Zorn's lemma
statement equivalent to the axiom of choice, about the existence of a maximal element in a poset with a maximal chain condition
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Zorn's lemma
Summary
Zorn's lemma is a lemma[1]. It ranks in the top 1% of lemma entities by monthly Wikipedia readership (405 views/month).[2]
Key Facts
- Zorn's lemma's instance of is recorded as lemma[3].
- Zorn's lemma's instance of is recorded as equivalent of the axiom of choice[4].
- Max August Zorn is named after Zorn's lemma[5].
- Kazimierz Kuratowski is named after Zorn's lemma[6].
- Zorn's lemma's part of is recorded as list of axioms[7].
- Zorn's lemma's said to be the same as is recorded as axiom of choice[8].
- Zorn's lemma's Freebase ID is recorded as /m/0dkrp[9].
- Zorn's lemma's PSH ID is recorded as 7138[10].
- Zorn's lemma's Gran Enciclopèdia Catalana ID is recorded as 0073388[11].
- Zorn's lemma's Encyclopædia Britannica Online ID is recorded as topic/Zorns-lemma[12].
- Zorn's lemma's defining formula is recorded as \left(\forall C\subset P\colon(\forall c,c'\in C\colon c\le c'\lor c\ge c')\implies\exists u\in P\colon C\le u\right)\implies\exists m\in P\forall p\in P\colon m\not\le p[13].
- Zorn's lemma's studied by is recorded as set theory[14].
- Zorn's lemma's MathWorld ID is recorded as ZornsLemma[15].
- Zorn's lemma's nLab ID is recorded as Zorn's lemma[16].
- Zorn's lemma's maintained by WikiProject is recorded as WikiProject Mathematics[17].
- Zorn's lemma's Microsoft Academic ID is recorded as 78538056[18].
- Zorn's lemma's ProofWiki ID is recorded as Zorn's_Lemma[19].
- Zorn's lemma's in defining formula is recorded as P[20].
- Zorn's lemma's in defining formula is recorded as m[21].
- Zorn's lemma's in defining formula is recorded as C[22].
- Zorn's lemma's in defining formula is recorded as \le[23].
- Zorn's lemma's generalization of is recorded as axiom of choice[24].
- Zorn's lemma's Lex ID is recorded as Zorns_lemma[25].
- Zorn's lemma's Treccani's Enciclopedia della Matematica ID is recorded as lemma-di-zorn[26].
- Zorn's lemma's ScienceDirect topic ID is recorded as mathematics/zorn-lemma[27].
Why It Matters
Zorn's lemma ranks in the top 1% of lemma entities by monthly Wikipedia readership (405 views/month).[2] It has Wikipedia articles in 25 language editions, a strong signal of global cultural recognition.[28] It is known by 11 alternative names across languages and contexts.[29]