Zorn's Lemma

up:: 020 MOC Mathematics

”If you are building a mathematical object in stages and find that
(i) you have not finished even after infinitely many stages, and
(ii) there seems to be nothing to stop you continuing to build,
then Zorn’s lemma may well be able to help you.”
How to use Zorn’s lemma | Gowers’s Weblog

Let $X$ be a Partially Ordered Set such that every Totally Ordered subset has an upper bound. Then $X$ contains a maximal element.

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References

• Um Curso de Álgebra Linear, Flávio Ulhoa Coelho & Mary Lilian Lourenço. Editora EDUSP.