Waclaw (01)
From the point of view of practical mathematics, probability
over continuous distributions is defined through probability density
functions, with the probability for any interval being the integral of
the pdf over that interval. If you reduce the interval to zero, then the
probability goes to zero. No problem there. (02)
I'm not sure what you want to say with "P(exists x: > X=x) = 1"
since the domain of X is fixed by definition, and therefore "the
probability that X takes a value in its domain" doesn't seem to mean
very much - probability is about random events, not things that are true
by definition. (03)
Sean Barker
Bristol, UK (04)
This mail is publicly posted to a distribution list as part of a process
of public discussion, any automatically generated statements to the
contrary non-withstanding. It is the opinion of the author, and does not
represent an official company view. (05)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Waclaw Kusnierczyk
> Sent: 19 June 2007 09:03
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Probabilistic Ontologies
>
>
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> Barker, Sean (UK) wrote:
> > Waclaw
> >
> > Any interval of real numbers has cardinality Aleph-1 (not
> > Aleph-0) - that is rather the point of real numbers.
>
> Right. Actually, card(R) = 2^aleph_0, which equals aleph^1
> according to the continuum hypothesis.
>
> > In the usual
> > axiomatizations of Real numbers (and numbers in general)
> division is
> > the inverse of multiplication and 0 is not equal to 1 (the
> > multiplicative identity). The use of the Alephs is not part
> of the real number system.
>
> Is this to say that the paradox (P(X=x) = 0 and P(exists x:
> X=x) = 1) is supported by this axiomatization?
>
>
> vQ
>
>
>
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> (06)
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