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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.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences, set-theory
Examples
- The axiom of choice is logically equivalent to the assertion that every vector space has a basis.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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).
Across languages
Translations
16 source translations are retained for this English entry.
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Armenian:
ընտրության աքսիոմ
(əntrutʻyan akʻsiom)
— axiom that any product of non-empty sets is non-empty
-
Chinese Mandarin:
選擇公理 /选择公理
— axiom that any product of non-empty sets is non-empty
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Czech:
axiom výběru
— axiom that any product of non-empty sets is non-empty
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Dutch:
keuzeaxioma
— axiom that any product of non-empty sets is non-empty
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Finnish:
valinta-aksiooma
— axiom that any product of non-empty sets is non-empty
-
French:
axiome du choix
— axiom that any product of non-empty sets is non-empty
-
German:
Auswahlaxiom
— axiom that any product of non-empty sets is non-empty
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Hungarian:
kiválasztási axióma
— axiom that any product of non-empty sets is non-empty
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Italian:
assioma della scelta
— axiom that any product of non-empty sets is non-empty
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Japanese:
選択公理
(sentaku-kōri)
— axiom that any product of non-empty sets is non-empty
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Japanese:
選出公理
(senshutsu-kōri)
— axiom that any product of non-empty sets is non-empty
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Polish:
aksjomat wyboru
— axiom that any product of non-empty sets is non-empty
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Polish:
pewnik wyboru
— axiom that any product of non-empty sets is non-empty
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Serbo-Croatian:
aksiom izbora
— axiom that any product of non-empty sets is non-empty
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Slovak:
axióma výberu
— axiom that any product of non-empty sets is non-empty
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Swedish:
urvalsaxiom
— axiom that any product of non-empty sets is non-empty
