There's a great Radiolab episode[0] that talks about divide by zero in perhaps more conceptual terms.
KARIM ANI: If you take 10 and divide it by 10, you get one. 10 divided by five is two. 10 divided by half is 20. The smaller the number on the bottom, the number that you're dividing by, the larger the result. And so by that reasoning ...
LULU: If you divide by zero, the smallest nothingness number we can conceive of, then your answer ...
KARIM ANI: Would be infinity.
LULU: Why isn't it infinity? Infinity feels like a great answer.
KARIM ANI: Because infinity in mathematics isn't actually a number, it's a direction. It's a direction that we can move towards, but it isn't a destination that we can get to. And the reason is because if you allow for infinity then you get really weird results. For instance, infinity plus zero is ...
LATIF: Infinity.
KARIM ANI: Infinity plus two is infinity. Infinity plus three is infinity. And what that would suggest is zero is equal to one, is equal to two, is equal to three, is equal to four ...
STEVE STROGATZ: And that would break math as we know it. Because then, as your friend says, all numbers would become the same number.
