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

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'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'

'You made a human being happy! There is no further achievement.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,418

hi Agnishom,

Hhhhmmmm. Nice one!

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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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'

'You made a human being happy! There is no further achievement.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 557

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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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'

'You made a human being happy! There is no further achievement.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

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!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

So, where does the other root go?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You made a human being happy! There is no further achievement.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

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!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 557

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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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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You made a human being happy! There is no further achievement.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,418

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Oh. I did not think of that.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You made a human being happy! There is no further achievement.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,555

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Nice division by 0 in line 5.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,555

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Explain this

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You made a human being happy! There is no further achievement.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,418

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

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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Oh. I see

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You made a human being happy! There is no further achievement.' -bobbym

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

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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