On Dec 22, 10:14 am, "porky_pig...@my-deja.com" <porky_pig...@my- deja.com> wrote: > On Friday, December 21, 2012 11:41:44 PM UTC-5, Bill Taylor wrote: > > On Dec 22, 5:23 am, FredJeffries <fredjeffr...@gmail.com> wrote: > Dirac delta, infinitesimals, irrational numbers, transfinite ordinals, > ... are legitimate not because they have been rigorously defined Yes, that is PRECISELY why they are legitimate. > 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. -- Blunderbuss Bill ** Dogma is a bitch! (pun intended) > > So, you're saying there *exists* the uniform distribution of positive integers (or natural numbers if you wish). Well, well, well, would you please then enlighten the unwashed masses like myself and tell us that's the probability of selecting an arbitrary positive integers?
Zero, of course. Needless to say, the probability measure will not be countably additive. Finite additivity is good enough for many purposes, and in this case it will have to do.