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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

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
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Registered: 2012-06-22
Posts: 290

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
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

Re: Limit

Hi;

I would say ∞.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

phanthanhtom
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Registered: 2012-06-22
Posts: 290

it is infinity.

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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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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
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

Re: Limit

Which one is number 4?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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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
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,728

Re: Limit

The whole thing about why that limit now exists.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,536
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'
I'm not crazy, my mother had me tested.

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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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