See countably infinite on Wiktionary
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"text": "1953 [Addison-Wesley], Bruce Elwyn Meserve, Fundamental Concepts of Algebra, 1982, Dover, page 36,\nThis one-to-one correspondence between the set of positive integers and the set of pairs of positive integers indicates that the set of pairs is countably infinite. Since the set of positive rational numbers is a subset of the set of all pairs of positive integers, the set of positive rational numbers is at most countably infinite. Then, since it is also at least countably infinite, the set of positive rational numbers is countably infinite."
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"text": "The term “countably infinite” would seem to suggest that such a set is infinite. However, the definitions of “countably infinite” and “infinite” were made separately, and so we have to prove that countably infinite sets are indeed infinite (otherwise our notation would be rather misleading).",
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"(set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set."
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-29 from the enwiktionary dump dated 2025-05-20 using wiktextract (e937b02 and f1c2b61). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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