Re: What does a "uniformly randomly picked subset from N" mean?

In article <1174062637.786933.31580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
oliu321@xxxxxxxxx wrote:

On Mar 16, 4:27 am, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1174024384.426336.247...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

oliu...@xxxxxxxxx wrote:
Well, I guess you may say, uniformly randomly pick one, again.

Except that if selecting one member "at random" from a set of objects
means that each object must have 'the same probability' of being
selected, then for selecting from a countably infinite set, such as the
set of natural numbers, it cannot be done in any way compatible with the
rules of probability.

It would require that a countably infinite number of equal values add up
to 1.

First a random subset of N could be finite set.

If one could pick a subset of N in such a way that every subset of N had
the same probability of being chosen, then the probability of choosing a
finite subset at all would have to be zero, as there are only countably
many such finite sets versus uncountably many infinite subsets.

Second I am asking for Pr(x = 2k for some k | x \in RS where RS is a
random subset
from N) = ?, so even when RS is infinite the {x| x = 2k for some k AND
x \in RS} is still quite possibly a infinte set and by asking Pr I
basically asking the measure of this set, well I admitted thad I
didn't define the measure here but that's my question - how could you
define all these measures.

You seem to be asking for the probability that a "randomly chosen"
subset of N contains an even number.

Is that what you are asking for?
.

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