Abstract
Pick a positive integer at random. What is the probability of it being even? As stated, this question is not well posed, because there is no uniform probability measure on the set \(\mathbb{N}\) of positive integers. However, what one can do is fix a positive integer n, and choose a number uniformly at random from the finite set [n] = { 1, …, n}. Letting
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References
Nathanson, M.: Elementary Methods in Number Theory. Graduate Texts in Mathematics, vol. 195. Springer, New York (2000)
Tenenbaum, G.: Introduction to Analytic and Probabilistic Number Theory. Cambridge Studies in Advanced Mathematics, vol. 46. Cambridge University Press, Cambridge (1995)
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Pinsky, R.G. (2014). The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers. In: Problems from the Discrete to the Continuous. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-07965-3_2
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DOI: https://doi.org/10.1007/978-3-319-07965-3_2
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