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Types of Whole Numbers (Mathematics Lesson)

What Are Whole Numbers?

Whole numbers have no fractional part.

Some examples of whole numbers are given below:



Some numbers that are NOT whole numbers are given below. They all have a fractional or decimal part:

Types of Whole Numbers

Different names are given to different types of whole number.

Natural Numbers

A natural number is a whole number from 1 upwards:



Natural numbers are sometimes called counting numbers. They are the numbers you would use to count objects.

Whole Numbers

While whole numbers are any number without fractions, we (confusingly) also call the whole numbers from 0 upwards whole numbers:

Integers

An integer is a whole number. An integer may be positive, negative, or zero:

The Difference Between Natural Numbers, Whole Numbers and Integers

Clearly there is a lot of overlap between these three sets of numbers.

Start with the natural numbers...



...then add 0 to get the whole numbers...



Finally, take the negatives of all the natural numbers, and place them in reverse order, to the left of 0 to get the integers...

Positive and Non-Negative Integers

Unfortunately, some people use terms like natural numbers, counting numbers and whole numbers to refer to different sets of numbers than we have defined them here.

Because of this, there are more specific terms to use:
  • The natural numbers {1, 2, 3...} are positive integers
    (because they only use the positive integers).

  • The whole numbers {0, 1, 2, 3...} are non-negative integers
    (because they include all integers apart from the negative integers {-1, -2, -3...}).
Note: The non-positive integers will be {0, -1, -2, -3...}.

Interactive Test
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Here's a second test on the types of whole numbers.
Here's a third test on the types of whole numbers.