I like your little spiel on zero and infinity. I myself am a huge fan of number theory.
I'm also sorry to hear that your high school liked to "shield" you. I was taught in 9th grade that anything divided by zero equals infinity...though we didn't learn how to work with this until senior year (calculus).
Something else you might have fun writing about are the different *kinds* of infinity.
There is the infinitely far-reaching, increasing infinity (which can go in positive or negative direction). You count 1, 2, 10, 458, 239808235, and up, the whole way to infinity!
But there's *another* kind of infinity within the set of real numbers (I think you know where I'm going). Between 0 and 1 are .1, .6, .314, .536365678, .64396702474350, all the way out to infinity. There are an infinite amount of values between *any two* other values!!! That's a mind-boggling thought. Pick any two values. No matter how close they are together, between them is an infinite amount of other values.
Thinking in this way, there are an infinity amount of little infinities stretching between negative infinity and infinity.
...yeah. That's a fun one to ponder. There are lots of interesting hypotheses and theories based on these different "types" of infinity. They're used to prove all sorts of crazy shit.
Ramza