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Topic: Continuous and discrete uniform distributions of N
Replies: 27   Last Post: Dec 28, 2012 9:45 PM

 Messages: [ Previous | Next ]
 David Bernier Posts: 3,892 Registered: 12/13/04
Re: Continuous and discrete uniform distributions of N
Posted: Dec 22, 2012 2:58 PM

On 12/22/2012 11:14 AM, porky_pig_jr@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?
>
> Regards,
>
> PPJr.

From topological groups, I remember the concept of
"amenable group".

The additive groups Z, Z^2, Z^3 and so on can be given
the discrete topology, where each sigleton, say {(1, 3)}
for the group Z^2, is a closed set.

Then as I recall, a theorem says some type of abelian groups are
amenable.

I don't remember the type condition for abelian groups.

cf.:
http://en.wikipedia.org/wiki/Amenable_group

Of course, N with addition isn't a group. It's a ? semigroup?
(yes), and also a monoid if by N one means the thing that has
zero in it:
http://en.wikipedia.org/wiki/Monoid

Amenability means a sensible, consistent with translations,
averaging procedure exists e.g. for bounded functions on
the group.

For the probabilistic GCD is 1 argument for "random"
elements (m, n) in N^* x N^* , I don't know if it can be
recast using the amenability of Z x Z ...

gcd of (0, 0) : I know "modulo theory" is linked to
ideals in rings. Anyway, since everything non-zero
divides zero, it's dubious about sensibly defining
gcd of (0, 0).

But then, (0, 0) is just 1 element of ZxZ, so
coprimeness yes/no of (0,0) should be irrelevant
to an argument based on amenability.

I don't know what that argument might look like,
assuming it exists, i.e. that I'm on some sort of
"right track" ...

dave

David Bernier

Date Subject Author
12/20/12 ross.finlayson@gmail.com
12/21/12 FredJeffries@gmail.com
12/21/12 Bill Taylor
12/22/12 Porky Pig Jr
12/22/12 ross.finlayson@gmail.com
12/24/12 FredJeffries@gmail.com
12/22/12 David Bernier
12/22/12 Butch Malahide
12/24/12 FredJeffries@gmail.com
12/24/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/25/12 Virgil
12/25/12 Butch Malahide
12/26/12 gus gassmann
12/26/12 Butch Malahide
12/27/12 ross.finlayson@gmail.com
12/27/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/28/12 Virgil
12/28/12 ross.finlayson@gmail.com
12/25/12 Shmuel (Seymour J.) Metz
12/25/12 Butch Malahide