# Real Numbers

**Real numbers** are rational numbers plus irrational numbers.

Since rational numbers include integers and fractions, then real numbers include:

- integers {..., -5,-4,-3,-2,-1,0,1,2,3,4,5,...}
- fractions (proper, improper, mixed numbers)
- irrational numbers (like $$$\sqrt{{{2}}}$$$, $$${\sqrt[{{3}}]{{-{15}}}}$$$, $$$\pi$$$, $$${e}$$$ etc.)

A set of real numbers, i.e. a group of real numbers, is denoted by $$$\mathbb{R}$$$.

As we already saw, all these numbers can be placed on a number line, which is called **real number line.**

Real numbers are called "real", because they are used in math to represent something:

- $$$\pi$$$ is used to describe the ratio of circumference of any circle and its diameter
- $$$\sqrt{{{2}}}$$$ is used to describe diagonal of unit square
- $$$\frac{{5}}{{7}}$$$ is used to describe 5 pieces of cake, that is divided into 7 pieces.