Types of Numbers
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 unnatural, 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.