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What Is a Natural Number? (Mathematics Glossary)

What Is a Natural Number?

A natural number is a whole number from 1 upwards:



Mathematicians use the symbol to represent the set of natural numbers.

Dictionary Definition

The Oxford English Dictionary defines a natural number as "a positive whole number (1, 2, 3, etc.)"

Natural Numbers As Counting Numbers

A natural number is a counting number.

Natural numbers are the numbers you would use to count objects.

Natural Numbers on the Number Line

The image below shows the natural numbers on the number line.



Note: The natural numbers are whole numbers only. They are not found in between the numbers shown.

Natural Numbers, Whole Numbers and Integers

The difference between natural numbers, whole numbers and integers can be quite confusing.

Remember,
  • Natural numbers start from 1: {1, 2, 3 ...}
  • Whole numbers start from 0: {0, 1, 2, 3 ...}
  • Integers have negative numbers: {-3, -2, -1, 0, 1, 2, 3 ...}


Read more about the types of whole numbers
Interactive Test
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Here's a second test on natural numbers.
Here's a third test on natural numbers.
Note

What Natural Numbers Are

Natural numbers are positive integers.

What Natural Numbers Are Not

Natural numbers are not negative (such as -1) and are not fractions (part of a whole number, such as ½ or 0.3).

What Natural Numbers Are (Usually) Not

0 is (usually) not a natural number.

A child learning to count would not count zero objects.



(Some mathematicians do count 0 as a natural number. We do not. The idea of 0 is more abstract and less natural - it was invented later. If you include 0, you have the whole numbers).