Axiom of choice

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In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, one can identify another set containing one element chosen from each set, even if the collection is infinite. Formally, the axiom establishes existence rather than a construction; it states that for every set I {\displaystyle I} and every I {\displaystyle I} -indexed family ( S i ) i ∈ I {\displaystyle (S_{i})_{i\in I}} of nonempty sets, there exists an I {\displaystyle I} -indexed set ( x i )...

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