Re: Cantorian pseudomathematics


Han.deBruijn@xxxxxxxxxxxxxx wrote:
> Jesse F. Hughes wrote:
> >
> > I understand the probability a divides n when we have a uniform
> > distribution on initial segments of N (although my terminology may be
> > off).
>
> Your terminology is clear enough.
>
> > It seems you're right that the limit of these values is 1/a.
> >
> > But there is no uniform distribution on N, so I don't see what Han
> > means there and your explanation doesn't clarify it.
>
> Who the hell has decided that "there is no uniform distribution on N"
> !?

It isn't "decided". It is "proven". The fact that people like you,
Ross, and Tony think theorems are arbitrary "decisions" and
alternate decisions could be made from the same axioms,
does not make those theorems false.

You can define a uniform distribution over a finite set of
n discrete points. The probability that X = any particular
point from the set is 1/n.

You can define a uniform distribution over an interval
containing uncountably many points, such as [a,b].
There is a probability density 1/(b-a), defined such
that the probability of picking a point in any sub-interval
of length s is s/(b-a). If you divide [a,b] into n intervals,
the probability of each is 1/n.

A probability distribution must satisfy the condition
that the total probability over all events is 1. There is
no way to do that with a countable set of discrete
points.

Feel free to prove us wrong. Define the uniform
distribution over N. Show us a procedure to generate
a random integer.

- Randy

.

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