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December 26th, 2014, 05:04 PM   #1
afk
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Smile Dividing by 0

y=-2x/z is undefined at z=0

but if you multiply the z over to the other side:

zy=-2x, at z=0. is 0=-2x => x=0


Why is this? Would this work on concepts like:

y=x/0 => 0=x ?


[Thanks in advance!]

Last edited by skipjack; December 26th, 2014 at 06:45 PM.
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December 26th, 2014, 05:38 PM   #2
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You can't say that $x = 0$ because $y$ is undefined by the equation $yz = -2x$ when $z = 0$. If $y$ is experiencing unbounded growth as $z \to 0$ then $x$ may not be zero at $z = 0$, but undefined (possibly with a finite limit).

And no, it doesn't work on $y = \frac{x}{0}$.
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December 26th, 2014, 06:57 PM   #3
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Whereas division by 0 is undefined, suppose that we define ONE exception.

Suppose we define $\displaystyle \frac {0}{0}$ as $\displaystyle 0$.

Would that eliminate the problem, afk?
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December 26th, 2014, 09:18 PM   #4
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No. Your original post and v8archie's reply were both incorrect.

Using x, y and z as Cartesian coordinates, the equation zy = -2x defines a surface that intersects the x-y plane in the entire y-axis. If one removes the y-axis from that surface, the resulting surface corresponds to the equation y = -2x/z.
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