what is 1 divided by 0? - Amidst a tangled web: "dan, I don’t think it’s actually an ‘alternate question’, it’s a question for which you might use the limit to find a reasonable answer that matches your intuition. It must be noted that you can’t actually treat infinity as a real number, or you end up with the same issues discussed earlier and a mathematical system that is nonsensical.

All this mess surrounding zero is part of why the Greeks and their intellectual followers fought against it for so long. Though it’s hard to believe now, for a long time there was no such thing as a number zero. Even when computations involving a number zero were introduced in the East, it was considered a heretical idea in the West due to philisophical implications. Eventually the utility of it won out, and now if you try to tell people that at one point no one knew about zero, you get a lot of funny looks. I’m probably getting a funny look from you now, in fact, but it’s true!"