Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2006-05-31 21:03:59

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

... equation ...

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 ...

Offline

#2 2006-05-31 21:09:43

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

Re: ... equation ...

x = 0 counts as a solution right?

Offline

#3 2006-05-31 21:22:13

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

Re: ... equation ...

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 ...

Offline

#4 2006-05-31 21:29:51

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

Re: ... equation ...

3/x = 4/x

is the same as

x/3 = x/4

So x = 0 works in this case smile

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

Offline

#5 2006-05-31 22:21:20

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

Re: ... equation ...

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


Bang postponed. Not big enough. Reboot.

Offline

#6 2006-05-31 23:20:33

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

Re: ... equation ...

numen wrote:

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

only if you dont like infinity tongue

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.

Offline

#7 2006-05-31 23:47:35

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,122

Re: ... equation ...

A simple solution:-

3X=4X

4X-3X=0

X=0

Simple, isn't it? smile big_smile smile


Character is who you are when no one is looking.

Offline

#8 2006-05-31 23:55:58

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

Re: ... equation ...

no solution = anything expect the zero


ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

Offline

#9 2006-06-01 00:43:54

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: ... equation ...

Reductio Ad Absurdum (Proof by Contradiction):

Let us assume it is a true equation smile

Start with: 3/x = 4/x
Multiply both sides by x: 3=4

Awww, it din't work sad

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


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Offline

#10 2006-06-01 01:34:36

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

Re: ... equation ...

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

Offline

#11 2006-06-01 06:32:17

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

Re: ... equation ...

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..."

Offline

#12 2006-06-01 08:08:21

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,564

Re: ... equation ...

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

Offline

#13 2006-06-01 08:49:45

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

Re: ... equation ...

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..."

Offline

#14 2006-06-01 09:32:25

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

Re: ... equation ...

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 tongue


The Beginning Of All Things To End.
The End Of All Things To Come.

Offline

#15 2006-06-01 12:24:04

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

Re: ... equation ...

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..."

Offline

#16 2006-06-02 05:24:43

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

Re: ... equation ...

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.

Offline

#17 2006-06-02 15:25:08

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,564

Re: ... equation ...

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

Offline

#18 2006-06-02 16:10:09

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

Re: ... equation ...

x=0 or x=∞
I think...


Blog: www.lassic.blogspot.com

Offline

#19 2006-06-02 16:33:05

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

Re: ... equation ...

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.


"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..."

Offline

#20 2006-06-02 20:20:18

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

Re: ... equation ...

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

)
smile
::Edited. Changed some latex text.

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#21 2006-06-02 20:33:23

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

Re: ... equation ...

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

\mbox{if x is irrational}

Produces:


"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..."

Offline

#22 2006-06-02 20:48:37

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

Re: ... equation ...

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#23 2006-06-03 01:43:15

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

Re: ... equation ...

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

Offline

#24 2006-06-03 03:59:42

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

Re: ... equation ...

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#25 2006-06-03 21:18:52

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

Re: ... equation ...

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

Offline

Board footer

Powered by FluxBB