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## #1 2013-07-24 00:50:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Find out the fallacy

'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 2013-07-24 03:38:43

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

Hi;

The second line is off.

because it is the principal value.

4 ≠ 5

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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## #3 2013-07-24 03:41:25

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,525

### Re: Find out the fallacy

hi Agnishom,

Hhhhmmmm.  Nice one!

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #4 2013-07-24 18:58:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

I do not get it.

'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 2013-07-24 20:02:10

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

Hi;

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.

Online

## #6 2013-07-24 21:39:33

SteveB
Member
Registered: 2013-03-07
Posts: 577

### Re: Find out the fallacy

I agree with bobbym in that it is the second line where the problem starts.

The square root function can only be used in this way if a disabiguation is made where
we either take the positive value so reverse a square of a positive number, or I suppose
take the negative value provided the original number was negative before being squared.
If there is no guarantee of the sign then both negative and positive cases of the number
squared then square rooted should be checked to see whether the equation is still true
in every case. Otherwise a true statement can imply an untrue one as you did purposefully.

However in the quadratic formula for instance the square root sign is used to indicate
that you can take both the positive and negative square root so the square root has to
allow you to take either the positive or negative case.

So let us start with a negative number so -1 then square it and get 1 then square root it
and we get 1. That is the trouble with using a function like square root as an inverse.
It is good for calculating things, but in a formal proof I find it difficult, because care has
to be taken for instance not to accidentally make a sign error which I have sometimes
done by accident in a tutor marked assignment (I remember I accidentally fudged the sign
of an otherwise correct proof and had a couple of marks taken off. I think that I had done
the proof first with one sign error which I knew must be there somewhere. I searched for
the "error" and "corrected it" only to find that according to the tutor it had 2 sign errors
which cancelled).

Anyway your example gives a good case something of the kind happening with a very
amusing consequence.

Last edited by SteveB (2013-07-25 00:27:05)

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## #7 2013-07-25 14:21:57

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

What is principle value?

'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 2013-07-25 15:26:52

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

I guess it is better called the principal square root, got my principals wrong again.

Anyway

Because √ means the principal square root ... the one that isn't negative!

http://www.mathsisfun.com/algebra/square-root.html

http://hotmath.com/hotmath_help/topics/ … -root.html

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.

Online

## #9 2013-07-25 15:58:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

Because √ means the principal square root ... the one that isn't negative!

So, where does the other root go?

'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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## #10 2013-07-25 16:11:11

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

So, where does the other root go?

You just do not use it.

When we are solving an equation we take both positive and negative roots. But generally  the √ operator means the principal square root which is always positive.

If you really want to see a tough one look at this fellow prove -1 = 1.

Kaboobly doo!

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.

Online

## #11 2013-07-26 00:19:52

SteveB
Member
Registered: 2013-03-07
Posts: 577

### Re: Find out the fallacy

You had 4 - 4.5 in effect.
This is -0.5
when you square that you get 0.25 then take the square root and you get 0.5 and the sign is removed.
So the assumption "if you square something then take the square root then the two cancel so you get the thing you started with"
has an exception caused by the fact that you either must not square a negative input to cause this problem - or must guarantee that the
sign is preserved always. If no such guarantee can be made the assumption is flawed.
In practice it is usually when you are trying to formally prove something that this is a problem because of the degree of rigour
expected, and because of the fact that you will want to consider a wide range of cases.
I am rather reluctant to say "you can never take the negative square root" because the quadratic formula and other results in maths
do depend upon the negative square root and sometimes real problems do need both solutions to a quadratic, but I cannot think
of any of the top of my head (some A level problems did need both solutions, or all 3 order 3 polynomial solutions etc.).

Last edited by SteveB (2013-07-26 03:27:32)

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## #12 2014-03-06 15:54:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

Confusing, very, that is, hmmm. Talk about another one, I shall.

Okay, is that? Hah?

Differentiating both sides with respect to n, you get

Yes, hmmm? Herh , herh

'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 2014-03-06 20:16:16

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,525

### Re: Find out the fallacy

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #14 2014-03-06 20:30:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

Oh. I did not think of that.

'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 2014-03-08 05:10:55

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Find out the fallacy

Another one:
a = 1, b = 1 so a = b
a*a = b * a
a^2 = ba
a^2 - b^2 = ba - b^2
(a+b)(a-b)=b(a-b)
a+b=b
1+1 = 1
2=1

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## #16 2014-03-08 05:15:20

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

Nice division by 0 in line 5.

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.

Online

## #17 2014-03-08 05:17:28

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Find out the fallacy

The thing is, it's kind of hard to notice if you look at it casually. Just looks like simple cancellation of factors. You can use it to prove 64=65 and there is a picture which supports that (except one error- one of the lines is not straight).

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## #18 2014-03-08 05:19:55

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,911

### Re: Find out the fallacy

Hi;

It does look like it is okay. It is noticeable because everybody knows 1 does not equal 2 so you going looking for it. But sometimes it is not so easy to find.

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.

Online

## #19 2014-03-08 05:42:09

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

Explain this

'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 2014-03-08 06:03:30

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,525

### Re: Find out the fallacy

Don't explain, just send me a bar please.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #21 2014-03-08 13:50:49

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,352

### Re: Find out the fallacy

Cycle through the pics and you'll see the bottom of the large middle piece that moves from L-R magically lengthen...no doubt by a total amount equalling 1 extra square of choccy.

If you look at the first image it is very apparent that the length of the right-hand side of the vacating piece (the one in the top right-hand corner) is much greater than that of the large middle piece whose two right-most vertical strips take its place. Subsequent images in the sequence show that length increasing by a small amount each time until it reaches the length of the vacating piece.

Maybe that stretchy bit contains some special growth ingredient, and if so, I wonder where you can get that ingredient? Any clues, anyone? I'm thinking of utilising just one block of choccy and opening a massive franchise business for selling chocolate pieces.

Last edited by phrontister (2014-03-08 20:03:55)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #22 2014-03-08 20:17:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,323
Website

### Re: Find out the fallacy

Oh. I see

'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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## #23 2014-03-08 23:59:31

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,000

### Re: Find out the fallacy

Hi phro

And you can always get funding by putting a dollar in your pocket and pulling out two dollars!

Last edited by anonimnystefy (2014-03-08 23:59:51)

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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## #24 2014-03-09 10:14:16

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,352

### Re: Find out the fallacy

Hi stefy,

You've reminded me of this old puzzle of mine - and maybe you've recalled it too, and your reference to producing the \$2 is to that, perhaps?

If the second scenario in my puzzle recurred often enough (or well before that, more likely) to cover the amount of funding required, that dumb shop assistant would find himself thrown out the door on his ear!

Last edited by phrontister (2014-03-09 21:02:38)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #25 2014-03-10 11:24:38

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,352

### Re: Find out the fallacy

The bottom section of the top right-hand corner piece also lengthens.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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