My Math Forum Dividing by 0

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 December 26th, 2014, 05:04 PM #1 Newbie   Joined: Dec 2014 From: Australia Posts: 1 Thanks: 0 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.
 December 26th, 2014, 05:38 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra 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 $y = \frac{x}{0}$.
 December 26th, 2014, 06:57 PM #3 Senior Member   Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 393 Thanks: 71 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?
 December 26th, 2014, 09:18 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,019 Thanks: 2254 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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