Author Topic: Why doesn't zero divided by zero work  (Read 12593 times)

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Offline 3rik

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Re: Why doesn't zero divided by zero work
« Reply #15 on: February 23, 2012, 04:23:40 pm »
The division of zero is the reason why L'Hôpital's rule is necessary for finding some limits in calculus.
« Last Edit: February 23, 2012, 04:25:43 pm by 3rik »
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Offline Adriweb

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Re: Why doesn't zero divided by zero work
« Reply #16 on: February 23, 2012, 04:24:11 pm »
This is also why L'Hôpital's rule is necessary for finding some limits in calculus.
which is awesome :)

(but sadly rarely usable on complex cases :( )
« Last Edit: February 23, 2012, 04:24:36 pm by adriweb »
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Offline 3rik

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Re: Why doesn't zero divided by zero work
« Reply #17 on: February 23, 2012, 04:30:22 pm »
(but sadly rarely usable on complex cases :( )

On what sort of cases is it unusable?
« Last Edit: February 23, 2012, 04:31:03 pm by 3rik »
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Offline Adriweb

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Re: Why doesn't zero divided by zero work
« Reply #18 on: February 23, 2012, 04:34:10 pm »
These :D
(see attached : it's a math homework about calculating limits of the functions written)


(maybe some of them are doable, but probably not all)
(since you can't always take the derivative (easily))
« Last Edit: February 23, 2012, 04:34:38 pm by adriweb »
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Offline 3rik

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Re: Why doesn't zero divided by zero work
« Reply #19 on: February 23, 2012, 04:55:04 pm »
These are tricky (especially since I'm not very familiar with the hyperbolic trig functions), so I cheated and used Wolfram Alpha. http://www.wolframalpha.com/input/?i=lim_x-%3E0%281%2Fsin%28x%29%5E2-1%2Fsinh%28x%29%5E2%29
If you look in the steps, it uses L'Hôpital's rule.

Many functions need to be rewritten to properly use L'Hôpital's rule though.

I don't really understand the ones in Exercice 5-7 since I don't read french very well yet. They sort of look like integrals though.
« Last Edit: February 23, 2012, 05:00:56 pm by 3rik »
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Offline BlakPilar

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Re: Why doesn't zero divided by zero work
« Reply #20 on: February 23, 2012, 05:06:16 pm »
Well it seems that all of the fancy and complex responses have been taken... The simplest way it was described to me was that you can't take nothing from nothing, because there's nothing to give and you're really not getting anything in return.

inb4 someone finds some logical fallacy with that.

Offline Adriweb

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Re: Why doesn't zero divided by zero work
« Reply #21 on: February 23, 2012, 05:06:27 pm »
These are tricky (especially since I'm not very familiar with the hyperbolic trig functions), so I cheated and used Wolfram Alpha. http://www.wolframalpha.com/input/?i=lim_x-%3E0%281%2Fsin%28x%29%5E2-1%2Fsinh%28x%29%5E2%29
If you look in the steps, it uses L'Hôpital's rule.

Indeed, but that's because it's well-adapted for this function (simple trig). Or not ? (Look at all the steps... it works but it's kind of ridiculous :P)
But it's probably not the easiest/fastest way to solve this limit...

Anyway, for trigs functions I know it can be quite helpful, but for what I'm studying so far at school, we don't do these anymore, since it's always the same thing, but rather do limits of series and difficult things :(



(Edit : I love WolframAlpha 9001%, but it sometimes fails, and can't always give you steps ( :( ) for example : http://www.wolframalpha.com/input/?i=lim_x-%3E1+ln%28x%29%5E%28x-1%29 )
« Last Edit: February 23, 2012, 05:09:19 pm by adriweb »
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Offline 3rik

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Re: Why doesn't zero divided by zero work
« Reply #22 on: February 23, 2012, 05:23:09 pm »
I understand what you're saying. I learn about series next year.

Wolfram Alpha is great but it feels frustrating that it now costs money to use all of its cool new features (and a couple of its old features).
Since it's still getting new things added to it, it's fine that it doesn't always show exactly what I want, yet. (I'll wait until it can read minds.)
« Last Edit: February 23, 2012, 05:23:52 pm by 3rik »
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Offline Juju

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Re: Why doesn't zero divided by zero work
« Reply #23 on: February 24, 2012, 12:59:00 am »
Yeah, I had to cope with divisions by zero in limits in my math courses, we just had to move the x's around until the division by zero disappears.

And yeah, any number multiplied by 0 is 0, so 0 divided by 0 should be any number, which makes no sense, therefore 0/0 is undefined.

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Offline Builderboy

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Re: Why doesn't zero divided by zero work
« Reply #24 on: February 24, 2012, 01:12:44 am »
The interesting thing is when you start working with limits.  Lets say you have two equations that both equal zero at X=1, and lets say we divide one equation by the other.  If we find the ratio at X=1, obviously that is undefined.  But if we get reeeeallly close to X=1 (take the limit as X->1) the ratio can actually approach any number!  Depending on the equation of course, I once devised an equation that was undefined at X=0, but the limit approached 42 :D

Offline aeTIos

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Re: Why doesn't zero divided by zero work
« Reply #25 on: February 24, 2012, 03:50:28 am »
0/0?
You can't even write that out ;P
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Offline Jonius7

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Re: Why doesn't zero divided by zero work
« Reply #26 on: February 24, 2012, 03:51:44 am »
Yeah, we're learning Calculus (mostly differential atm) in Year 12, and we had a long discussion about limits.
The limit technically does not exist at the given value e.g.: lim h->0 f(x)=3x^2+7x-5.
At h=0 the equation is undefined as we're dividing by 0 (The answer could be infinity, for all we know, or it could be 9000.00000032), but the point of Calculus (well at least this part of calculus) is that we are to find the theoretical derivative of the equation when h=0, even though it technically does not exist.

Hope that made some sense, and I may have made a mistake.
« Last Edit: February 24, 2012, 03:51:58 am by Jonius7 »
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Offline aeTIos

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Re: Why doesn't zero divided by zero work
« Reply #27 on: February 24, 2012, 03:53:51 am »
I hate limits.
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Offline ACagliano

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Re: Why doesn't zero divided by zero work
« Reply #28 on: February 24, 2012, 10:21:48 am »
Think about this....

Take a number, n. Subtract 0 from it and keep going until n=0. Let me know when you're done. ;)

If you think about it that way, you get infinity. Technically, infinity IS an undefined number (the textbook definition of infinity is the inability to assign a definite quantity).

Offline Jonius7

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Re: Why doesn't zero divided by zero work
« Reply #29 on: February 25, 2012, 05:40:31 am »
There is one flaw in that tho, what if n were 0 to start off with then taking 0 from n would still equal 0 and I'd be done!!! :D. It's a good simple example tho, not taking the flaw into account.
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