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Dividing by zero
#19
RE: Dividing by zero
(September 22, 2013 at 9:00 pm)bennyboy Wrote: Simsim that's interesting, but I think it's still ambiguous. If the reduction is valid, you should be able to prove it by plugging your answer into the original formula-- which is obviously impossible.

Sorry, Bennyboy, this is the first time I log to the forum since you had posted your comment.

I am not sure I understand your question well but I hope this is the required answer:

There are two cases of dividing by zero:

1- The first is when numerator doesn't equal zero, i.e: a/0 , where "a" doesn't equal zero.
In this case the division operation has no meaning. You can't find a number which is when multiplied by zero gives another number other than zero. This is a hopeless case. Smile i.e, there is no number "b" when multiplied by "0" gives the number "a" (if "a" doesn't equal zero)

2- The second is when the numerator equals zero like the denominator. Generally the result of dividing zero by zero is undefined. Why do we use the expression undefined?? Because there is an infinite number of numbers when multiplied by zero give zero. So every number can be a result of the division operation 0/0

In Limits mathematicians deal with these cases when a operation such dividing by zero is undefined. In stead of dividing by zero directly they observe the function's value when the denominator approaches zero and then they find that there is a definite value the function approaches when the denominator approaches zero. For instance in the example which I posted previously:

x*(x+1)/x

when you make x equal these values:
1, 0.9, 0.7, 0.5, 0.3, 0.1, 0.05, 0.01, 0.001, 0.0000000001

you find that the fraction (or function) equals these values respectively:

2, 1.9, 1.7, 1.5, 1.3, 1.1, 1.05, 1.01, 1.001, 1.0000000001

i.e when x approaches zero the total fraction approaches 1.

Since making such calculations every time is difficult the easy way is to reduce the fraction into a simpler formula. The reduction process should include the omission of the "zero" in the denominator (x in our case).

