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Line 6: ==Properties== The set of [[natural numbers]] (whose existence is postulated by the [[axiom of infinity]]) is infinite.<ref name=":0" /><ref>{{Citation\|last=Bagaria\|first=Joan\|title=Set Theory\|date=2019\|url=https://plato.stanford.edu/archives/fall2019/entries/set-theory/\|~~work~~encyclopedia=The Stanford Encyclopedia of Philosophy\|editor-last=Zalta\|editor-first=Edward N.\|edition=Fall 2019\|publisher=Metaphysics Research Lab, Stanford University\|access-date=2019-11-30}}</ref> It is the only set that is directly required by the [[axiom]]s to be infinite. The existence of any other infinite set can be proved in [[Zermelo–Fraenkel set theory]] (ZFC), but only by showing that it follows from the existence of the natural numbers. A set is infinite if and only if for every natural number, the set has a [[subset]] whose [[cardinality]] is that natural number.{{cn\|date=August 2020}}

Infinite set: Difference between revisions