Re: A little lesson for sqrt(144) year olds.

From: Jesper Pedersen (jesper_at_befunk.com)
Date: 07/01/04 

Date: Thu, 1 Jul 2004 10:33:29 +0200

"Androcles" <androc1es@nospamblueyonder.co.uk> wrote in message
news:kwCEc.88$rd1.1081531@news-text.cableinet.net...
<snip>
> | You need to understand the fundamental difference between solving x^2=2
> for
> | x
>
> I think the solution is -1.4142135623730950488016887242097.
> Let's see.
> -1.4142135623730950488016887242097 *
> -1.4142135623730950488016887242097 = 2.
> Yep, I'm right.

Almost, but not quite right. There are two solutions to the equation, yours
is one of them. I suspect that you know this, or at least I sincerely hope
so.

> and applying the function sqrt(2). the sqrt is DEFINED as being positive.
>
> Is it?
> if x = [-b +/- sqrt(b^2 - 4ac]/2a, is b always positive?

What does that have to do with sqrt(x) being positive by definition?
sqrt(b^2-4ac) is always positive, but you may choose b to be whatever suits
your fancy. Why do you even choose to write the equation the way you do? If
you believe sqrt(x) to be both positive and negative, why the need for the
+/- in front of it?

> | Otherwise how would equalities such as sin(Pi/4) = sqrt(2)/2 make any
> sense
> | at all? Surely you wouldn't claim that sin is dual-valued?
> That rather depends on whether you use (x, iy) or (x,y), doesn't it?
> Androcles.

I fail to see how sin(Pi/4) can ever be anything other than sqrt(2)/2 > 0.
And let's just stick to x belonging to R shall we? Would you at least agree
then, that sin(x) is not dual-valued? Or am I wasting time on a troll?

/ Jesper P

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