Talk:Set-theoretic definition of natural numbers

message: I really don't think the gif in the first section contributes anything. It's just confusing.  — Preceding unsigned comment added by 68.232.122.172 (talk) 20:12, 10 October 2016 (UTC)
replies: text: I agree. — Carl (CBM · talk) 00:05, 11 October 2016 (UTC)
thread_title:  Introductory gif 

message: I added a discussion of the definition of Frege and Russell which works in naive set theory,
type theory, and New Foundations.
Randall Holmes 18:02, 15 December 2005 (UTC)
replies: text: It would be interesting to discuss the relation of this definition to logicism. Tkuvho (talk) 10:13, 20 October 2010 (UTC)

text: What does it mean for a definition to “work” in a theory known to be inconsistent such as naive set theory? 2604:6000:B405:F200:45EC:9BBE:F1C5:A9D9 (talk) 16:01, 12 February 2017 (UTC)
thread_title:  Definition per Frege and Russell 

message: Randall, I've given this article my usual polish but remain dissatisfied with it. The way you set out the Frege-Russell definition catches me off-guard. I do not have a sense that you have clearly demarcated Frege-Russell's way from Von Neumann's way. You did not mention that you were defining the Von Neumann ordinals, and that extracting the corresponding cardinals from these ordinals requires Choice. (The entry says this now, but only because I added it.) I am not confident that the two definitions in this article are killingly accurate, and maximal accuracy is important here, otherwise a poor reader might take Julius Caesar for a number, as per Frege's notorious worry! I'm adding a link to your wonderful 1998 text.
As I have told you before via another channel, the Frege-Russell way has always struck me as "just right." The fact that the resulting equivalence classes are not sets in ZFC does not damn Frege-Russell; rather it damns ZFC. A foundational system of mathematics should come with an elementary and intuitive definition of the finite cardinals, period. ZFC fails that test, NFU does not.202.36.179.65 18:13, 16 July 2006 (UTC)
thread_title:  This entry needs more and better content 

message: The description of the empty set in bracketts after the empty set symbol was a) wrong and b) unnecessary, so i replaced it with a link to the empty set page. I don't mean the description was incorrect it was just very poor english, and confusingly similar to saying "the set containing zero" which is of course incorrect. Triangl 01:12, 12 November 2006 (UTC)
thread_title:  Small edit 

message: The symbol used to describe the empty set is incorrect.  {} denotes the empty set as does the symbol Ø.  Then {Ø} is truly an non-empty set, because it is a set that contains the empty set.  To formally define zero to be {Ø} might be true, but placing a link to the empty set after {Ø} is misleading.
bradskins 22:21, 27 November 2006 (UTC)
replies: text: I changed it, and you could have changed it as well. CMummert 11:54, 28 November 2006 (UTC)
replies: text: It would be interesting to know where the symbolism { } came from. Granted that it seems now to be an obvious extension of "empty" and "set", Zermelo 1908 and Fraenkel 1922 used "0" and worked from there. von Neumann 1925 used O (as in "oh", not the zero-symbol). wvbaileyWvbailey 14:59, 8 October 2007 (UTC)
thread_title:  Non-equivalence of "the empty set" and the symbol used before "(the empty set)" 

message: After editing this page, I noticed that most of its content is duplicated at natural number. Do we really need a separate page?
Quux0r 07:24, 13 October 2007 (UTC)
thread_title:  Merge with natural numbers? 

message: To the editor: the writing under section Problem is great, an really should be preserved on a math blog before somebody comes along and deletes it for being "unencyclopedic" (as if formal math can ever be conceptualized in an encyclopedic manner, discounting prodigies). I especially love this insight: "After all, if any concept is to be left formally undefined in mathematics, it might as well be one which everyone understands." Yes, editor, please save this somewhere. SamuelRiv (talk) 03:02, 18 March 2013 (UTC)
thread_title:  Terrific prose but 

message: Some of the sections discuss only the first topic (construct individual natural numbers, for instance as an equivalence class under the equinumerosity relation, or as a set like in the von Neumann section). The second topic (the set of all natural numbers) is mentioned in the first section but not in the other ones.  — Preceding unsigned comment added by MvH (talk • contribs) 15:02, 21 February 2020 (UTC)
thread_title:  Is the purpose of this page to construct individual natural numbers, or, to construct the set of all natural numbers? 

message: I realize this question doesn't always have an answer when it comes to mathematics, but in this case, it seems to me like there is some kind of motivation hinted at but never explicitly spelled out. The article on set theory itself states that "[s]et theory is commonly employed as a foundational system for mathematics", so I guess it's that? Just a short subclause in the introduction would be enough to make this more comprehensible to the layperson. --129.13.72.197 (talk) 17:53, 23 July 2020 (UTC)
thread_title:  Why are we doing this? 

message: Shouldn't the Ackermann coding be added to this article? It is a set-theoretic definition of natural numbers. BIT predicate is linked from this article which is good, I'm wondering could the history section of that article be copied over (I haven't edited on wikipedia in forever)? --Erinius (talk) 21:59, 25 February 2021 (UTC)
thread_title:  Ackermann coding