Re: The Falsifiable Theory of Design/Existance

In message <earle.jones-A74991.20595825012006@xxxxxxxxxxxxxxxxxxxxxxxx>
Earle Jones <earle.jones@xxxxxxxxxxx> wrote:

> In article <932a4fed4d.tigger@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
> Nick Roberts <tigger@xxxxxxxxxxxxxxxxxxxxx> wrote:
>
> > In message <1137881664.784643.238610@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
> > "Navillus" <cwsullivan@xxxxxxxxxxx> wrote:
> >
> > > Hypothesis: The Universe and all Life was Designed
> > >
> > > Evidence: All life requires existance, and existance implies
> > > purpose.
> > >
> > > Falsifiable if you can show any of the following:
> > > * Life doesn't exist
> > > * Life can arise without actually existing
> > > * Existance doesn't imply purpose
> > > * Sqrt(-1) != i
> >
> > Well, there's your problem, you see. Technically, sqrt(-1) = +/-i.
> >
> > On your own rules, your hypothesis is falsified.
>
> *
> No.
>
> By convention the expression sqrt(x) refers to the positive square
> root of x.

But that is _just_ convention, rather than rigorous mathematics.

> I think you are confusing the solution to the polynomial equation:
>
> x^2 + 1 = 0

And that is different to x = sqrt(-1) because?

The problem with defining sqrt(-1) to be +i rather than +/-i is that
it (-1) becomes a special case. In the more general case, sqrt(a+bj)
has to consider both roots to make sense of the geometric
representation of complex numbers (i.e. Argand diagrams).

--
Nick Roberts tigger @ orpheusinternet.co.uk

.

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