The reason 0/0 is not usually defined to be 1 is that, "almost 0" / "nearly 0" is not always close to 1. This is expressed more precisely in calculus:

If for any error size, E, you can find an accuracy requirement, D, such that X and Y being within D of 0 means that X/Y will be within E of 1, then you could define 0/0 as 1.

There are cases where we can define some "edge case" calculation to have some specific value because doing so makes for a continuous function.

(Update) If you require X==Y (which is how you are thinking about it), then you do always get 1. But think of a 3-dimensional space where you fill in points where Z = X/Y. Then the plane where X==Y intersects with our graph such that we get Z==1 everywhere except at (X,Y)==(0,0). Which makes you think that Z==1 makes sense there.

But if you look at it other ways, you get different results. For example, look at the plane 2*X==Y and you'll think Z should be 2 at (X,Y)==(0,0).

Now, think of a circle of radius E around (X,Y)==(0,0) and intersect the vertical cylinder that passes through that with our graph. You get two curves, each that goes to both negative infinity and positive infinity (for Z) while always staying at distance E from the vertical line (X,Y)==(0,0).

So (X,Y) being almost (0,0) means that X/Y could be any value at all. So mathematicians don't define a value for 0/0.

And finally, (a much simpler argument) if you define 0/0==1, then 0/Y would be 0 for all but Y==0, which is exactly the type of problem you are complaining about.

        - tye (I'm nearly finished with almost explaining this)

In reply to (tye)Re: What is zero divided by zero anyway? by tye
in thread What is zero divided by zero anyway? by BrowserUk

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