If someone lived in ancient Egypt and wanted to count how many cats she had (cat ladies were in large supply back then), all she would need in order to do so would be the set of natural numbers, also known as counting numbers. These are, as the second name implies, the numbers 1, 2, 3, 4, etc. These numbers are very useful for counting things, as you might imagine. Who would've guessed, right? We'll try to make things a bit more interesting from here on out.
Natural Numbers on a Number Line
Let's try to answer the following questions using just the natural numbers:
John has 3 sheep. Mary gives him 4 more sheep. How many sheep does John have now? Do a little addition, and 3 + 4 = 7. Don't worry about Mary though...she held onto a little lamb.
John has 5 goats. He gives Mary 2 goats. How many goats does John have now? Answer: 5 - 2 = 3 goats. And he's got those listed on eBay, so hopefully he will soon be 100% goat-free.
John has 5 cows. He gives Mary 5 cows. How many cows does John have?
Whoa, there, Bessie! Before you get a little too cocky and start shouting "zero" from the rooftops (which is dangerous, by the way...why not just open a window?), notice that 0 is not a counting number. We can't really answer this question as written. Unfortunately, in order to list 0 as an answer, we would need to be able to include whole numbers, which aren't all that different from natural numbers. Read on...