[NatureNS] Christmas brain teazer

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Date: Wed, 20 Dec 2006 09:14:10 -0800 (PST)
From: Paul MacDonald <paulrita2001@yahoo.com>
To: naturens@chebucto.ns.ca
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Hi Dave
( a - b - c) = 0;
What he says is nothing equals nothing!
Sound good to me.
Many a computer programmer spent long hours figuring
that one out - been there - done that!
Have a nice winter
Paul

--- David & Alison Webster <dwebster@glinx.com> wrote:

> Dear All,     Dec 20, 2006
>     I recently came across an old article about
> Raymond Smullyan, a
> highschool dropout who e.g. satisfied the course
> requirements for a PhD
> in Math and Philosophy by teaching the required
> courses. He also created
> many logic puzzles. One thing leads to another, so I
> blew the dust off
> of an old copy of Martin Gardner's 1959 Mathematical
> Puzzles and
> Diversions.
> 
>     One of his fallacies follows. I hope you have
> not seen this previously.
> Proof that unequal numbers are equal
> 
>     Given two numbers a & b such that b is smaller
> than a by an amount
> c; thus
> 
> a = b + c
> 
> prove that a = b
> 
> multiply both sides by (a - b) to obtain--
> 
> a^2 - ab = ab +ac - b^2  - bc
> 
> subtract ac from both sides to obtain
> 
> a^2 - ab - ac = ab - b^2  - bc
> 
> Factor :
> a ( a - b -c) = b ( a - b -c)
> 
> Divide both sides by ( a - b - c) to obtain
> 
> a = b
> 
> QED
> 
>     "The road to correct conclusions is full of
> pitfalls" (DHW, Dec 20, 
> 2006).
> 
> Merry Christmas, Dave Webster, Kentville
> 
> 
> 
> 


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