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In article <MPG.1e9dd8e096dfe76398abee@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> Han's original point is that calculus is very precise and works, whereas the
> case where you have a uniform probability distribution over an infinite set
> of
> possibilities is not well handled by the classical notion that all individual
> probabilities sum to 1, because the individual probabilities are considered
> equal to zero. It is the opinion of both of us that this can be resolved,
> among
> other ways, by assigning infinitesimal nonzero probabilities to each
> possibility, leaving intact the notion that the sum of the individual
> probabilities sums to 1. I am not sure why this is roundly rejected. Can you
> address that?
Because there is no model of the reals, either standard or nonstandard,
in which the sum of countably many equal values can equal 1.
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