Talk:Russell's paradox

message: The 1st statement of Lao-tzu's book says "道可道 非常道 A describable statement doesn't hold true for all the time." a statement which is described but if not hold true all the time, it defies what it says.
:Sounds a bit closer to the Liar paradox, which is related to Russell but not exactly the same thing (because it doesn't deal with sets). --Trovatore 05:47, 4 November 2005 (UTC)
replies: text: Perfect application of asshole chinese culture, wow. voidnature 13:06, 14 May 2011 (UTC)
thread_title:  Applied Version: Chinese Lao-tzu's Tao-te-ching 

message: Nice this discussion.. I think the following argument has not been stated so far:
If you say "x := 3+2" this is a definition.
If you say "x = x*x - 6" this is an equation that may have any number of solutions (in this case, it has exactly one). Some equations have no solution, or an infinite number of them.
In a way we can say a definition is an equation with one unique solution.
To define a set, you would say "M = {x | A(x) }" where A is a statement. Normally, this is a definition.
However, if the statement A refers to something on the left side of the "=", the whole thing becomes an equation where M is the variable, and therefore it doesn't need to have a solution any more. For the Russel set "definition", the reference to the object M exists, though it may not be visible at the first sight. So the "definition" is simply an equation that has no solution. Fine?
lemon-head.
yes, this is the truth, thanks for stating it so clearly :)
:The problem of the paradox is (I think) that its mostly about the consistency of the language to describe sets.  In English, we're always speaking in terms which by some view might seem inconsistent, but we've got a common culture and set of ideas that we can correct for any inconsistencies so most ideas can, in general, be communicated. When we speak in mathematics, we speak of absolutes.  In a language of absolutes there can be no inconsistencies.  However, using the theories of sets at the time, Russell described such a set.  Once a flaw like that has been established to exist, one has to wonder about mathematics as a whole. Two plus two will probably still equal four, but some of the more advanced theories you or someone else may have discovered may in fact now be proven false by this new discovery (because their "truth" may rely on the inconsistency).
:Don't get from this article that there's something wrong with defining a entity in terms of itself.  Think of the perfect numbers, where we discuss the set {x is an Integer | x = \sum n, n is an integer, n divides x, 1<=n<x}.   Without this ability we'd be very limited in power.  You just need to prove a solution exists to make sure you are discussing a topic of any worth.  In this case I can give at least 6 = 1 + 2 + 3 and 28 = 1 2 + 4 + 7 +  14. Otherwise, you might be discussing the null set, from which you can prove has any property you desire! Why? There's nothing in the set to prove otherwise.
:Btw, you never said what "type" x is in your original argument. If x is a natural number, you're fine. If x is real or complex,  x^2 -x - 6 either has two real distinct real solutions or it has none since x^ -x - 6 is not a quadradic.  It factors as (x+2)(x-3). For quaternions, there's infinitely many.  For any other type we'd probably have to define what "*", "-", and "6" mean for that type.    Root4(one) 23:55, 20 January 2007 (UTC)
thread_title:  the truth about Russell's non-paradox 

message: 1903 for the former, 1910 for the latter:  Principia Mathematica is really "later".  Randall Holmes 06:04, 29 December 2005 (UTC)
thread_title:  Principles of Mathematics vs. Principia Mathematica 

message: remote it Full Decent 04:03, 28 March 2006 (UTC)
thread_title:  Remove: Responses illustrated 

message: The barber is a woman.
 What do you mean, according to whom, and why does it matter?
22:52, 22 March 2021 (UTC)
replies: text: Because of the way the riddle is classically stated: The barber shaves all and only men who do not shave themselves. This is a paradox only if the barber is a man. Svenonius (talk) 13:08, 18 August 2023 (UTC)
thread_title:  Barber 

