My Math Forum Why isn't dividing by zero = zero?

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April 2nd, 2019, 11:02 PM   #11
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Quote:
 Originally Posted by Benit13 Because it depends on what you're dividing by zero. More specifically, if you consider a function $\displaystyle f(x) = \frac{g(x)}{x}$ and then try and find the limit of that function as x tends to zero, then the limit obtained is not always zero. It changes depending on what g(x) is. A typical example is $\displaystyle g(x) = \sin x$. If you look at the attached table, which shows somes evaluations of the function with decreasing values of x, the function tends towards 1, not 0.
What does this have to do with the OP? If you repeat the same process but take the limit as $x \to 4$ would you conclude that you can't divide by 4 either?

April 3rd, 2019, 01:24 AM   #12
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Quote:
 Originally Posted by SDK What does this have to do with the OP? If you repeat the same process but take the limit as $x \to 4$ would you conclude that you can't divide by 4 either?
The OP was asking about why divide by zero was undefined instead of always evaluating to 0. I gave an example of a function which, at first glance, looks like a divide by zero, but the function evaluates to 1 instead.

April 3rd, 2019, 01:46 AM   #13
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Quote:
 Originally Posted by Benit13 The OP was asking about why divide by zero was undefined instead of always evaluating to 0. I gave an example of a function which, at first glance, looks like a divide by zero, but the function evaluates to 1 instead.
But it's not a divide by 0. It has nothing to do with it. You have written a limit, but limits have nothing to do with these algebraic operations. You can't argue for or against division by 0 by starting about limits.

 April 3rd, 2019, 04:24 AM #14 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 You cannot divide by 0 because there is nothing to divide . The only number that can be divided by 0 is 0 .
April 3rd, 2019, 04:38 AM   #15
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Quote:
 Originally Posted by idontknow The only number that can be divided by 0 is 0 .
No.

 April 3rd, 2019, 04:41 AM #16 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timey-wimey stuff. Let me second that. Nooooooooooooooooooooooooooooooo!!!!!! -Dan Thanks from SDK
 April 3rd, 2019, 04:58 AM #17 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 I mean 0/0 makes sense but it is undefined. Division by 0 makes sense in limits. Last edited by idontknow; April 3rd, 2019 at 05:03 AM.
April 3rd, 2019, 05:14 AM   #18
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Quote:
 Originally Posted by idontknow I mean 0/0 makes sense but it is undefined. Division by 0 makes sense in limits.
Limits are irrelevant to an algebraic operation. I don't know why people keep bringing them up. The operation 0/0 is undefined, whether some limit exists or not.

 April 3rd, 2019, 05:39 AM #19 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 0/0 may be indeterminate in the context of limits. Algebraic operations come into play during direct substitution, among other things. Thanks from topsquark
April 3rd, 2019, 05:40 AM   #20
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Quote:
 Originally Posted by Micrm@ss I don't know why people keep bringing them up.
Perhaps you should pay more attention to people's posts then, in particular the OP, so that you can get an insight into how they are thinking.

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