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, ... }, 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, ... }

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 isn't a whole number. So there you go, not everyone agrees on a simple thing!

My Standard

I usually stick to this:

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

So when you only want positive integers, say "positive integers". It isn't only accurate, it makes you sound intelligent. Like this:

• 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