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Abstract
A randomly selected number from the infinite set of positive integers—the so-called de Finetti lottery—will not be a finite number. I argue that it is still possible to conceive of an infinite lottery, but that an individual lottery outcome is knowledge about set-membership and not element identification. Unexpectedly, it appears that a uniform distribution over a countably infinite set has much in common with a continuous probability density over an uncountably infinite set.
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References found in this work BETA

What Conditional Probability Could Not Be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Countable Additivity and the de Finetti Lottery.Paul Bartha - 2004 - British Journal for the Philosophy of Science 55 (2):301-321.
God’s Lottery.Storrs McCall & D. M. Armstrong - 1989 - Analysis 49 (4):223 - 224.

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