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"the sum across the appropriate universe" for Reals is an integral. An integral can go from -Infinite to Infinite and still equal 1. This is the reason, for instance, why Zeno's Paradox of movement doesn't really forbid all movement.



This comment is more or less irrelevant. The third axiom of probability is about sums of countably many terms: http://en.wikipedia.org/wiki/Axioms_of_probability#Third_axi...




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