- Topics At a Glance
**Different Types of Numbers**- Natural Numbers
**Whole Numbers**- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

Zero is the only **whole number **that is not also a natural number. If we start there and take a look at our new collection of numbers, we have 0, 1, 2, 3, 4, and so on. You can easily remember this because it looks as if we literally added a hole (whole) to the beginning of the set. Not to mention that 0 and a hole have something in common in addition to their shape: they're a whole lot of nothing.

**Whole Numbers on a Number Line**

Now let's go back and try again to answer that question about the cows:

John has 5 cows. He gives Mary 5 cows. How many cows does John have? 5 - 5 = 0.

Well...that's a shame. Where's he going to get his whole milk? See how it always comes back to "whole"?

It probably seems obvious to you that 0 is a number, but the symbol 0 actually took quite a while to work its way into mathematics. Think about the Romans. They had their fancy Roman numerals, but they didn't have a symbol for 0. It took years for that concept to occur to them. 0 wasn't built in a day.

If you're fascinated by this topic, you're in luck, because the number 0 is the star of several books available for your reading pleasure:

*The Nothing That Is: A Natural History of Zero*, by Robert Kaplan

*Zero: The Biography of a Dangerous Idea*, by Charles Seife

Now that this makes sense to you and you've got it locked away inside your brain, we're going to throw you a curve ball. Isn't that nice of us?

The unfortunate truth of the matter is that mathematicians have not been able to agree unanimously on whether or not 0 is, in fact, a natural number. The very fact that it took so long for anyone to think it up indicates to us that it's pretty *un*natural, but who are we to say? Our point is this: When entering into a discussion on natural and/or whole numbers, make sure you and your partner in discourse are on the same page when it comes to 0. Many a bestie has been lost in the midst of a heated natural number/whole number squabble.