When you divide x by y, you're basically figuring out how many y's fit into x. No matter how many 0's you have, you'll never end up with anything more than 0. And even if x itself is 0, division still doesn't work, because who's to say 0 can only contain 0 0's? Can't 0 also contain 2 0's? For that reason, division is undefined rather than infinite--because it contains an infinite *amount* of answers, not a single infinite answer.