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Posted 13 May 2007 - 04:39 PM


we all know that \frac{0}{x} = 0 and that \frac{x}{0} =undefined and that \frac{x}{x} = 1

so....what does \frac{0}{0}= ?



Posted 13 May 2007 - 04:49 PM

Black hole. Vortex. Whatever you want to call it. You can't divide by zero, whatever the scenario. \frac{0}{0} is just undefined.


Posted 13 May 2007 - 04:57 PM

Here's the long answer biggrin.gif

\frac00 is also undefined, since you can't divide by 0.

The reason is that when we write x=\frac{a}{b}, we want x to be the unique solution of the equation bx=a.

In the case of b=0 (i.e. dividing by zero) the equation is 0.x=a, and if a is nonzero, it's impossible to find an x which will make that work.

So what if a=0? Well, then you have to solve 0.x=0 - meaning x could be anything you like. But then that's not a unique solution, so it goes against what I said above.

So why do we want it to be unique?

Well, what if we just pick one of the possible solutions, and say \frac00=1?

Then multiplying by 2,

2\times \frac00 &= 2 \\
\frac{2 \times 0}0 &= 2 \\
\frac00 = 2

So trying to just use \frac00=1 leads us to say 1=2, and the universe blows up tongue.gif The same thing would happen if we tried to make \frac00 any other fixed number. So we just agree not to smile.gif


Posted 14 May 2007 - 02:34 PM

Thats pretty cool biggrin.gif

think it'll come up in the exam lol biggrin.gif

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