Probability, Hyperreals, Asymptotic Density, and God’s Lottery

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Gwiazda, Jeremy
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Consider a subset, S, of the positive integers. What is the probability of selecting a number in S, assuming that each positive integer has an equal chance of selection? The purpose of this short paper is to provide an answer to this question. I also suggest that the answer allows us to determine the relative sizes of two subsets of the positive integers.