## What Is the Difference Between Real & Integers? : Mathematics: All About Integers

## What is an integer?

Positive or negative whole numbers with no fractional or decimal parts are known as integers. Whole number and natural numbers are two subsets of integers, which are a subset of real numbers. Integers are typically written as “-3, -2, -1, 0, 1, 2, 3” to demonstrate that they are infinite in both directions, whole numbers, and contain the number zero.

Integers have the following characteristics:

## What is a real number?

Any number on the number line, including natural, whole, integer, rational, and irrational numbers, is referred to as a real number. Simply put, all numbers are real except imaginary numbers, a collection of complex numbers that were once believed to be impossible to calculate.

Real numbers can be divided into two categories: irrational and rational numbers. In addition, you can further divide the category of rational numbers into the subsets integers, whole numbers, and natural numbers. To understand how these groups and subsets of numbers operate, there are many diagrams and visual aids available. You can easily find one online if you want to search for one.

The definitions of the numbers that constitute all real numbers are as follows:

**Irrational numbers**

A real number that cannot be expressed as a straightforward fraction is said to be irrational. Decimals that go on indefinitely without repeating themselves are numbers that cannot be expressed as fractions.

For example, some famous irrational numbers are:

**Rational numbers**

A rational number is one that can be expressed as the ratio of two integers, or alternatively, as a straightforward fraction. Integers, whole numbers, and natural numbers are subsets of rational numbers.

For example, the following numbers are rational numbers:

**Integers**

Positive or negative whole numbers with no fractional or decimal parts are known as integers. Integers include the subsets, whole numbers and natural numbers.

For example, the following numbers are integers:

**Whole numbers**

A positive whole number without a fraction or decimal is referred to as a whole number. Whole numbers include the subset natural numbers. Whole numbers represent entire objects without any pieces or fragments.

For example, the following numbers are whole numbers:

**Natural numbers**

A natural number, also known as a “counting number,” is similar to a whole number except that zero is not included in the set. If you were to naturally begin counting the contents of a bag, you would begin with one item rather than zero.

For example, the following numbers are natural numbers:

## Real numbers vs. integers

Although not all real numbers are integers, they are all real numbers. Here are some differences:

## Integers vs real numbers comparison table

To make it simpler for you to compare integers to real numbers, here is a table: