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High School Algebra I: Homework Help Resource25 chapters | 271 lessons

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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.

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.

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.

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:

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.

If you add or multiply two natural numbers, you always get another natural number. For example, suppose you have 27 friends on Facebook (a natural number). After impressing everyone with your amazing dance moves at Homecoming, you add 49 more friends (another natural number). When you add the two to get your new total number of Facebook friends, you get a natural number, 76. Of course, this is pretty logical because, if you are only adding whole amounts, or countable objects, you can't end up with anything but wholes when you're done.

The same thing doesn't work for division or subtraction. If you have 6 whole pizzas (as a natural number) and divide them evenly among 12 friends (another natural number), everyone only gets one half. Natural numbers do not include fractions. Or, start with $10 in your bank account (a natural number) and spend $12 (another natural number). Now you have a balance of -$2. Negative numbers are also not natural.

**Natural numbers**, or counting numbers, are easy to define - they are the first numbers any child learns as he learns to count objects. Some mathematicians believe 0 is a natural number, while others prefer to begin with 1. Negative numbers and fractions are not natural numbers.

You should have the ability to do the following after watching this video lesson:

- Define natural numbers
- Recall whether zero is a natural number
- Explain how to describe a set of natural numbers
- Describe the outcomes when adding, subtracting, multiplying and dividing natural numbers

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High School Algebra I: Homework Help Resource25 chapters | 271 lessons

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
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