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

Q.E.D Smile

Regards.
* Illusion is a big world ... and the world is a bigger illusion.
* Try to live happy ... try to make others live happy.
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Messages In This Thread
Dividing by zero - by Tea Earl Grey Hot - August 10, 2013 at 2:57 am
RE: Dividing by zero - by Silver - August 10, 2013 at 3:12 am
RE: Dividing by zero - by Tea Earl Grey Hot - August 10, 2013 at 3:14 am
RE: Dividing by zero - by Chas - October 9, 2013 at 7:10 pm
RE: Dividing by zero - by Darth - August 10, 2013 at 3:15 am
RE: Dividing by zero - by CleanShavenJesus - August 10, 2013 at 11:34 am
RE: Dividing by zero - by Captain Colostomy - August 10, 2013 at 3:42 am
RE: Dividing by zero - by FallentoReason - August 10, 2013 at 3:59 am
RE: Dividing by zero - by ITChick - August 10, 2013 at 7:18 am
RE: Dividing by zero - by Whateverist - August 10, 2013 at 10:21 am
RE: Dividing by zero - by Faith No More - August 10, 2013 at 11:58 am
RE: Dividing by zero - by LostLocke - August 10, 2013 at 11:53 am
RE: Dividing by zero - by Cyberman - August 10, 2013 at 9:08 am
RE: Dividing by zero - by Cyberman - August 10, 2013 at 10:43 am
RE: Dividing by zero - by Zidneya - September 7, 2014 at 12:21 am
RE: Dividing by zero - by FifthElement - August 10, 2013 at 11:37 am
RE: Dividing by zero - by pineapplebunnybounce - August 10, 2013 at 1:34 pm
RE: Dividing by zero - by bennyboy - August 17, 2013 at 9:05 pm
RE: Dividing by zero - by Simsim - September 18, 2013 at 5:03 am
RE: Dividing by zero - by bennyboy - September 22, 2013 at 9:00 pm
RE: Dividing by zero - by Simsim - September 30, 2013 at 6:17 am
RE: Dividing by zero - by Rational AKD - September 30, 2013 at 8:12 am
RE: Dividing by zero - by bennyboy - September 30, 2013 at 11:12 am
RE: Dividing by zero - by Simsim - September 30, 2013 at 9:06 am
RE: Dividing by zero - by little_monkey - September 30, 2013 at 9:26 am
RE: Dividing by zero - by Cyberman - September 30, 2013 at 10:58 am
RE: Dividing by zero - by little_monkey - October 1, 2013 at 12:20 pm
RE: Dividing by zero - by Simsim - October 1, 2013 at 4:57 pm
RE: Dividing by zero - by little_monkey - October 1, 2013 at 6:40 pm
RE: Dividing by zero - by Alex K - September 7, 2014 at 12:13 pm
RE: Dividing by zero - by Cyberman - October 1, 2013 at 12:32 pm
RE: Dividing by zero - by Cheerful Charlie - October 9, 2013 at 3:39 pm
RE: Dividing by zero - by feeling - December 1, 2013 at 8:26 am
RE: Dividing by zero - by Chas - December 1, 2013 at 5:48 pm
RE: Dividing by zero - by bennyboy - December 2, 2013 at 2:18 pm
RE: Dividing by zero - by reality.Mathematician - June 16, 2014 at 11:20 am
RE: Dividing by zero - by vorlon13 - June 16, 2014 at 12:51 pm
RE: Dividing by zero - by reality.Mathematician - June 17, 2014 at 8:35 am
RE: Dividing by zero - by ShaMan - June 16, 2014 at 7:25 pm
RE: Dividing by zero - by Madness20 - September 6, 2014 at 6:51 pm
RE: Dividing by zero - by StealthySkeptic - September 6, 2014 at 9:20 pm
RE: Dividing by zero - by Whateverist - September 6, 2014 at 6:54 pm
RE: Dividing by zero - by naimless - September 6, 2014 at 9:28 pm
RE: Dividing by zero - by vorlon13 - September 6, 2014 at 9:30 pm
RE: Dividing by zero - by Mudhammam - September 7, 2014 at 1:46 am
RE: Dividing by zero - by StealthySkeptic - September 7, 2014 at 1:53 am
RE: Dividing by zero - by Mudhammam - September 7, 2014 at 12:42 pm
RE: Dividing by zero - by Alex K - September 7, 2014 at 3:10 pm
RE: Dividing by zero - by robvalue - September 8, 2014 at 3:37 am
RE: Dividing by zero - by StealthySkeptic - September 8, 2014 at 1:05 pm
RE: Dividing by zero - by Madness20 - September 8, 2014 at 3:26 pm
RE: Dividing by zero - by L.A.F.2. - October 1, 2014 at 7:12 pm
RE: Dividing by zero - by Alex K - October 1, 2014 at 7:17 pm
RE: Dividing by zero - by L.A.F.2. - October 1, 2014 at 8:17 pm
RE: Dividing by zero - by bennyboy - October 2, 2014 at 5:17 am
RE: Dividing by zero - by Alex K - October 2, 2014 at 5:38 am
RE: Dividing by zero - by Aractus - October 2, 2014 at 6:52 am
RE: Dividing by zero - by vorlon13 - October 2, 2014 at 9:25 am
RE: Dividing by zero - by Alex K - October 2, 2014 at 10:33 am
RE: Dividing by zero - by Cyberman - October 2, 2014 at 10:37 am
RE: Dividing by zero - by vorlon13 - October 2, 2014 at 10:40 am
RE: Dividing by zero - by Chas - October 3, 2014 at 3:05 pm
RE: Dividing by zero - by *Deidre* - October 4, 2014 at 10:57 am
RE: Dividing by zero - by Chas - October 4, 2014 at 10:59 am
RE: Dividing by zero - by *Deidre* - October 4, 2014 at 11:05 am
RE: Dividing by zero - by Alex K - October 4, 2014 at 7:26 pm
RE: Dividing by zero - by Chas - October 4, 2014 at 7:50 pm
RE: Dividing by zero - by little_monkey - October 5, 2014 at 11:20 am
RE: Dividing by zero - by Jenny A - October 5, 2014 at 11:35 am
RE: Dividing by zero - by *Deidre* - October 5, 2014 at 1:27 pm
RE: Dividing by zero - by Surgenator - October 5, 2014 at 3:00 pm
RE: Dividing by zero - by Jenny A - October 5, 2014 at 3:54 pm
RE: Dividing by zero - by *Deidre* - November 7, 2014 at 10:51 am
RE: Dividing by zero - by Magilla - October 24, 2014 at 9:06 pm
RE: Dividing by zero - by Smaug - November 19, 2014 at 3:45 pm
RE: Dividing by zero - by Mental Outlaw - January 5, 2015 at 9:58 pm
RE: Dividing by zero - by bennyboy - January 8, 2015 at 11:40 am
RE: Dividing by zero - by Grandizer - January 18, 2015 at 12:31 am

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