completeness axiom

noun

The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).

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Meanings

nouncompleteness axiom (plural completeness axioms)

plural completeness axioms

  1. mathematicsThe following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).
Cite this entry
APA

completeness axiom. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/completeness%20axiom

MLA

“completeness axiom.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/completeness%20axiom. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “completeness axiom,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/completeness%20axiom.

Source: completeness axiom on Wiktionary, CC BY-SA 4.0.