message: I think that the author of the "Independance from excluded middle" passage has made a mistake.
...
Often, as is done above, showing the absurdity of such a proposition is based upon the law of excluded middle, by showing that absurdity follows from assuming P true and from assuming it false. Thus, it may be tempting to think that the paradox is avoidable by avoiding the law of excluded middle, as with Intuitionistic logic.
On the contrary, assume P iff not P. Then P implies not P. Hence not P. And hence, again using our assumption in the opposite direction, we infer P. So we have inferred both P and its negation from our assumption, with no use of excluded middle.
...
This argument appears to make use of the same reasoning as the earlier examples. At first I thought that none of the earlier arguments really used the law of excluded middle, but then I realized that this argument (quoted) implicitly uses the law of excluded middle.
This argument goes:
"...assume  P iff not P. Then P implies not P..."
The reasoning is fine so far...
"... Hense not P..."
This is where the reasoning is flawed, since we have not assumed P, so the fact that P => ~P does not assist us, and thus we cannot conclude ~P.
In other words, since we are not assuming the law of excluded middle, it is possible to assume that neither P nor ~P are true (is it correct to talk about truth in this context?).
Thus the fact that we can show both P and ~P to be self contradictory does not lead to a paradox, since without the law of excluded middle, they can both be false at the same time.
DonkeyKong the mathematician 04:05, 2 May 2006 (UTC)
replies: text: No, P and ¬P can't exactly be false at the same time for an intuitionist; it's just that neither has to be true. (P → ¬P)→¬P is valid in intuitionistic logic. Intuitionistically, you should think of A → B as meaning "I have a way of transforming any proof of A into a proof of B", and think of ¬A as meaning "I have a way of transforming any proof of A into a proof of false". Now if you have a way of turning a proof of P into a proof of ¬P, and you also have a proof of P, then you can put them together to get a proof of P∧¬P, which then gives you a proof of false. Thus you can turn a proof of P into a proof of false; that proves ¬P. --Trovatore 05:38, 2 May 2006 (UTC)

text: Just the same, you have a point about the passage as written. The deduction of ¬P from P ↔ ¬P is valid, but the deduction of P from the same assumption, as far as I can tell, is not; what you actually get by the same argument is ¬¬P. But this does give us a contradiction, namely ¬P∧¬¬P. And of course from that you can deduce P, because ex falso quodlibet is intuitionistically valid. But the paragraph should be corrected. --Trovatore 18:07, 2 May 2006 (UTC)
replies: text: Okay, I'm totally out of my depth with this stuff, so I'll just have to take your word for it. Anyway, I think we need an expert on the topic to help us out with this. DonkeyKong the mathematician (in training) 01:31, 19 June 2006 (UTC)
replies: text: The passage as I found it was correct, although it seems to me you can, in fact, deduce P directly rather than using indriect proof a second time to get ¬¬P. I amended it to try to make the key step clear, let me know if it is still unclear (or if I have made it incorrect). 192.75.48.150 14:36, 19 June 2006 (UTC)
thread_title:  Falicy in "Independence from excluded middle"? 

