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Topic: Continuous and discrete uniform distributions of N
Replies: 27   Last Post: Dec 28, 2012 9:45 PM

 Messages: [ Previous | Next ]
 Butch Malahide Posts: 894 Registered: 6/29/05
Re: Continuous and discrete uniform distributions of N
Posted: Dec 25, 2012 12:53 AM

On Dec 24, 11:22 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  Butch Malahide <fred.gal...@gmail.com> wrote:
>

> > On Dec 21, 8:41 pm, Bill Taylor <wfc.tay...@gmail.com> wrote:
>
> > > On Dec 22, 5:23 am, FredJeffries <fredjeffr...@gmail.com> wrote:
>
> > > > No one has ever anywhere actually used the concept of a uniform
> > > > distributions on N to solve any problem.

>
> > > Sure they have.  You can use it to calculate the probability
> > > that two randomly chosen naturals will be co-prime, for example.
> > > And many others of that type.

>
> You cannot do it using the standard reals because it would require the
> existence in the standard real number system of e an infinitesimal
> non-zero lambda smaller than any positive standard real but itself
> positive, and an infinite cardinality, card(|N), of the infinite set of
> naturals such that lambda * card(|N) = 1.

You are tacitly assuming that probability must be a countably additive
(as opposed to finitely additive) measure. It seems kind of arbitrary
to say that probability has to be countably additive but does not have

> Which cannot occur within the essentially unique (up to isomorphism of
> complete ordered Archimedian fields) standard real number system.

"Archimedean" is redundant; a complete ordered field is necessarily
Archimedean.

Date Subject Author
12/20/12 ross.finlayson@gmail.com
12/21/12 FredJeffries@gmail.com
12/21/12 Bill Taylor
12/22/12 Porky Pig Jr
12/22/12 ross.finlayson@gmail.com
12/24/12 FredJeffries@gmail.com
12/22/12 David Bernier
12/22/12 Butch Malahide
12/24/12 FredJeffries@gmail.com
12/24/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/26/12 gus gassmann
12/26/12 Butch Malahide
12/27/12 ross.finlayson@gmail.com
12/27/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/25/12 Shmuel (Seymour J.) Metz
12/25/12 Butch Malahide