# Real Numbers (Definition, Set of Real Numbers, Properties)

Concepts related to the actual numbers have been expanded here with examples and practice questions. The key concept of the number system is included in this post.

## Real Numbers

A group of rational numbers and irrational numbers are called real numbers. In other words, a number whose square is always a positive number is called a real number.

In mathematics, a real number is a value representing a sum along a straight line. Real numbers include all rational numbers such as -7, -9, etc. and fractional numbers such as 5/2, 7/4, etc. and all irrational numbers such as √3, √7, etc.

Real numbers can be understanding of as points on an infinitely long line called a number line or real number line, where points comparable to integers are evenly spaced. Any real number can possibly be purposeful by an infinite decimal representation, such as 3.245, where each consecutive digit is measured in units one-tenth the size of the previous one. Real lines can be understanding of as a part of a complex plane, and real numbers can be understanding of as a part of complicated numbers.

### Examples

3/4, 7/12, 5.6, 8.3, -6, -9, √6, √2, 5√3, 78√5, etc. are examples of real numbers.

## Set of Real Numbers

### 1. Natural Numbers

### 2. Whole Numbers

### 3. Integers

### 4. Rational Numbers

**p/q**. where

**q≠0**

### 5. Irrational Numbers

**p/q**for any integer

**p**and

**q**.

## Properties of Real Numbers

**m**,

**n**, and

**r**are three real numbers. The above properties can be described using

**m**,

**n**, and

**r**.

### 1. Commutative Property

**m**and

**n**are two numbers, then generally

**m + n = n + m**will be for addition and

**m × n = n × m**for multiplication.

**Examples**

### 2. Associative Property

**m**,

**n**, and

**r**are three numbers, then generally

**(m + n) + r = m + (n + r)**will be for addition and

**(m × n) × r = m × (n × r)**for multiplication.

**Examples**

### 3. Distributive Property

**m**,

**n**, and

**r**are three numbers, then the distributive property is represented as:

**m (n + r) = m × n + m × r**and

**(m + n) r = m × r + n × r**.

**Examples**

### 4. Identity Property

**Examples**