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Author Topic: 1 = -1?  (Read 11614 times)

Offline myriam

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1 = -1?
« on: 15/05/2010 11:40:34 »
Some thing wrong right here ....  ???

1= -(-1)
1= -[(-1)˛]˝
1= -(1)˝
1=-√1
1=-1


« Last Edit: 15/05/2010 20:39:13 by myriam »


 

Offline JP

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1 = -1?
« Reply #1 on: 15/05/2010 13:20:34 »
Some thing wrong right here ....  ???

1= -(-1)
1= -[(-1)˛]˝

Since [(-1)˛]˝=(1)˝=1, line 2 doesn't follow from line 1.
 

Offline myriam

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1 = -1?
« Reply #2 on: 15/05/2010 13:45:22 »
Some thing wrong right here ....  ???

1= -(-1)
1= -[(-1)˛]˝

Since [(-1)˛]˝=(1)˝=1, line 2 doesn't follow from line 1.

good try JP but no , this isn't the right answer

 

Offline imatfaal

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1 = -1?
« Reply #3 on: 15/05/2010 16:06:46 »
finding a root gives two possibilities +/-1; and in situations like this when the square root is extracted, it is the negative root −1, not the positive root, (which is absurd for this equation).  which leaves the next line of your equation as 1=-(-1).
 

Offline myriam

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1 = -1?
« Reply #4 on: 17/05/2010 00:38:59 »
sorry imatfaal
The answer is more simple than you think
Give it an other try



 
 

Offline imatfaal

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1 = -1?
« Reply #5 on: 17/05/2010 12:19:16 »
as JP and I have both given valid answers from different perspectives - your correct answer better be a good one :-)
 

Offline myriam

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1 = -1?
« Reply #6 on: 17/05/2010 12:31:22 »
:)

well , lets give a chance to some other people to try also
till this Friday I'll see how much easy  or difficult maths are    :)
 

Offline graham.d

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1 = -1?
« Reply #7 on: 17/05/2010 13:53:06 »
I rather think imatfaal had it. Maybe it could be expressed more simply but you could show the faulty reasoning as follows:


let a=b=1
a=b
a˛=b˛
a˛-b˛=0
(a-b)(a+b)=0

so, as a≠0, b≠0
a+b=0 iff a-b≠0, which is false
a-b=0 iff a+b≠0, which is true

so a-b=0
a=b
so a=1 and b=1


Taking the square root give two answers (±1) and one is false because you are creating a quadratic equation then factorising to get the roots. The factorisation that gives you the false answer involves dividing by zero.
 

Offline myriam

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1 = -1?
« Reply #8 on: 17/05/2010 16:45:57 »
you showed that 1≠-1 which is true ,so you can do something easier,
you could show the faculty finding the error in my equations

try again graham.d :)
 

Offline graham.d

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1 = -1?
« Reply #9 on: 17/05/2010 17:22:01 »
The square root of 1 does not have one answer. It can be +1 or -1. You chose it (incorrectly) to be +1. I thought I showed, reasonable rigorously, why this choice was erronious because your solving of the quadratic equation involved a division by zero. Is there a fault in the proof? I give up.

This is why I'm a physicist and engineer and not a mathematician :-)
 

Offline Geezer

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1 = -1?
« Reply #10 on: 17/05/2010 19:17:03 »
1= -(-1)
1= -[(-1)˛]˝
1= -(1)˝
1=-√1
1=-1[/b]


Line 2 is invalid. The power 1/2 has to be inside the square bracket which makes the square brackets redundant and the power 2/2 which is of course, 1.
« Last Edit: 17/05/2010 19:40:32 by Geezer »
 

Offline myriam

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1 = -1?
« Reply #11 on: 17/05/2010 20:22:55 »
for all real numbers
√x˛ =|x|
    = x if x≥0
    =-x if x≤0


I don't see the error in the line 4  ,  √1 = 1 since  1>0 already

But the really error is no there :)

Geezer it is great you found the faulty line but the reasoning is not this,
find the theorem that demonstrates the error in line 2

just to tell you there are other faulty proof for 1=-1 like for example

-1=i.i=√-1 .√-1 =√(-1.-1) = √1 = 1  but where is the fault ???
this is an other challenge

I'm not telling the answer rapidly ;D  ,  think about it   



 

Offline Geezer

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1 = -1?
« Reply #12 on: 17/05/2010 20:46:32 »
1= -(-1)
1= -[(-1)˛]˝

1 = -(-1)
  = -[-(1˛)˝]
 

Offline myriam

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1 = -1?
« Reply #13 on: 17/05/2010 20:53:57 »
ok, where is the theorem telling that i can't  write  1= -[(-1)˛]˝  ??
 

Offline Geezer

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« Reply #14 on: 17/05/2010 21:22:45 »
ok, where is the theorem telling that i can't  write  1= -[(-1)˛]˝  ??


No theoerm required. You are substituting something that is not equal to -1. Show me how you get from my line 2 to your line 2.
 

Offline myriam

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1 = -1?
« Reply #15 on: 17/05/2010 21:30:51 »
ok, where is the theorem telling that i can't  write  1= -[(-1)˛]˝  ??


No theoerm required. You are substituting something that is not equal to -1. Show me how you get from my line 2 to your line 2.
oh yes there is a very important theoerme there
 

Offline Geezer

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1 = -1?
« Reply #16 on: 17/05/2010 21:40:53 »
Well, I suppose if you want to try to take the square root of a negative number, that's up to you.
 

Offline myriam

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1 = -1?
« Reply #17 on: 17/05/2010 21:53:07 »
 ;D

but do you know that  if x is any positive number, then the principal square root of −x is √-x =i.√x

The theorem is ..uhm ... not now, maybe someone is about to find it , lets wait   ;D


 

Offline Geezer

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« Reply #18 on: 18/05/2010 06:14:05 »
Yes, but it was j in my day.
 

Offline JP

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1 = -1?
« Reply #19 on: 18/05/2010 06:33:24 »
... then you all realized how silly it was to talk about jmaginary numbers.   ;D
 

Offline Geezer

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« Reply #20 on: 18/05/2010 06:50:47 »
I'm not even going to respond to that.

(OK - that will be my only response to that - apart from this one. Bummer! OK, well I .....heck with it!)
 

Offline myriam

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« Reply #21 on: 18/05/2010 11:53:03 »
lol
 

Offline imatfaal

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« Reply #22 on: 18/05/2010 14:05:33 »
Sorry Myriam but your maths is confused - the answer to your second question is at heart exactly the same as your first.

if
x^2=y^2
x = +/-y

with numbers
if x^2=1 then x= -1 or x= +1

it is for this reason that you CANNOT always say that (xy)^1/2 equals x^1/2.y^1/2 which disproves your second quiz. 


I find it much easier to understand and simpler to state that the root of a number can be either positive or negative and that this might create absurd and discardable results rather than your formulation.  You are saying that once you square a number that somehow the information of the number's sign is stored, waiting to be extracted once a root is taken - these are multistage procedures and there is no memory in the operand of the process which created it. Matthew

 

Offline myriam

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« Reply #23 on: 18/05/2010 22:25:59 »
Matthew you are so close to the theorem , very good
 

Offline myriam

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1 = -1?
« Reply #24 on: 20/05/2010 14:16:23 »
any other suggestions before the solution release
 

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1 = -1?
« Reply #24 on: 20/05/2010 14:16:23 »

 

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