axiom of choice
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axiom of choice
Where it comes from
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).
noun 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.
Translations
Every language
noun axiom that any product of non-empty sets is non-empty
| 日本語 | 選択公理 sentaku-kōri, 選出公理 senshutsu-kōri |
|---|---|
| 中文 | 選擇公理 /选择公理 |
| Français | axiome du choix |
| Deutsch | Auswahlaxiom |
| Italiano | assioma della scelta |
Talk about this word "axiom of choice." Wiktionary, via Micwyn, micwyn.com/word/axiom%20of%20choice. Accessed 6 Nov. 2026. axiom of choice. (n.d.). In Wiktionary, via Micwyn. Retrieved November 6, 2026, from https://micwyn.com/word/axiom%20of%20choice "axiom of choice." Wiktionary, via Micwyn. Accessed November 6, 2026. https://micwyn.com/word/axiom%20of%20choice.Cite this
@misc{axiom_of_choice_2026,
title = {axiom of choice},
howpublished = {Wiktionary, via Micwyn},
year = {2026},
url = {https://micwyn.com/word/axiom%20of%20choice},
urldate = {2026-11-06}
}
