Argue with my High School math teacher guys.. not me please??..
PM me for her details, if you feel that strongly about what she taught me.
It's a pretty abstract concept.. therefore I am sure no answer is correct, nor can we use math to explain something abstract.
It's fun trying though.
Your math is neither correct, nor not correct. It's complicated. Think of it this way:
There's a sequence of numbers (1/2),(1/3),(1/4),(1/5)...(1/0)
and then you've got 1/(1/2), 1/(1/3), 1(1/4)...+∞ (ie. 2,3,4...+∞)
On the other hand you have (-1/2),(-1/3),(-1/4),(-1/5)...(-1/0)
and 1/(-1/2), 1/(-1/3), 1(-1/4)...-∞ (ie. -2,-3,-4...-∞)
So you want to "define" (1/0) as infinity (you want to give it that value). Despite the fact that ∞ isn't a real number, we'll call it a real number here for argument's sake.
So we've got our whole numbers increasing until positive infinity and we have our fractions going down further towards our limit of (1/0). But wait, now we've named that number ∞. Is it +∞ or -∞ if the other numbers are all increasing towards +∞?
Ok, well, let's look at it from the other side. We have our negative integers decreasing towards -∞ and our negative fractions going up towards....what? +∞? -∞?
Oh no what do we call it??
We can't just call it negative or positive based on how we feel about it at that time (or based on which direction we're approaching it from - whether from the positive integer's viewpoint or the negative integer's viewpoint). So we say that (1/0) is undefined and infinity isn't a number.
It makes things much less messy and our mathematical axioms remain flowery and virginal.