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#1 babeasc

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Posted 13 May 2007 - 04:39 PM

Right....

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}= ?


???


Beyond it, and us, shines a greater hope and a brighter future
Can't wait 'til the exams are over!

#2 Pete

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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.

#3 George

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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,


\begin{align*}
2\times \frac00 &= 2 \\
\frac{2 \times 0}0 &= 2 \\
\frac00 = 2
\end{align*}

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

#4 babeasc

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Posted 14 May 2007 - 02:34 PM

Thats pretty cool biggrin.gif

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


Beyond it, and us, shines a greater hope and a brighter future
Can't wait 'til the exams are over!





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