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Mathematics
Set Theory, Logic, Probability, Statistics
Is there a "smallest" infinite subset of the naturals?
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[QUOTE="nuuskur, post: 6859580, member: 519618"] We could view this as a density problem. In this case, the subset of primes has density zero, so the primes could be considered minimal in this respect. Density roughly refers to the proportion of primes up to a fixed range. Cardinality wise only, there is no smallest countably infinite set. Any subset of ##\mathbb N## is either bounded (hence finite) or has the same cardinality as ##\mathbb N##. Without the axiom of choice, one could have infinite sets that are incomparable to ##\mathbb N## in terms of cardinality (e.g [URL='https://en.wikipedia.org/wiki/Dedekind-infinite_set']Dedekind-infinite sets[/URL]). [/QUOTE]
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Is there a "smallest" infinite subset of the naturals?
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