Re: An uncountable countable set

In article <450d6d1e@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Mike Kelly wrote:
Tony Orlow wrote:
Han.deBruijn@xxxxxxxxxxxxxx wrote:
Mike Kelly wrote:

Given that any second-year student of probability theory knows that
there are no uniform distributions over countable sample spaces, [ ... ]
This "given" is most disturbing. Mainstream mathematics is so certain
about its own right that no sensible debate is possible.
There IS no LUB on the finites, omega notwithstanding. Omega's a
phantom. That's why you can't get any average value or any uniform
probability distribution.

Vaguely correct, minus reflexive whining about Omega.

In general, it doesn't make sense to talk
about probability without a uniform probability distribution over a
finite set.

That's absurd. I don't think you meant to say what you said here. Of
course there are non-uniform probability distributions and probability
distributions on infinite sets.

Okay. I misspoke. But what about uniform probability distributions on
infinite sets in general?

The answers to such questions are part of the content of measure theory,
q.v.


However, since probability is really a percentage,

That is, a real number between 0 and 1.

Yes.


any
subset which is a finite fraction of the whole can certainly have a
probability associated with it: that fraction.

Only if a uniform distribution can be defined on the whole.

Why? A probability IS a fraction.

Not necessarily. It is always a real between 0 and 1 inclusive, but not
all reals in that range are fractions.
.

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