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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Continuous and discrete uniform distributions of N
Posted: Dec 25, 2012 12:22 AM

In article
Butch Malahide <fred.galvin@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.

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

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