[lmm]

> This seems just as bizarre, since zero times anything shouldn't become 1, no matter how big or how many times you do it.

It isn't bizarre, because there's an equal and opposite argument that anything times infinity is infinity, no matter how small the thing you multiply by.

If you actually do infinity * 0 you get NaN since there's no way to determine (without more information) whether the result should be 0, infinity, or anything in between.