I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets of vector spaces). I have a few questions of which I have been able to get few insights online:(adsbygoogle = window.adsbygoogle || []).push({});

1) Does every family of sets have a maximal element? How can I make a family of sets that does not have a maximal element? I have to obviously make the hypothesis of Zorn's lemma fail, but I can't quite see how to do that.

2) Does every chain of sets have a maximal element? It seems that a chain of sets necessarily satisfies the criteria for Zorn's lemma but I am not sure.

Thanks!

BiP

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# Family of sets without maximal element

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