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Natural Numbers

Now you know that every number on the number line is a real number. What are natural numbers? Natural numbers are called a subset of real numbers. A subset means that all natural numbers are real, but not all real numbers are natural. Natural numbers are numbers that are greater than zero and have no fractions. Starting with 1, just keep counting up and those are the natural numbers.

Examples of Real Numbers:
• 0, 15, -365, 8,000,000, 5/16, 321/895, p, v2... any number on that line in any direction.

Examples of Natural Numbers:
• 1, 2, 5, 500, 2,000,000, 5 trillion... it just keeps going up. (There are no fractions or special number like pi.)

Some people call them counting numbers. There are a lot of numbers on that line, but only the ones used to count complete objects are considered natural.

Whole Numbers

This will be easy. We almost used the word "whole" when talking about natural numbers. Whole numbers are all of the natural numbers and zero. They only have that little zero added to the set. Because math has very specific rules, that little zero makes a big difference. Think about it this way: when you count, you don't count zero things. There is nothing to count. That's why there are two different groups.

Examples of Real Numbers:
• 0, 15, -365, 8,000,000, 5/16, 321/895, π, √2 ... any number on that line in any direction.

Examples of Natural Numbers:
• 1, 2, 5, 500, 2,000,000, 5 trillion... it just keeps going up.

Examples of Whole Numbers:
0, 1, 2, 5, 10, 150, 2,800, 9,654,987... and on up.

Before We Go...

• Is 5/16 a whole number? No.
• Is 0 a natural number? No.
• Is 365 a whole number? Yes.
• Is 365 a natural number? Yes.
• Is 365 a real number? Yes.

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