1 = -1?

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Offline myriam

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« 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 »
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Offline JP

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« 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.

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Offline myriam

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« 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

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Offline imatfaal

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« 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).
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

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Offline myriam

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



 
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Offline imatfaal

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« 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 :-)
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

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Offline myriam

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« 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    :)
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Offline graham.d

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« 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.

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Offline myriam

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« 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 :)
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Offline graham.d

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« 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 :-)

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Offline Geezer

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« 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 »
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Offline myriam

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« 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   



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Offline Geezer

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

1 = -(-1)
  = -[-(1˛)˝]
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline myriam

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« Reply #13 on: 17/05/2010 20:53:57 »
ok, where is the theorem telling that i can't  write  1= -[(-1)˛]˝  ??
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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.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline myriam

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« 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
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Offline Geezer

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« 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.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline myriam

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« 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]


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Offline Geezer

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« Reply #18 on: 18/05/2010 06:14:05 »
Yes, but it was j in my day.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline JP

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

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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!)
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline myriam

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

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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
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Offline myriam

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« Reply #24 on: 20/05/2010 14:16:23 »
any other suggestions before the solution release
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Offline myriam

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« Reply #25 on: 24/05/2010 22:05:37 »
hello

(x)E(a*b)= ((x)E(a))E(b) if and only if x>0

[:)]
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Offline JP

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« Reply #26 on: 25/05/2010 02:25:15 »
What is E?  What do all the extra parentheses mean?

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Offline imatfaal

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« Reply #27 on: 25/05/2010 14:05:18 »
hello
(x)E(a*b)= ((x)E(a))E(b) if and only if x>0
[:)]

Do you mean this
[attachment=12075]

let x=-4, a=2, b=3

i.  (-4)^(2*3)    = 4096
ii. (-4)^2 = 16
             16^3 = 4096

A. I fail to see how this connects to initial problem (per TommyA)
B. Unless I am untangling your brackets incorrectly I don't agree with your statement
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Offline imatfaal

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« Reply #28 on: 25/05/2010 17:19:22 »
Tommy - E was in the past (I think) used to mean Exponential: similar to using x^2 to mean x squared we could write xE2. But I am by no means sure.

You're right, the initial problem was a "proof" that 1= -1.  And I don't see how the equation that Myriam gave (which I cannot interpret sensibly) has anything to do with it.
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline Geezer

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« Reply #29 on: 26/05/2010 03:09:20 »

I looked at a post JP asked what E was and I did not see a response.
And I see JP has allot on the ball from other prior posts
  

I think JP is too young to remember the Exponent button on calculators. I'm pretty sure he's never seen a slide rule either [;D] I've still got mine.

It's a bit scary to realize that I was raised in a different era, although, that would probably explain why my knees tend to seize up.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline JP

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« Reply #30 on: 26/05/2010 04:08:22 »
I think I saw one of those calculators in a museum once.  And slide rule?  Does that have something to do with playground behavior?

(The programs I use to do mathematics these days use (x)E(y)=xey rather than xy). 

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Offline Geezer

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« Reply #31 on: 26/05/2010 06:55:07 »
Yea and a book of log base 10
 

Ah yes! The dreaded log tables. If I can find mine, I'll post a photo for posterity.
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Offline imatfaal

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« Reply #32 on: 26/05/2010 19:19:34 »
Lovely stuff Tommy - I have an old cambidge scientific somewhere (led screen); one of the first pocket calculators easily available in UK.  I think it was bought for elder brothers doing o'level maths in 74 - maybe for a'level.
to my shame I still don't know how to use a slide rule
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Offline Geezer

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« Reply #33 on: 27/05/2010 00:22:38 »
Alas, my Sinclair Scientific has long since bit the dust.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline RD

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« Reply #34 on: 27/05/2010 02:11:28 »
Alas, my Sinclair Scientific has long since bit the dust.

Some Sinclair products can be "emulated" on your PC ...
 http://en.wikipedia.org/wiki/List_of_computer_system_emulators#Sinclair_ZX81

Texas instrument calculators too ...

[attachment=12111]
http://lpg.ticalc.org/prj_tiemu/images/tiemu-macosx-2.png

http://en.wikipedia.org/wiki/List_of_computer_system_emulators#Texas_Instruments_calculators

... 1992 vintage ... TI92
[attachment=12103]
« Last Edit: 27/05/2010 02:36:56 by RD »

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Offline RD

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« Reply #35 on: 27/05/2010 03:00:56 »
Imagine having this calculator for 19 years, then finding it in a lost corner of the house, with no an instructional guidebook. Hair is getting thin from constant head and scalp abuse.
My wife says, sure you save everything else.
It will Show in the most unlikely place.

Like the internet ...

[attachment=12113]
http://ec1.images-amazon.com/media/i3d/01/A/man-migrate/MANUAL000050415.pdf

« Last Edit: 27/05/2010 04:22:08 by RD »

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Offline imatfaal

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« Reply #36 on: 27/05/2010 12:36:50 »

o'level maths in 74 - maybe for a'level.
Terminology what are these related to in layman's terms they are really new to me.. does the prefix (AZ) apply?
Is it like the state here call it EEG... (math 101) etc... being the most elementry to the Diff EQ ?
 

Qualifications which are almost as outdated now as the sliderules.  O'levels (ordinary level) were taken at age 16 - and one would take a whole bunch ranging from physics to music, french to woodwork, english lit to philosphy (I ended up with 13); and were used, amongst other things, to filter access to last two years of school education (what we called the sixth form).  A'levels (advanced level) were much more specialised and taken at 18, one would generally take three or four; these were used to filter entrance to university.  Graded between A-E (and U for terrible), A-C were passes at O'level, A-E at A'level.  other wierder ones were AO (alternative ordinary - often maths) and S (special).   Its all changed now.  Someone with kids of right age can explain further   
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Offline BenV

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« Reply #37 on: 28/05/2010 17:28:57 »

o'level maths in 74 - maybe for a'level.
Terminology what are these related to in layman's terms they are really new to me.. does the prefix (AZ) apply?
Is it like the state here call it EEG... (math 101) etc... being the most elementry to the Diff EQ ?
 

Qualifications which are almost as outdated now as the sliderules.  O'levels (ordinary level) were taken at age 16 - and one would take a whole bunch ranging from physics to music, french to woodwork, english lit to philosphy (I ended up with 13); and were used, amongst other things, to filter access to last two years of school education (what we called the sixth form).  A'levels (advanced level) were much more specialised and taken at 18, one would generally take three or four; these were used to filter entrance to university.  Graded between A-E (and U for terrible), A-C were passes at O'level, A-E at A'level.  other wierder ones were AO (alternative ordinary - often maths) and S (special).   Its all changed now.  Someone with kids of right age can explain further  

I'll take that challenge.

This should be relatively up to date, but for the UK only...

At 16, you take GCSE exams (general certificate of secondary education) - roughly equivalent to O levels.

A Levels are now split, to encourage diversity - most 16+ students now take 6 AS levels for one year, then can chose to 'enhance' some of them up to full A levels by studying a subset of those subjects for an extra year.  Some (but very few) UK schools offer the International Baccalaureate - an alternative to A levels.

There are other options which are largely less academic and more practical - such as City & Guilds qualifications or GNVQs (general national vocational qualifications).