Real numbers include all rational and irrational numbers. Thus real numbers are integers, fractions and decimals. They even include all positive and negative numbers.

The real number system consists of whole numbers, integers, natural numbers, rational numbers and irrational numbers.

Natural numbers: 1, 2, 3,…
Whole numbers: 0, 1, 2, 3, …
Integers: -1, 0, 1, 2, 3, …
Rational numbers: $\frac{-1}{4}$, -0.5, 2, 41
Irrational numbers : $\sqrt{2}$ , $\pi$, sin 60
Non real numbers: When we consider a number $\sqrt{-25}$ , we may not write it this as 5 or -5 since 52 = 25 and (-5)2 = 25 and therefore $\sqrt{-25}$ is not a real number and that’s the reason $\sqrt{-25}$ is a non real or imaginary number.

Set of all rational and irrational numbers are called as real numbers. Imaginary numbers and infinity are not real numbers. We use real numbers to measure continuous quantities. The decimal numbers with an infinite sequence of digits to the right of the decimal point, are also real numbers.

The set of Natural numbers is {1, 2, 3, .....}
The set of Whole numbers is {0, 1, 2, 3, .....}
The set of Integers are {....-2, -1, 0, 1, 2,...}
The set of Rational numbers is { all numbers of the form $\frac{p}{q}$ are a set of rational numbers. Where p, q are integers and q $\neq$ 0}
Irrational numbers are non - repeating and non - terminating decimals, that cannot be written in the form of a quotient of two integers.

Real Number Definition: Rational numbers and Irrational numbers combined together are known as Real numbers. Real numbers include terminating as well as non terminating repeating and non repeating decimals. The Set of Real numbers is a Super Set of many Sets like a set of Rational numbers, a set of Irrational numbers, a set of Natural numbers, a set of Whole numbers, a set of Integers etc. It can be represented by a Venn diagram as follows:

Real Numbers

Is zero a real number ?

Yes, zero is a real number, but it is not a counting number. It is an integer, a real number and a rational number.