Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Continuous and discrete uniform distributions of N
Posted:
Dec 25, 2012 12:22 AM
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In article
<6e340766-2e08-4966-b497-0c4d834979a1@10g2000yqo.googlegroups.com>,
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.
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