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## #1 2013-06-16 02:07:29

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Limit

0 or does not exist?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #2 2013-06-16 02:16:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889

### Re: Limit

Yes, it is 0. Why should it not exist?

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2013-06-16 02:24:02

phanthanhtom
Member
Registered: 2012-06-22
Posts: 215

### Re: Limit

Yup. It is 0. Probably you mean there should be a sign (negative or positive) for infinity? Not needed in this case.

Last edited by phanthanhtom (2013-06-16 02:25:18)

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## #4 2013-06-16 02:33:29

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

OK

∞ or does not exist?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #5 2013-06-16 03:10:49

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

Hi;

I would say ∞.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #6 2013-06-16 03:11:04

phanthanhtom
Member
Registered: 2012-06-22
Posts: 215

it is infinity.

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## #7 2013-06-16 03:25:17

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

But isn't it different from different directions??

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #8 2013-06-16 03:30:20

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

That is very good, I always forget that. You are correct. It is undefined.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #9 2013-06-16 04:20:33

{7/3}
Member
Registered: 2013-02-11
Posts: 210

### Re: Limit

The second limit does not exist,it would exist if absolute value was used.

There are 10 kinds of people in the world,people who understand binary and people who don't.

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## #10 2013-06-16 04:27:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

Or if the denominator was x[sup]2[/sup]

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #11 2013-06-16 04:29:00

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

Then I would say it is infinity, because it has the same limit from both sides.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #12 2013-06-16 04:36:32

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

Yes. I was adding an option to post 9 actually

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #13 2013-06-16 04:39:01

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

Mathematica believes the first limit is infinity. Something about a projective plane...

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #14 2013-06-16 04:41:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

OK but my কলনবিদ্যা (pronounced something like "Kalanbidya" meaning Calculus) book does not agree that #4 is infinity

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #15 2013-06-16 04:46:15

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

Which one is number 4?

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #16 2013-06-16 13:06:34

{7/3}
Member
Registered: 2013-02-11
Posts: 210

### Re: Limit

The limit would also exist,if it was one sided limit.

There are 10 kinds of people in the world,people who understand binary and people who don't.

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## #17 2013-06-16 13:28:44

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

Agnishom wrote:

OK

∞ or does not exist?

This is number 4

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #18 2013-06-16 14:01:06

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

Oh yes, I would say it is undefined. I was just mentioning that M does not agree. The Wiki page explains why but I do not understand.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #19 2013-06-16 14:08:55

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #20 2013-06-16 14:16:26

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

http://en.wikipedia.org/wiki/Limit_of_a_function

It starts with this line:

In contrast, when working with the projective real line, infinities (much like 0) are unsigned, so, the central limit does exist in that context:

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #21 2013-06-16 14:29:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

Which do you not understand?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #22 2013-06-16 14:42:06

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,920

### Re: Limit

The whole thing about why that limit now exists.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #23 2013-06-16 15:56:27

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 19,940
Website

### Re: Limit

Does it exist?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #24 2013-06-16 16:33:48

{7/3}
Member
Registered: 2013-02-11
Posts: 210

### Re: Limit

In projective space there are 2 points at infinity in any direction,since 2 lines intersect in one point and a parallel line intersects both points at infinity,the two points are considered same,thus in case of real projective line infinity and nagetive infinity are the same points and the limit is simply infinity(or minus infinity,doesn't matters cause they're same)

Last edited by {7/3} (2013-06-16 16:38:01)

There are 10 kinds of people in the world,people who understand binary and people who don't.

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