# Whole Numbers and Integers

## Whole Numbers

Whole Numbers are simply the numbers **0, 1, 2, 3, 4, 5, …** (and so on)

No Fractions!

## Counting Numbers

Counting Numbers are Whole Numbers, but **without the zero**. Because you can't "count" zero.

So they are
**1, 2, 3, 4, 5, …** (and so on).

## Natural Numbers

"Natural Numbers" can mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {**0**, 1, 2, 3, ...}, depending on the subject.

## Integers

Integers are like whole numbers, but they **also include negative numbers** ... but still no fractions allowed!

So, integers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0}

We can put that all together like this:

Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

### Example, these are all integers:

-16, -3, 0, 1, 198

(But numbers like ½, 1.1 and 3.5 are **not** integers)

## Confusing

Just to be confusing, *some* people say that whole numbers can also be negative, so that would make them
exactly the same as integers. *And* sometimes people say that zero is NOT a whole number. So there you
go, *not everyone agrees on a simple thing!*

## My Standard

I must admit that sometimes I say "negative whole number", but usually I stick to:

Name |
Numbers |
Examples |

Whole Numbers |
{ 0, 1, 2, 3, 4, 5, … } |
0, 27, 398, 2345 |

Counting Numbers |
{ 1, 2, 3, 4, 5, … } |
1, 18, 27, 2061 |

Integers |
{ ... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, … } |
-15, 0, 27, 1102 |

But nobody disagrees on the definition of an **integer**, so when in doubt say "integer", and
if you only want positive integers, say "positive integers". It is not only accurate, it makes you
sound intelligent. Like this (note: zero is neither positive nor negative):

- Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
- Negative Integers = { ..., -5, -4, -3, -2, -1 }

- Positive Integers = { 1, 2, 3, 4, 5, ... }

- Non-Negative Integers = { 0, 1, 2, 3, 4, 5, ... }
*(includes zero, see?)*

## Other Numbers

For an interesting look at other types of numbers read The Evolution of Numbers