# Real Numbers

### Real Numbers are just numbers like:

1 | 12.38 | −0.8625 | 3/4 | √2 | 198 |

In fact:

Nearly any number you can think of is a Real Number

### Real Numbers include:

Whole Numbers (like 0, 1, 2, 3, 4, etc) | ||

Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc ) | ||

Irrational Numbers (like π, √3, etc ) |

Real Numbers can also be positive, negative or zero.

### So ... what is NOT a Real Number?

Imaginary Numbers like √−1 (the square root of minus 1)are not Real Numbers |
||

Infinity is not a Real Number |

And there are also some special numbers that mathematicians play with that aren't Real Numbers.

### Why are they called "Real" Numbers?

**Because they are not Imaginary Numbers.**

The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!

## The Real Number Line

The Real Number Line is like a geometric line.

A point is chosen on the line to be the **"origin"**, points to the right are positive, and points to the left are negative.

A distance is chosen to be "1", then whole numbers are marked off: {1,2,3,...}, and also in the negative direction: {−1,−2,−3, ...}

Any point on the line is a Real Number:

- The numbers could be whole (like 7)
- or rational (like 20/9)
- or irrational (like π)

But you won't find Infinity, or an Imaginary Number.

## Real does not mean they are in the real world

They are **not** called "Real" because they show the value of something **real**.

In mathematics we like our numbers pure, when we write 0.5 we mean **exactly** half.

But in the real world half may not be *exact* (try cutting an apple **exactly** in half).