In article <firstname.lastname@example.org>, Butch Malahide <email@example.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. --