# Introduction

The most basic numbers are the natural numbers.

N = {1, 2, 3, 4, 5,â€¦}

The natural numbers are used for counting, and so are called as counting numbers . The set of natural numbers has infinite number of elements does not mean to say that infinity is a natural number. It is very important to have natural numbers for counting and comparison purposes.

In the 5^{th} century, Indian mathematician Aryabhatta invented the number zero, and the decimal system. This made it a lot easier to add and multiply than it had been before. Our word "zero" comes from the Sanskrit word meaning nothing. Indian mathematical ideas soon spread to West Asia and from there to Africa and Europe

**Aryabhatta**

Counting Numbers with the zero are called Whole Numbers. The set of whole numbers is denoted by W. The set of all integers is often denoted by a Z which stands for "Zahlen" meaning numbers in German.

In order to find the solutions, it is necessary to extend our number system. The natural numbers have been pushed as far as they will go. The first consideration is to devise an extended set that will allow subtraction in all cases.

Integers are like whole numbers, but they also include negative numbers.

The rational number is of the form.

Division by zero is not allowed for rational numbers. We can say that, integers form a subset of rational numbers.

Also, rational numbers include natural numbers and whole numbers.

**Rational Numbers**

The set of rational numbers is denoted by Q. Here, the symbol Q is derived from the German word â€˜Quotientâ€™, which can be translated as "ratio," and first appeared in Bourbaki's AlgÃ¨bre.

**Real Numbers**

The collections of rational and irrational numbers form the real numbers.

It includes all the numbers, namely, natural, whole, integer, rational and also irrational.

Since, all the numbers form the real numbers; we have named the system as Real number system.

The name "real number" was given by the Descartes. All the real numbers are placed by a unique point in the number line.

The rational numbers are nothing but the fractions. We can find equivalent rational numbers as we find for fractions.