What does axiom of choice mean?
Definitions for axiom of choice
ax·iom of choice
This dictionary definitions page includes all the possible meanings, example usage and translations of the word axiom of choice.
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Wiktionary
axiom of choicenoun
One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.
Wikidata
Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the product of a collection of non-empty sets is non-empty". More explicitly, it states that for every indexed family of nonempty sets there exists an indexed family of elements such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin. In many cases such a selection can be made without invoking the axiom of choice; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin. To give an informal example, for any collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks, such a selection can be obtained only by invoking the axiom of choice.
Numerology
Chaldean Numerology
The numerical value of axiom of choice in Chaldean Numerology is: 3
Pythagorean Numerology
The numerical value of axiom of choice in Pythagorean Numerology is: 9
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"axiom of choice." Definitions.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.definitions.net/definition/axiom+of+choice>.
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