Klarinet Archive - Posting 000739.txt from 1997/11

From: Dirk Kussin <dirk@-----.de>
Subj: Re: Nyquist and analog
Date: Thu, 20 Nov 1997 13:31:12 -0500

Ian> I realise that the situation I described would not be an issue in
Ian> practice. I was just questioning the definition of Nyquist's
Ian> theorem.

Ian> I don't understand why you say that the probability of obtaining
Ian> all 0 crossings is precisely 0. There is an infinitely large set
Ian> of possible sets of samples and the probability of obtaining any
Ian> one is the same as any other. Therefore, if the probability of
Ian> getting all 0 crossings is 0 then the probability of getting any
Ian> set of samples must also be 0. This is obviously not true so the
Ian> probability of getting all 0 crossings cannot be 0.

I don't not know what "0 crossings" are, nor am I a probability
theorist, but your argumentation is wrong: it is possible that
infinitely many events have probability zero; for example, a similar
thing:

If you pick (randomly) an arbitrary real number (=rational or
irrational number), the probabilty, that your number is rational is
exactly zero. But there are of course infinitely many rational
numbers.

On the other hand, the probability that we will get flamed by others
of this list is certainly greater than zero (even 1). ;-)

Dirk

--
Dirk Kussin dirk@-----.de
Fachbereich 17 Mathematik Raum D2.323
Universitdt-GH Paderborn Tel. (+49) (5251) 60-2636
D-33095 Paderborn --------- http://www-math.uni-paderborn.de/~dirk/