message: I realized that Russell's paradox can be resolved if you use fuzzy sets, then you can just say that the set of all sets that don't contain themselves contains itself halfway.--SurrealWarrior 19:19, 12 July 2006 (UTC)
replies: text: At first I was going to disagree, but after thinking about it, I think it might work. That's kind of weird... if there's a 50% chance that it contains itself (a, with a value of 1.0) and a fifty percent chance that it doesn't (b, with a value of 0.0), and (a) implies (b) and (b) implies (a) as the problem's definition, resolution of these implications brings it to the same state: 0.5 * 1.0 + 0.5 * 0.0 = 0.5, so any further resolution will again reach the same state, whereas using any other value than 50% will cause it to oscillate. ... Weird. - Rainwarrior 19:28, 12 July 2006 (UTC)
replies: text: Fuzzy set's do not define a probability, they define a degree of membership. In classical sets the degree of membership is either 1 or it is 0, it is either in a set or it is not. Using fuzzy logic to solve this;If the truth of the fact that the set contains intself is T(S) then following  T(S) = T(\bar{S}) = 1 - T(S) \therefore T(S) = 0.5 . In classical set theory 0.5 is not a valid answer, it must either be true, 1, or false, 0, which is where the contradiction occours. Fuzzy logic however lets us assign a degree of membership which in this case would be 0.5. Refer to Ross TJ 2004, 'Fuzzy Logic with Engineering Applications', 2nd edn, Wiley and Sons, West Sussex; specifically page 134 where this exact problem is discussed and where I got my equation from. K2kingy (talk) 12:40, 17 April 2012 (UTC)
replies: text: This isn't surprising since any linear feedback system so constructed will either end up "stuck in the center" or oscillate. But "stuck in the center" means you've allowed trivalent logic, i.e. an introduction of an acceptable third state (0.5) to sneak into your theory. cf Kosko 1993 Fuzzy Thinking, Hyperion, NY, -X. Russell's paradox is a paradox of bivalent logic. Maybe this article isn't clear on that. The deeper problem is this: Boolean logic encourages a mixture of the arithmetic with the logical signs, but the logical sign "0.5" does not exist in that theory, nor does arithmetic equality, i.e. you should be using the logical sign IFF (IF & ONLY IF, the biconditional), i.e. ↔ ≡ (P & Q) V (~P & ~Q), where the sign ≡ means "is defined as", and &, V, ~ are the usual logical signs. (Kusko does not make this mistake, see p. 26 where he specifies biconditionality). The way to avoid this blunder is (i) not use Boolean equivalents, and (ii) to set up a formal truth table with the above equation for IFF. Now allow only "1" and "0" or better yet two novel signs such T and F or  ■ and □ and keep in mind that the behavior of the signs is determined by the theory (i.e. the truth tables in the logical system of only two values). What will happen is the truth table will fail to produce a tautology (all 1's beneath the ↔). In fact what happens is the table yields all 0's in its two rows. The table is constrained: only two rows of the four are permitted (P ≡ ~Q, ~P ≡ Q: we assign the truth values 1 and 0 per the definition of ~: P=1, Q=0, and P=0, Q=1). Given these constraints the truth table yields 0 for both of these rows, meaning neither row can be satisfied (i.e. always false). BillWvbailey (talk) 16:08, 17 April 2012 (UTC)
thread_title:  Fuzzy Russell 

message: we say that sets A1,A2,...,An is a chain of set A1 if A(i+1) be in A(i) for i=1,2,...,n-1
and chain can be infinite(in this case each Ai has an infinite chain).
Let B=set of All sets that have no infinite chain ,so B has no infinite chain.
so B is in B ,but in this case B has the infinite chain BBBB... And this is Paradox.
--213.217.57.212 17:53, 17 July 2006 (UTC)
replies: text: Why do you say "B has no infinite chain"? How is this justified? Cornelius (talk) 00:01, 29 October 2016 (UTC)
thread_title: A closer and clearer Russell paradox by Ali nour mohammadi sharif university of tehran

message: Russell's paradox came to be seen as the main reason why set theory requires a more elaborate axiomatic basis than simply extensionality and unlimited set abstraction. The paradox drove Russell to develop type theory and Ernst Zermelo to develop an axiomatic set theory which evolved into the now-canonical Zermelo–Fraenkel set theory.
not that my english is that bad but....is that english?--Lygophile 09:26, 13 November 2006 (UTC)
replies: text: Seems OK to me. Any particular trouble with it? EdC 09:42, 17 November 2006 (UTC)
replies: text: "came to be seen" is a tad awkward, especially in the opening paragraphs. "was a primary motivation for the development of higher-complexity set theories" might be better, though I'm not sure if it's accurate as given. (Certainly Russell's paradox, along with Cantor's and a few others stimulated their development.) 12.103.251.203 05:57, 22 March 2007 (UTC)
replies: text: Thanks, I've used that fragment.  A little clearer now? –EdC 23:30, 23 March 2007 (UTC)
thread_title:  what? 

