Re: Probability in an infinite sample space


Han de Bruijn wrote:
Robert Low wrote:

it doesn't work. You *cannot* assign uniform infinitesimal probabilities
to the integers in such a way that the probability of choosing
a multiple of three is one-third. You can't assign infinitesimal
probabilities to the integers in *any way* so that the probability
of choosing integers from any particular set is a finite number:
it is always either infinitesimal or undefined.
That's the other way around: *you* can not do it, but *I* can.

You might *think* you can do it, but you've certainly provided
no evidence for why anybody else should share that opinion.

So go on: describe how your infinitesimals work (they certainly
aren't the usual infinitesimals of nonstandard analysis), and how
you get a uniform probability distribution on the naturals
using them.

.

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