Is zero a positive number of a negative number?
I'm reading a great book about zero: Charles Seife, "Zero: the Biography of a Dangerous Idea", Viking/Penguin 2000 ISBN 0-14-029647-6. Zero has a "close" relative, Infinity. Did you know the Greeks not only didn't have zero; the believed it was philosophically impossible. Taking a look at the history of the discovery of the numbers we have can only make me wonder which numbers we haven't discovered yet!
I remember that's what my Dad taught me too. He would draw a number line and place 0 right in the middle and would draw a little tick mark, explaining that it was a wall with a gate to pass from positive numbers to negative.
I tell my students that it's neither positive nor negative, but it's the boundary wall between them. But sometimes, when we make an absent-minded mistake in a problem, we will joke that "it's because I counted negative zero, too."
Zero is a great example. Of what? Of a set with only one member! A set with only one member in it is rather abstract. Kids (and many adults) are hesitant, or even angry, when they encounter a monstrosity like that. And yet, there it is. There are greatly many members in the set of positive numbers. There are greatly many members in the set of negative numbers. Then, there is zero! The one and the only! Tackle it, and you are ready for the idea of an empty set.