message: It seems to me that the Russell's paradox was known much before Russell 'discovered' it!
http://quixote.rincondelvago.com/2_51/
:I snipped the story itself; entertaining as it is, readers can follow the link themselves.
:So what we see here has something in common with the Russell paradox, in that it gives a proposition that if you assume it's true, you can immediately derive that it should be false, and vice versa (well, more or less; there are some complications involving the will of the prisoner versus the choice of the authorities that make it not quite pure).
:In any case, sure, that idea predates Russell, in many forms. The liar paradox is another similar thing, and a form of that one even made it into the Bible, long before Cervantes.
:The novelty in Russell's case was specifically that he applied the idea to refute Fregean set theory. If you don't have that piece of context, there may not seem to be much point to the paradox. --Trovatore 17:22, 5 April 2007 (UTC)
thread_title:  Sancho Panza as a governor 

message: Shouldn't the "Independence from excluded middle" section include something about how the paradox is resolved if fuzzy sets are used instead?  (See my previous comment under "Fuzzy Russell".) --SurrealWarrior 02:40, 12 April 2007 (UTC)
replies: text: Frankly, no. Certainly not without a reliable source. Even then it would be more about the liar paradox in general than about Russell, which, as I mentioned, is specifically a refutation of Fregean set theory. I've never heard of anyone making Fregean set theory work, as a foundation for mathematics, by using fuzzy logic. --Trovatore 03:08, 12 April 2007 (UTC)
replies: text: But it does work. voidnature 04:58, 15 May 2011 (UTC)
replies: text: See "Fuzzy Russell" for my reference of a reliable source, the reference has a discussion on a very similar point. K2kingy (talk) 12:54, 17 April 2012 (UTC)
thread_title:  Fuzzy logic 

message: I created the stub article Kleene-Rosser paradox, and linked it as "see-also" in this article, but I really really really think it should be expanded and made a lot more prominent in this article. The reason for this is that the resolution of the Kleene-Rosser paradox "shows the way", i.e. it states that recursion is central to computation. Insofar as the Russell paradox applies to logical systems (as opposed to set theory), it can thus be seen to lie at the very foundation of the theory of computation. Yes? Aside from a reference to Curry as the resolver of the paradox (see talk page of that article), I don't really know more about this, but certainly get the "this is really important" alarm bell going off in my head. linas 16:48, 15 November 2007 (UTC)
replies: text: Haven't read your article, looking forward to it, but let me just say that the Russell paradox is specifically about sets. Not anything else. That's what makes it different from the liar paradox and other self-reference/diagonalization notions. Please don't add any text that muddies that take-away message, because it's a constant battle to keep the distinctions clear. --Trovatore 17:48, 15 November 2007 (UTC)

text: I have put some comments on the talk page of the new article.  --Lambiam 19:43, 15 November 2007 (UTC)
thread_title:  [[Kleene-Rosser paradox]] 

message: Wikipedia:List_of_all_lists_that_do_not_contain_themselves it's up for WP:MFD but I most comments don't seem to understand the concept.  It appears to be an example of Russell's Paradox.  If so, is it worth keeping?  If the answer is yes, you may want to comment at WP:MFD#Wikipedia:List_of_all_lists_that_do_not_contain_themselves (if the answer is no you can too, but that's probably the consensus by now anyway). --Doug.(talk • contribs) 03:17, 16 November 2007 (UTC)
thread_title:  Is this a valid example of the paradox and if so, is it worth keeping as such? 

