Find out the fallacy

Agnishom · 2013-07-24 00:50:57

bobbym · 2013-07-24 03:38:43

Hi;

The second line is off.

because it is the principal value.

4 ≠ 5

Bob · 2013-07-24 03:41:25

hi Agnishom,

Hhhhmmmm. Nice one!

Bob

Agnishom · 2013-07-24 18:58:35

I do not get it.

bobbym · 2013-07-24 20:02:10

Hi;

SteveB · 2013-07-24 21:39:33

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)

Agnishom · 2013-07-25 14:21:57

What is principle value?

bobbym · 2013-07-25 15:26:52

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

Agnishom · 2013-07-25 15:58:41

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

So, where does the other root go?

bobbym · 2013-07-25 16:11:11

So, where does the other root go?

You just do not use it.

√36 = 6 not (- 6) read SteveB's comments.

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!

SteveB · 2013-07-26 00:19:52

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)

Agnishom · 2014-03-06 15:54:35

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

Bob · 2014-03-06 20:16:16

Bob

Agnishom · 2014-03-06 20:30:12

Oh. I did not think of that.

ShivamS · 2014-03-08 05:10:55

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

bobbym · 2014-03-08 05:15:20

Nice division by 0 in line 5.

ShivamS · 2014-03-08 05:17:28

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).

bobbym · 2014-03-08 05:19:55

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.

Agnishom · 2014-03-08 05:42:09

9cc842561b.b960c17883.OayQSW.gif

Explain this

Bob · 2014-03-08 06:03:30

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

Bob

phrontister · 2014-03-08 13:50:49

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)

Agnishom · 2014-03-08 20:17:08

Oh. I see

anonimnystefy · 2014-03-08 23:59:31

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)

phrontister · 2014-03-09 10:14:16

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)

phrontister · 2014-03-10 11:24:38

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

Math Is Fun Forum

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

Find out the fallacy

#2 2013-07-24 03:38:43

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

#5 2013-07-24 20:02:10

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

#8 2013-07-25 15:26:52

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

#13 2014-03-06 20:16:16

Re: Find out the fallacy

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

Re: Find out the fallacy

#15 2014-03-08 05:10:55

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

#20 2014-03-08 06:03:30

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

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

Re: Find out the fallacy

#24 2014-03-09 10:14:16

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

Re: Find out the fallacy

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