What is the difference between whole numbers and integers

In a nutshell, whole numbers are integers, but integers are not whole numbers. Whole numbers are the numbers that you would typically use when counting, such as 1, 2, 3, 4, and so on. Zero is also classified as a whole number.

Integers is a broader classification. It includes whole...

In a nutshell, whole numbers are integers, but integers are not whole numbers. Whole numbers are the numbers that you would typically use when counting, such as 1, 2, 3, 4, and so on. Zero is also classified as a whole number.

Integers is a broader classification. It includes whole numbers, as explained above, as well as numbers below zero, such as -4, -3, -2, and -1. If you imagine integers appearing along a straight line, they will continue forever. 123456 is still an integer, as is -123456. To put it simply, an integer is any number that does not include a fraction or decimal point.

For example, the number 5 is both a whole number and an integer. -5, on the other hand, is an integer but not a whole number. 5.5 is neither a whole number nor an integer.

It is important to understand that a fraction or number containing a decimal point can never be an integer. That means that 1/2 or 1.2 will never be considered an integer. In addition, because these are not made up of wholes, they can also not be whole numbers. 1.2 and 1/2 are somewhere between 1 and 2 and 0 and 1 respectively, and thus cannot be considered whole numbers.

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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:

numbers/images/number-line.js?mode=int

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:

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

422,423, 1058, 1059, 2988, 2989, 3980, 3981, 3982, 5346