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:
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?)
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