Re: Help with confirmation on a small bit of assembly?

["John B. Matthews" <nospam@nospam.com>]

In article <pvgcr2ljj2nilnh3em53656c16eiihj3to@4ax.com>,
 "Jeff Blakeney" <jeff.blakeney@a2central.com.remove-xme-this> wrote:

>   To: mdj
> On Tue, 23 Jan 2007 05:32:11 -0800, "mdj" <mdj.mdj@gmail.com> wrote:
> 
> >David Empson wrote:
> >
> >> I'm sure someone can come up with a proof that 16 = 15, based on the 1 =
> >> 0 concept. :-)
> >
> >Damn you Empson! I'd never seen that before, and now that I've Googled,
> >I'll be awake for days trying to decide if it's funny or not
> 
> A college classmate showed me one of those on a chalk board one day
> many years ago but the fact that he used a divide by zero in the
> process made the result meaningless.  :-)
> 
> Jeff Blakeney
> - to send me e-mail, CUT the obvious from my e-mail address
> --- Synchronet 3.13a-Win32 NewsLink 1.83
> A2Central.com - Your total source for Apple II computing.

It is well known that 16 = 15 for sufficiently large values of 15:-)

1. -240 = -240 ; identity
2. 256 - 496 = 225 - 465 ; still equal
3. 16^2 - 16(31) = 15^2 - 15(31) ; factor each side
4. 16^2 - 16(31) + (31/2)^2 = 225 - 15(31) + (31/2)^2 ; complete square
5. (16 - 31/2)^2 = (15 - 31/2)^2 ; factor each side again
6. 16 - 31/2 = 15 - 31/2 ; take square root & add 31/2, each side
7. 16 = 15 ; qed?

No division by 0; can you spot the bogus step? Analysis here:

http://en.wikipedia.org/wiki/False_proof, section 1.11

It appears that you can construct this "proof" for consecutive a and b 
(a > b), using the identity

a^2 - a(a^2 - b^2) = b^2 - b(a^2 - b^2).

But it's late, and I'm _way_ off topic:-)

-- 
John Matthews
jmatthews at wright dot edu
www dot wright dot edu/~john.matthews/