Comments on: Why Can’t We Divide By Zero?

By: Vlad

Vlad — Sat, 26 Sep 2009 17:41:39 +0000

@Steve:

You’re absolutely right. I was just demonstrating a simple example of what can go wrong if you DO treat infinity as a number.

By: Steve

Steve — Sat, 26 Sep 2009 16:46:46 +0000

I’m not great at math or anything, but this part bugged me; you say “Infinity is not a number. Seriously. It’s an abstract concept. It’s a shorthand for “gets as big as you like”. You can’t treat it as a number” and then immediately go on to plug it into an equation where you treat it just like a number, rather than the ‘abstract concept’ it is. Correct me if I’m wrong, but I’m fairly certain you can’t subtract infinity from itself.

By: Vlad

Vlad — Mon, 16 Feb 2009 08:50:51 +0000

@Holly:
That’s the thing. I think that’s one of the few things that can’t be done.

Remember what I said about division being just anti-multiplication? Well, that means that “divided by three” means just “multiplied by anti-three” (that is, multiplied by one third). And there’s no anti-zero under multiplication.

Then again, people used to think that square roots of negative numbers were ridiculous, or that you can’t compare the sizes of infinite things. (Turns out there is the same “size” infinity of natural numbers as there are fractions, but there is a “bigger” infinity of real numbers. Fun stuff!)

So if you find a way to divide by zero that doesn’t make all mathematics break down afterwards (like the event horizon of a black hole), please let me know

By: Holly

Holly — Mon, 16 Feb 2009 00:30:49 +0000

Great articles! They’re interesting and informative.
I wonder what would happen if we invented a form of number that could be divided by zero. After all, negatives and imaginaries were created to make the mathematical impossible possible, weren’t they?