axiom of choice
axiom of choice noun: one of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.
Noun
axiom of choice (plural axioms of choice)
- One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.
- The axiom of choice is logically equivalent to the assertion that every vector space has a basis.
- If V = L then the axioms of choice and the continuum hypothesis are both true, and the assertion that a measurable cardinal exists is false.1993, Thomas Tymoczko, editor, Penelope Maddy: Does V Equal L?: New Directions in the Philosophy of Mathematics: An Anthology, page 357
axiom of choice meaning in Tamil
axiom of choice in Tamil
- தெரிந்தெடுத்த அடிக்கோள், தெரிவுசெய்த அடிக்கோள்
Examples of axiom of choice in a sentence
- Throughout this work we adopt the Zermelo–Fraenkel (ZF) axioms of set theory with the Axiom of Choice, commonly abbreviated as ZFC.1993, Gary L. Wise, Eric B. Hall, Counterexamples in Probability and Real Analysis, page vii:
- In contrast, there are weak forms of the axiom of choice that are not provable.2000, Bruno Poizat, translated by Moses Klein, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, page 169:
- Prominent amongst these axioms is this Axiom of Choice!2012, 47:31 – 49:50 from the start, in Difficulties with real numbers as infinite decimals (I) Real numbers + limits Math Foundations 91...
Synonyms of axiom of choice
Forms of axiom of choice
| plural | axioms of choice |
|---|
Origin of axiom of choice
A calque of German Axiom der Auswahl (now more commonly Auswahlaxiom), which first appeared in print with a description of the axiom in 1908, Ernst Zermelo, Untersuchungen über die Grundlagen der Mengenlehre I ["Investigations in the foundations of set theory I"], Mathematische Annalen, 65 (although the paper was dated 1907).
Words formed from axiom of choice
- axiom of countable choice
- axiom of denumerable choice
- axiom of dependent choice
Questions about axiom of choice
- What does axiom of choice mean?
- Axiom of choice means one of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.
- What is axiom of choice in Tamil?
- Axiom of choice in Tamil is தெரிந்தெடுத்த அடிக்கோள், தெரிவுசெய்த அடிக்கோள். See Axiom of choice meaning in Tamil.
- How do you use axiom of choice in a sentence?
- Throughout this work we adopt the Zermelo–Fraenkel (ZF) axioms of set theory with the Axiom of Choice, commonly abbreviated as ZFC.
- What part of speech is axiom of choice?
- Axiom of choice is a noun.
- What is the plural of axiom of choice?
- The plural of axiom of choice is axioms of choice.
Words near axiom of choice in the dictionary
Source and license
Adapted from Wiktionary: axiom of choice (page history and authors); axiom of choice (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “axiom of choice.” Word.ws, https://word.ws/axiom_of_choice. Based on Wiktionary, CC BY-SA 4.0.