One of the interestingly odd things about how people understand math is *numbers*. It's

astonishing to see how many people don't really understand what numbers *are*, or what different kinds of numbers there are. It's particularly amazing to listen to people arguing

vehemently about whether certain *kinds* of numbers are really "real" or not.

Today I'm going to talk about two of the most basic kind of numbers: the naturals and the integers. This is sort of an advanced basics article; to explain things like natural numbers and integers, you can either write two boring sentences, or you can go a bit more formal. The formal

stuff is more fun. If you don't want to bother with that, here are the two boring sentences:

- The natural numbers (written
**N**) are zero and the numbers that can be

written without fractions that are greater than zero. - The integers (written
**Z**) are all of the numbers, both larger and smaller than

zero, that can be written without fractions.