```Date: Dec 20, 2012 1:12 AM
Author: ross.finlayson@gmail.com
Subject: Continuous and discrete uniform distributions of N

In the consideration of what a uniform probability distribution overthe natural integers would be, we can begin as modeling it with realfunctions, basically as the Dirac delta defined not just at zero, butat each natural integer, scaled or divided by the number of integers,with commensurate width, preserving the properties of a p.d.f. thatit's everywhere greater than or equal to zero and less than or equalto one, and that its area or integral evaluates to one.Then, where Dirac's delta is described as a spike to infinity at zerowith unit area, then to have a spike to one at each natural integer,basically dividing the spike fairly among the natural integers, theconsideration then is in as to whether that still would have area one,besides that each of the points would have f(x)=1.  (Of course this isall modeled standardly with real functions.)  Yet, it has area two(exactly because the integral of EF = 1).Another notion of what would be the nearest analog to a uniformprobability distribution over the entire set of naturals would be foreach to have probability 1/omega, that as a discrete instead ofcontinuous distribution, the sum over them equals one.  Here thenthere's a consideration that there is a continuous distribution, of N,because a p.d.f. exists and a p.d.f. (or CDF) defines a continuousdistribution.  Then there's also a consideration that there's adiscrete distribution, of N, defined as one iota for each.	EF: continuous uniform distribution of N	(EF + REF)/2: continuous uniform distribution of N	f(x)=iota: discrete uniform distribution of NRegards,Ross Finlayson
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