zero (0), to get what is called the system of whole numbers Thus, the whole numbers are

0, 1, 2, 3, ................

What is Integers ?

While dealing with natural numbers and whole numbers we found that it is not always possible to subtract a number from another.

The integers are

..., – 7, – 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6, 7, ...

Consider the situation, when an integer a is divided by another non-zero integer b. The following cases arise:

What is rational number ?

A number which can be put in the form p/q, where p and q are integers and q ≠ 0, is called a rational number

What is irrational number ?

The number that which cannot be written as a proportion (or fraction). 

What is real numbers ?

The real numbers are the set of numbers containing all the irrational numbers and all the rational numbers. The real numbers consist of “all the numbers” on the number scale.

Complex numbers ?

The complex numbers are the set {a+bi | the real numbers are a and b}, where the imaginary unit is i, −1−√-.