Re: Calculus XOR Probability

Tony Orlow wrote:
David R Tribble said:
Tony Orlow wrote:
I think if you are talking about a uniform probability distribution over the
naturals, you may have a point, but I don't think it exactly applies here.
Let's consider the vase, and we'll add ball 1 at 11:00, ball 2 at 11:30, ball 3
at 11:45, etc, so that all finite natural labeled balls are in the vase. Now
shake it at 12:00, and again at 12:30, then 12:45, etc. At 1:00, remove a ball
from the vase. Is there a uniform probability distribution, or are some of
those naturally-labeled balls more likely than others to be chosen?
Matt Gutting wrote:
I don't see that there's a probability distribution at all. What would be the
consequences of the existence of a probability distribution on this set?
If a probability distribution actually exists, then we can answer the
following questions:
1. If n values are chosen, what is their expected average value?
2. If a value x is chosen, what is the probability that the next
chosen value y is greater than x?

I don't see these having any answers, so the conclusion is that there
is no valid probability distribution.



Yes, you're right, over the finite naturals, of course. It seems impossible to define what the range or count is, and trying to assume any such thing leads to contradiction. Correct. Of course, in the above example, I can't see, despite the inability of calculating any such numbers, that any ball has any different chance than any other. If there is some set of balls in the vase, then whatever size that set is, each ball has the reciprocal of that size as a probability.

Assuming that one can define a reciprocal for that number, okay. But how
does one compare the probability (say) of drawing one of the first ten balls
dropped in with the probability of drawing one of the first twenty? Can you
show that the numbers you use there exist?

Matt
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Relevant Pages

  • Re: Calculus XOR Probability
    ... at 11:45, etc, so that all finite natural labeled balls are in the vase. ... consequences of the existence of a probability distribution on this set? ... Yes, you're right, over the finite naturals, of course. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... at 11:45, etc, so that all finite natural labeled balls are in the vase. ... consequences of the existence of a probability distribution on this set? ... Yes, you're right, over the finite naturals, of course. ...
    (sci.math)