Re: Infinite series are aproximations?

From: Dirk Van de moortel (dirkvandemoortel_at_ThankS-NO-SperM.hotmail.com)
Date: 11/18/04 

Date: Thu, 18 Nov 2004 17:33:27 GMT

"Emil" <epleite@hotmail.com> wrote in message news:faef3d8d.0411180703.5f1b8c8@posting.google.com...
> I've just read the text from this site:
> http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/TVFSeries.html
>
> Perhaps this is not the right NG to ask about this but I saw that the
> context involved GTR.
>
> What is wrong in saying that expansions of functions into a infinite
> series are technically "aproximations"?

Because "infinite series" are are not approximations at all.
This is exact:
    exp(x) = lim { n -> inf ; Sum{ i=0...n; x^i/(i!) } }
This is an approximation:
    exp(x) ~ Sum{ I=0...10; x^i/(i!) }

> If one is comparing an
> infinite series with an observation one must trucate the series
> somewhere. To me this constitutes a "technical aproximation" (if by
> technical we mean "practical") because no one can calculate infinity
> terms of a series.
>
> Can someone explain to me what is so wrong about that statement? :-)

>
> Emil.

I hope this helped a bit :-)

Dirk Vdm