What are Natural Numbers? - Definition & Examples

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  • 0:01 Natural Numbers
  • 0:36 Some Confusion About Zero
  • 1:28 The Set of Natural Numbers
  • 2:22 Combining Natural Numbers
  • 3:30 Lesson Summary
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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

The natural numbers are simply the counting numbers you first learned as a child. In this lesson, you will learn a little about the natural numbers, as well as a little about the confusion surrounding zero.

Natural Numbers

The natural numbers are simply the numbers you first learned - the numbers you count with. Some mathematicians count 0 as a natural number, and others start at 1. The natural numbers are what you would use to count objects, such as the chocolate chips in a cookie or the people ahead of you in the roller coaster line. The people ahead of you in the line may seem like they go on forever; of course, they don't really. The natural numbers, however, do go on forever. While you can count them in theory, you would never be done.

Some Confusion About Zero

Depending on the mathematician, the natural numbers include: 1, 2, 3, 4, 5, . . . (also called the positive integers), or 0, 1, 2, 3, 4, 5, . . . (also called the nonnegative integers or whole numbers). If you are taking a mathematics class, then it is safest to ask your teacher, or look at your text, to make sure you know whether or not to include 0.

To be clear, mathematicians will sometimes use a large N to refer to the natural numbers. They may put a 0 subscript after the N if they mean for 0 to be included and a 1 after the N if they do not want the 0 included.

The Set of Natural Numbers

One easy way to describe the numbers you want to include is to use set notation. A set is a group of items that you have carefully listed or described. If you want to list the items in a set, such as the set of natural numbers excluding zero, it looks like this: {1, 2, 3, 4, 5, ...}.

Another way to describe the set, or group, you want to include is to use a number line. This number line shows the set of natural numbers, including 0:

Number Line
number line

Notice that there is an arrow after the 11, meaning that the numbers go on forever. One thing to notice is that the numbers in between the counting numbers, such as 2 1/2 or 4.15, are not included - they are not natural numbers.

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