# Whole Numbers and Integers

## Whole Numbers

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

No Fractions!

### Examples: 0, 7, 212 and 1023 are all whole numbers

(But numbers like ½, 1.1 and −5 are **not** whole numbers.)

## 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, ... }, positive {1, 2, 3, 4, ... }, or zero {0}

We can put that all together like this:

Integers = { ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }

### Examples: −16, −3, 0, 1 and 198 are all integers.

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

These are all integers (click to mark), and they continue left and right infinitely:

## Some People Have Different Definitions!

* Some* people (not me) say that whole numbers can also be negative, which makes them exactly the same as integers.

* And* some people say that zero is NOT a whole number. So there you go,

*not everyone agrees on a simple thing!*

## My Standard

I usually stick to this:

Name |
Numbers |
Examples |

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

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

Integers |
{ ... −4, −3, −2, −1, 0, 1, 2, 3, 4, ... } |
−15, 0, 27, 1102 |

And everyone agrees on the definition of an **integer**, so when in doubt say "integer".

And when you only want positive integers, say "positive integers". It is not only accurate, it makes you sound intelligent. Like this (note: zero isn't positive or negative):

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

## Other Numbers

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