Talk:Set theory

message: The first sentence is: "Mathematical topics typically emerge and evolve through interactions among many researchers. Set theory, however, was founded by a single paper in 1874 by Georg Cantor: "On a Characteristic Property of All Real Algebraic Numbers"."
This viewpoint has been seriously contested, among other places in books mentioned as references. Let me suggest a look at this entry in the SEP, http://plato.stanford.edu/entries/settheory-early/  — Preceding unsigned comment added by 90.169.125.151 (talk) 17:30, 2 April 2014 (UTC)
thread_title:  The exposition of history is rather outdated and uncritical. 

message: This phrase is currently found in the article.  What is the definite article meant to imply?  Tkuvho (talk) 18:01, 1 February 2012 (UTC)
thread_title:  The modern understanding of infinity began in 1867-71, with Cantor's work on number theory 

message: I edited once, but my edit was discarded, so I'm stating here what I dislike about the statements on Category Theory/Topos Theory:
I am not happy with this formulation. It seems to imply that Category Theory can interpret those "alternatives", while set theory cannot - this is in fact not the case, all those can also be modelled inside of set theory. I'm not arguing that Category Theory is not a completely different approach, but the way it's written here seems to indicate it's superior in those ways, while this is not true.  — Preceding unsigned comment added by Ftonti (talk • contribs) 18:38, 21 June 2012 (UTC)
thread_title:  Foundational debate/Category Theory 

message: The huge quantity of text Multipundit is insisting on adding in the Generalizations section is massively out of proportion with the importance of these topics to set theory.  It cannot possibly stay.  --Trovatore (talk) 04:47, 18 January 2013 (UTC)
replies: text: I agree and have reverted it again. —David Eppstein (talk) 06:36, 18 January 2013 (UTC)
thread_title:  Multipundit's additions 

message: W. R. Hamilton used the phrase "theory of sets" in the Preface of his Lectures on Quaternions (1853). At that time he was wrestling with units, compounds, and collections, in particular his efforts at "triplets" that led eventually to quaternions. See his comments at page 29 and 64 where he looks back to his work of 1835 and 1848 for set theory. Since set theory has evolved in mathematics to mathematical structures and category (mathematics), Hamilton’s essays offer early evidence of the need to discriminate between compound and collection, and early suggestions of terminology in algebra. — Rgdboer (talk) 22:09, 24 August 2016 (UTC)
thread_title:  Hamilton 

message: We are told that "The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s". Finite set theory is a statement of the obvious and has always been known.  — Preceding unsigned comment added by 188.39.71.98 (talk) 08:15, 1 February 2018 (UTC)
replies: text: If it's so obvious, why is the union-closed sets conjecture not yet proven? —David Eppstein (talk) 08:35, 1 February 2018 (UTC)
replies: text: In any case, it says "the modern study", which is primarily about infinite sets. --Trovatore (talk) 08:57, 1 February 2018 (UTC)
replies: text: The conjecture mentioned by Eppstein is carefully worded so as to refer to finite sets only.  — Preceding unsigned comment added by 86.1.37.70 (talk) 11:50, 1 February 2018 (UTC)
replies: text: I agree, that a non-trivial problem does appear in finite set theory.  — Preceding unsigned comment added by 86.1.37.70 (talk) 11:54, 1 February 2018 (UTC)
replies: text: See https://arxiv.org/pdf/1512.00083.pdf All these conjectures seem to refer to finite sets only.  — Preceding unsigned comment added by 86.1.37.70 (talk) 12:03, 1 February 2018 (UTC)
replies: text: I'm certainly not saying there's nothing interesting to say about finite sets.  But the study of them is usually not called "set theory".  I think people who study this would consider themselves to be doing combinatorics. --Trovatore (talk) 22:58, 1 February 2018 (UTC)
thread_title:  Finite sets 

message: Removed the false sentence: "Modern understanding of infinity began in 1867–71, with Cantor's work on number theory." Joseph Dauben's Georg Cantor (p. 30) states: "Like his dissertation, Cantor's Habilitationsschrift reflected his early interest in the theory of numbers, though his great creation of transfinite set theory was not indebted to this early work." --RJGray (talk) 18:44, 15 April 2018 (UTC)
replies: text: It might be more accurate to say it began with Cantor's work on real analysis.  It's not that unusual to see editors confuse real analysis with number theory, I suppose because it does after all deal with "numbers". --Trovatore (talk) 21:26, 15 April 2018 (UTC)
thread_title:  Removed false sentence: "Modern understanding of infinity began ... with Cantor's work on number theory." 

message: I think these phrases must be provided with some references:Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Set theory as a foundation for mathematical analysis, topology, abstract algebra, and discrete mathematics is likewise uncontroversial; mathematicians accept that (in principle) theorems in these areas can be derived from the relevant definitions and the axioms of set theory. I found a useful phrase for this in K.Kunen's book (page xi): Set theory is the foundation of mathematics. All mathematical concepts are defined in terms of the primitive notions of set and membership. In axiomatic set theory we formulate a few simple axioms about these primitive notions in an attempt to capture the basic "obviously true" set-theoretic principles. From such axioms, all known athematics may be derived. If there are no objections, I will input it into the text. Perhaps, somebody knows other useful citations, I think it would be good to add them as well. Eozhik (talk) 17:37, 8 October 2019 (UTC)
replies: text: It might be illuminating to add that, in fact, mathematical analysis, topology, abstract algebra, and discrete mathematics can be derived from a very small part of set theory - the theory of P(P(P(N))), I believe. I'll try to nail down a good citation; it's a common observation. Sunyataivarupam (talk) 02:57, 9 January 2023 (UTC)
thread_title:  References for the claim that set theory is a foundational system for mathematics 

message: A discussion is taking place to address the redirect :SetTheory/OldVersion. The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 December 5#SetTheory/OldVersion until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  Q28 (talk) 01:05, 5 December 2021 (UTC)
thread_title:  "SetTheory/OldVersion" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has identified a potential problem with the redirect :SetTheory/OldVersion and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 January 17#SetTheory/OldVersion until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  Q28 (talk) 15:27, 17 January 2022 (UTC)
thread_title:  "SetTheory/OldVersion" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: There seems to be a {{}} on end of the article, should it be removed? It looks like it's remains of a previous template has been added if possible can someone restore it, I can't find what it is.
Qwea1 (talk) 08:11, 29 July 2022 (UTC)
thread_title:  There is a {{}} can it be removed? 

message: For example :-•complement laws 
•De Morgan's law 
•double complementation
•empty and universal set law Yuthfghds (talk) 05:20, 27 May 2023 (UTC)
replies: text: See truth table. --Ancheta Wis    (talk  | contribs) 10:25, 27 May 2023 (UTC)
thread_title:  Advanced laws of set theory should be included 

message: I am very surprised to see not a single mention in this article of Gottlob Frege. His work on the foundations of mathematics is inseparable from both the history of set theory and the development of Principia Mathematica. I will do my best to remedy this issue myself but would love others to help. Jbermingham123 (talk) 01:44, 19 September 2023 (UTC)
replies: text: I don't think much of Frege has survived in terms of modern set theory, except for making an error for Russell to instructively refute, and then Principia Mathematica itself was basically a dead end.  But sure, he's part of the history that should be presented. --Trovatore (talk) 04:25, 19 September 2023 (UTC)
thread_title:  Frege is missing? 

message: In the article Indian logic it is mentioned that the school Navya-Nyāya had anticipated the development of modern set theory before Georg cantor so is it better to give credit to that school rather than Georg cantor? Myuoh kaka roi (talk) 05:12, 14 November 2023 (UTC)
thread_title:  History of set theory