Abstract
The standard Zermelo-Fraenkel axioms of set theory lay out conditions of identity of sets, then methods of forming new sets from old – via unions, power sets and the like. When those methods are fed finite sets they yield finite sets and when they are fed infinite sets they (can) yield infinite sets. But there is no way to build an infinite set from finitely many finite sets. The ZF axioms cope with that limitation by adding a bald ‘Axiom of Infinity’, which states ‘there is an infinite set’.
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© 2014 James Franklin
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Franklin, J. (2014). Infinity. In: An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137400734_9
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DOI: https://doi.org/10.1057/9781137400734_9
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