Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Continuous and discrete uniform distributions of N
Posted: Dec 25, 2012 1:48 AM

In article
Butch Malahide <fred.galvin@gmail.com> wrote:

> 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

The standard definition of probability requires that the sum of the
probabilities over ANY set of sets making up a partition of the space be
equal to one.

If you want to impose some non-standard definition, that is your
prerogative, but you must not expect all others to accede to it.
>
> > 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