According to the standard definition of division, 1/0 does not equal infinity. It doesn't equal anything. It is undefined.

Yes, that's correct. The fact that 1/0 shouldn't be defined as infinity isn't an argument that it should be defined as 0.

There are many contexts where defining either 1/0 = -1/0 = ∞ or 1/0 = +∞ and –1/0 = –∞ is better than the alternatives, especially when working in an approximate number system like floating point.

In geometric modeling kinds of applications, I would say that these definitions are typically desirable, with 1/0 = undefined only better in unusual cases. As a simple example, it is typically much more useful for the “tangent” of a right angle to be defined as ∞ than left undefined.

But anyhow, there are no “facts” involved here. Only different choices of mathematical models, which can be more or less convenient depending on context / application.

Yes, exactly, I have no idea why you're being downvoted.

Look up the dirac delta function. It's a spike thats infinitely tall and infinitely narrow, with an area of 1. It's established now as a very useful tool in EE. But many people fought it tooth and nail because of this logic.

> 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.