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**RauLiTo****Member**- Registered: 2006-01-11
- Posts: 142

hi guys ... how are you all ?

well ... my friend said that there is a solution for the equation :

3 / X = 4 / X ... i told him immediately thats impossible

whats ur opinion ? and if not why ?!:cool:

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**naturewild****Member**- Registered: 2005-12-04
- Posts: 30

x = 0 counts as a solution right?

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**RauLiTo****Member**- Registered: 2006-01-11
- Posts: 142

i don't think so !!!

we cant divide be zero !!! its unknown

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**naturewild****Member**- Registered: 2005-12-04
- Posts: 30

3/x = 4/x

is the same as

x/3 = x/4

So x = 0 works in this case

Or you can multiple the quesiton by x² and you will get 3x = 4x, which gives you x = 0.

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**numen****Member**- Registered: 2006-05-03
- Posts: 115

But if x=0 is a solution, the original question is invalid!

Bang postponed. Not big enough. Reboot.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

numen wrote:

But if x=0 is a solution, the original question is invalid!

only if you dont like infinity

but really, i think you can say x = 0 is a solution.

as x approaches 0, the value of 4/x and 3/x both approach infinity, and become infintisamely different

*Last edited by luca-deltodesco (2006-05-31 23:29:43)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,968

A simple solution:-

3X=4X

4X-3X=0

X=0

Simple, isn't it?

Character is who you are when no one is looking.

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**RauLiTo****Member**- Registered: 2006-01-11
- Posts: 142

no solution = anything expect the zero

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

Reductio Ad Absurdum (Proof by Contradiction):

Let us assume it is a true equation

Start with: 3/x = 4/x

Multiply both sides by x: 3=4

Awww, it din't work

So equation is invalid (within the rules of algebra anyway, but that doesn't rule it out completely)

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

NO SOLUTION Because X in the equation do not have a defination on 0.

But you can just put a very large number (positive or negative) as a "solution".

When X is very large, the difference between 3/X and 4/X is very small, hence neglactable in some sense.

Praticly, think of a pair double stars from far far away, does the gravity from the two make any difference for you?

Still, I will not say the answer is infinity, since it is my belief to deny a single nonvariable infinity.

**X'(y-Xβ)=0**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

When you simplify equations, you can gain solutions that weren't originally there.

For example:

y = x/x

If you try to graph that without simplifying first, you would get a line at y = 1 with a hole at zero. Because of this, upon simplification, we must say:

y = 1, except when x = 0.

The same must be done here as well.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

luca-deltodesco wrote:

as x approaches 0, the value of 4/x and 3/x both approach infinity, and become infintisamely different

Anyone care to dispute this limit luca-deltodesco suggests is zero? I do.

**igloo** **myrtilles** **fourmis**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Sure.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

Ricky wrote:

Sure.

yeh i realised that about 20 minutes after i posted it, but the thread seemed to have came to an end, so i didnt change it

The Beginning Of All Things To End.

The End Of All Things To Come.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Even worse is when you realize you made a really dumb mistake in a post you just wrote, but you know you won't have computer access for 5 hours and there is no way for you to change it. Those can be one of the longest times on earth.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

For the limes thingy:

If

that doesn't imply:

and...again...NO SOLUTION!!!

(If there was some limmy solution, then all math theory would have been contradictory-and this would have been TERRIBLE!!)

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

Are you saying "limits" thingy, which means approaching an x number and coming as close as you can get to x which then suggests an f(x), but it might not be exactly the f(x) at the number x?

**igloo** **myrtilles** **fourmis**

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**Nigel****Member**- Registered: 2006-05-25
- Posts: 14

x=0 or x=∞

I think...

Blog: www.lassic.blogspot.com

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The only time that

is when f(x) is continuous at c. If it's not, then f(c) can be any value, including no value at all.Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Consider a function: {x} - the real part of x. ({2.5}=0.5, {5/3}=1/3, {sqrt(2)}=sqrt(2)-1}).

Let see what's the limit as x goes to 2.

Here we have 2 different limits: left-limit and right-limit:

See? You can't conclude what is f(x) using only limits.

(and there are more interesting examples: the function

)

::Edited. Changed some latex text.

*Last edited by krassi_holmz (2006-06-02 20:50:12)*

IPBLE: Increasing Performance By Lowering Expectations.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Just to let you know, you can use \mbox to put in text:

`\mbox{if x is irrational}`

Produces:

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Thank you. I tryed with \text{...}, but it gave an error.

IPBLE: Increasing Performance By Lowering Expectations.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

krassi_holmz wrote:

For the limes thingy:

,

If

that doesn't imply:and...again...NO SOLUTION!!!

(If there was some limmy solution, then all math theory would have been contradictory-and this would have been TERRIBLE!!)

No perfect solution.

But accepted solution. If you find a 0 on a calculator display credible for 0. Then there are many answers.

**X'(y-Xβ)=0**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

OK. x is not "exactly" null. But what's happening if x is infinitesimal?

IPBLE: Increasing Performance By Lowering Expectations.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

I don't know real infinity thing, what i know is an amount divided by a small number.

I find a case. do you think there is too much difference between enjoying Bill Gates' fortune and owning Warrant Buffet's investment?

Besides, it's not me who proposed infinity is an answer.

Anyway, to Raulito, if you accept some error and do not persuit absolute accuracy, there are accepted solutions.

Otherwise, there is none.

**X'(y-Xβ)=0**

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