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The introduced set-theoretical concepts allow us to formulate a famous lemma which was stated by Max Zorn (1906 – 1993).

Lemma: Zorn's Lemma

If every chain $S\subseteq X$ in a poset $(V,\preceq )$ has an upper bound, then the poset $V$ contains at least one maximal element.

| | | | | created: 2019-02-02 14:33:58 | modified: 2019-02-02 16:05:06 | by: bookofproofs | references: [979], [1038], [8055]

1.Proof: (related to "Zorn's Lemma")


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Bibliography (further reading)

[8055] Hoffmann, D.: “Forcing, Eine Einführung in die Mathematik der Unabhängigkeitsbeweise”, Hoffmann, D., 2018

[979] Reinhardt F., Soeder H.: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10

[1038] Wille, D; Holz., M : “Repetitorium der Linearen Algebra”, Binomi Verlag, 1994

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