----- Original Message -----
From: "Reef Fish" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Wednesday, March 31, 2004 9:20 AM
Subject: Re: [SCUBA-SE] SCUBA-SE Digest - 24 Mar 2004 to 25 Mar 2004
(#2004-79)


> On Tue, 30 Mar 2004 21:42:04 +0700, Susanne Vitoux <[log in to unmask]>
> wrote:
>
> >> Bjorn, you're a remarkably well-read man about mathematicians even
> >> though he couldn't even find the error in the clever Chinese proof
> >> that 64 = 65.  :-)
> >>
> >
> >Would you please share this proof? Just out of curiosity.
>
> Bjorn should share it, because it is really a VERY CLEVER proof
> that required NO mathematical background, and it stumped one of
> our Great Minds, Bjorn!  :-)  Besides, I don't have the pictures
> of the geometric figures that constituted the proof.
>
>
> >In the very
> >unlikely case you never saw the one on 0.99999(ad infinitum) = 1,
> >I'll be happy to give it.
>
> Please do.  I've never seen it put that way.  But that's a truth
> in limits or asymptotics.  :-)   Something like the opposite of Z
> eno's paradox ... 1/2 + 1/4 + 1/8 + 1/16 + ... = 1.
> >

Let's set x = 0.99999()   (since I do not know the proper notation on the
computer, the () indicates the period 9)

10x = 9.99999()
10x - x = 9.99999() - 0.99999()
9x = 9
x = 9/9 = 1

CQFD :-)

Jean-Marc