Larry Fontaine wrote: 
> I can prove 1 does not equal 1.
> 
> Start with -1 = -1. (An assumption) (Note... to line up the equation
> processes, put this message on "fixed width" font.)
> 
> -1               =               -1 (assumption)
> -1/1             =             1/-1 (fraction form)
> sqrt(-1/1)       =       sqrt(1/-1) (sqrt both sides)
> sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) (radicals)
> sqrt(-1)*sqrt(-1)=  sqrt(1)*sqrt(1) (cross-multiply)
> -1               =                1
> 
> Here we have just shown that 1 = -1.
> 
> And indeed, all mathematical proofs are based on thoery.
	May I point out that sqrt(-1) isn't defined? sqrt is only a function
from the set of positive reals into itself... (I know, if you take the
complexes, you can find a number (well two actually, that's the problem)
whose square is -1, but since you couldn't know wich to choose you can't
define *the* square root)

		Jerome

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