Last Updated
：2025/11/25
Zorn's lemma
Proper noun
Japanese Meaning
集合論における補題で、任意の偏序集合について、すべての鎖（全順序部分集合）が上界を持つならば、その集合には少なくとも一つの極大元が存在することを主張する。
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(set theory) A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element.
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Zorn's lemma
In many proofs of the existence of algebraic bases, Zorn's lemma is used to guarantee a maximal element in a partially ordered set of linearly independent subsets.
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In many proofs of the existence of algebraic bases, Zorn's lemma is used to guarantee a maximal element in a partially ordered set of linearly independent subsets.
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