On Dec 24, 11:22 pm, Virgil <vir...@ligriv.com> wrote: > In article > <6e340766-2e08-4966-b497-0c4d83497...@10g2000yqo.googlegroups.com>, > 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 to be, say, aleph_2-additive.
> 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.