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Comment by cvoss | Hacker News Reader

This explanation isn't logically complete. It starts by asking why division by zero is undefined and concludes with "0/0 = 2, which is just not true."

But how can it be "just not true"? The point of this exercise was to investigate whether we can find a definition for division by zero, and here we've just produced a candidate! You could just define division by zero to be 2 and move on. To throw away this possibility at this point is to assume the conclusion.

It's not obviously false that 0/0 = 2 (yet).

The problem comes in when you repeat the exercise on a different example and find that also 0/0 = 3, or whatever. And now you start to see something is really amiss.

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Could be that dividing by zero is every number so it's 2 and it's also 3.

Or in the blog terms, the inverse of multiplying by nothing is dividing by everything.

I would say: Dividing by nothing gives you everything. It is undefined.

> The problem comes in when you repeat the exercise on a different example and find that also 0/0 = 3, or whatever. And now you start to see something is really amiss.

Yes, that's the obvious part.

In this case, but the induction step is still important...

That really sounds like it would be the identity.

If dividing by nothing is congruent with no operation, then the original set, unmodified should be returned.

I think that this proves that dividing by zero produces the set of all numbers, which is what it looks like to me when you graph this problem (y=1/x) using increasingly small positive and negative values for x. Smaller positive x values tend to positive infinity, smaller negative x values tend to negative infinity. When the x value reaches zero you have a vertical line from positive to negative infinity. ie dividing by zero corresponds to all numbers. That's how it appears to me. So 0/0=2 and it equals 3 etc. I admit this doesn't seem that useful.

But there is no black square at the end of the blog post, therefore it is not a mathematical proof. QED

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