Talk:Zorn's lemma

message: The assertion is not true. Only connected graphs have spanning trees. The mistake in the proof happens here:
:Zorn's lemma says that a maximal tree must exist, which is a spanning tree.
Maximal trees in disconnected grpahs aren't spanning trees. --Jobu0101 (talk) 20:41, 5 January 2015 (UTC)
thread_title:  Zorn's lemma CAN'T be used to show that every graph has a spanning tree 

message: I have little doubt that this is a fine article. If any part of this article were comprehensible in plain English, I'd be tempted to read it. The convenience of mathematical language/jargon should maybe not prelude an explanation in English. Just a thought. IP address, because I can't be bothered logging in.  — Preceding unsigned comment added by 122.59.202.135 (talk) 20:38, 23 April 2016 (UTC)
replies: text: What would it take to make the article more comprehensible? I'm not trying to be difficult, but I struggle to think of ways to describe Zorn's lemma without lots of mathematical language. After all, one has to understand the terms partially ordered set, chain, upper bound and maximal element just to be able to state the lemma. —Tobias Bergemann (talk) 09:53, 25 April 2016 (UTC)
thread_title:  Too technical 

message: A new motivation section has been added. It is probably a good idea to have one, but I'm not sure the current one does the job. "Sometimes, one wishes" is okay during a mathematical talk, but in Wikipedia we need to provide reliable source or risk engaging in original research. The issue of transfinite induction is actually complicated, and the current paragraph is glossing it a bit too much. "Tidies up the conditions"... no, I really don't like that wording. Also, transfinite induction is not the only way to prove maximal elements exist, so the implication that Zorn's Lemma is used so as not to have to do "transfinite induction" each time is overbroad. And finally, every lemma and theorem is about proving a general situation so that one does not have to prove it by hand each time. There is nothing special about Zorn's Lemma in that respect to warrant highlighting it like that, in my opinion. This section should be tidied up considerably. Magidin (talk) 15:56, 2 August 2019 (UTC)
replies: text: Thanks for your suggestion. I agree that it is not perfect as it is. I personally don't know how to improve it at the moment, but I think such an informal explanation of the motivation is better than no motivation section, because in my opinion it gives at least a feeling for what the intuition behind Zorn's lemma is (this is especially important here because Zorn's lemma can be quite overwhelming if one only reads the formal statement and asks oneself what the point is).Zaunlen (talk) 16:56, 2 August 2019 (UTC)
thread_title:  Motivation section 

message: If Zorn's lemma is ultimately the same as axiom of choice, what does it mean to "prove" it: "Proved by Kuratowski in 1922 and independently by Zorn in 1935"
Apparently this question was asked and answered here: https://math.stackexchange.com/questions/1777443/original-proof-of-zorns-lemma
The most relevant-looking line seems to be "As a consequence, maximal principles were rediscovered independently several times, the most important instances occurring in articles by Kazimierz Kuratowski [1922] and Max Zorn [1935]."
Is what we're saying that certain implications of Zorn's lemma were proved in 1922 and 1935? KVenzke (talk) 22:50, 21 December 2021 (UTC)
replies: text: It probably means proved using the axiom of choice.  The axiom of choice is intuitively clear; Zorn's lemma is not. --Trovatore (talk) 22:57, 21 December 2021 (UTC)
thread_title:  What was proved? 

message: Interestingly, Zorn's Lemma is useful in considerations of non-classical approaches to the notion of truth and the Liar's paradox in Philosophy of Language; specifically, Kripke uses it to show that any fixed point can be extended to a maximal fixed point. I'd be up for writing up on this under this article, but it's unclear under which seciton organisationally it would be worth mentioning ...  HerbertDibDab (talk) 10:52, 16 May 2024 (UTC)
thread_title:  Application in Philosophy of Logic/Language