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 <6e3407662e084966b4970c4d834979a1@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 coprime, 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 nonzero 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. 