message: Russell’s paradox considers “set of all sets that are not members of themselves”. (BTW  “all” is replaced by “exactly” on Wiki page – while it is supposed to have the same meaning it may be misleading to some readers). Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.
Lets start exploring Russell’s paradox by trying to imagine how a “set that IS a member of itself” would look like in reality, shall we? 
We know that a “set” is a collection of objects. Let’s assume that we have a collection of beers, not a huge one, just a few bottles. Let’s put them in a refrigerator (aka fridge) to chill. Also, we have a collection of snacks – beacon, salted pork, fish and such – lets put it all in the fridge as well. 
Now, as you may realize our fridge is a collection (set) of collections. What Russell’s logic (which is part of naïve set theory of cause) wants us to do is to include this set as a member (and hence, a subset) of itself. In real life this translates into a request to put the fridge with everything it holds into itself. I hope we’ll come to agree that this request just doesn’t make any sense. Neither should such operation be allowed in a consistent theory.
But let’s keep following Russell’s paradox’s logic. We are supposed to collect all the sets that are NOT members of themselves. Trust me, there’s a bunch of those. Collections of stamps, tea mugs, paintings, luxurious cars, bridges, cities, stars in the universe. Man, we’ll need a bigger fridge. But we are not to be afraid of infinites. Let’s just imagine that we’ve bested this enormous task. Now what Russell’s paradox wants us to do is to realize that our fridge that holds all those stuff is a set that is not a member of itself and therefore should be included into itself thus creating the paradox. Yet again, we are asked to put the darn fridge with everything in holds into itself and we already know that this just ain’t gonna happen. 
Thus in my understanding, Russell’s paradox arise due to performing an illegal (non-sense) operation that should not be allowed in a theory to be consistent.
--Orlangoor (talk) 15:13, 16 April 2008 (UTC)
replies: text: What you seem to be arguing is that the Russell paradox should not be surprising. That's fine. Not too many mathematicians or logicians really think it is surprising, these days, with benefit of the developments in the intervening hundred years. But matters were different at the time. Gottlob Frege had proposed a project to reduce all of mathematics to logic alone (the so-called logicist idea), starting with his interpretation (probably misinterpretation) of Cantor's set theory. The Russell paradox completely demolished Frege's approach. (It didn't destroy logicism completely, because it didn't rule out that mathematics might be reduced to logic alone in some other way. Many, but by no means all, mathematical logicians consider that possibility to have been ruled out by Goedel's incompleteness theorems.) --Trovatore (talk) 21:38, 25 April 2008 (UTC)

text: Well, I do believe sets can contain themselves. Read the natural numbers article. Now take the construction of natural numbers in set theory where S(a)=a ∪ {a}. Then, lets start with ∅. Then, keep making sure "this set contains itself". You end up with \aleph_0. Is \aleph_0 consistent? What do you think? voidnature 12:07, 14 May 2011 (UTC)
thread_title:  Russell’s paradox – let’s talk about beers in a fridge 

message: I know what I'm about to write may not endear me intellectually to my more intelligent superiors but this is one of a stream of articles I have been trying to read of the last few days which I can only gain a mild understanding of the subject from. I know that this is an encylopedia, but IMO (perhaps that dosen't count at all) encyclopedias are not intended to give an in depth mathy or sciency discussion or description of the subjects that they deal with, but an accessible overview. Perhaps I am just very stupid, but this article seems quite hard to understand, and the reason for this seems to be that whoever is writing this is being either unecessarily prolix in their description in order to show off they big brain, or that the people who are writing this are so far above the average mortal they don't seem to understand that people may be casually intrested in this subject and may not have a Phd in mathematics. The technical jargon here is all linked, but whenever I find I embarck on a journey to find the meaning of a mathematical term I have never seen before, I find five others on its article page, all described in such an unecessarily long-winded manner as Russel's paradox. If some sympatheitc demigod of the mathematical world is out there, would you take heart and see that stupid people such as myself would like to understand these problems, but would also like to do this without having to take a university course. Perhaps a way around this, as I have seen on some of the chemistry-related articles (a subject with which I am better acquainted with) would be to give the lead and most of the article in simple English (i.e. using terms that may see light outside the maths deparment at a Uni), and create sections where an in-depth knowledge can be granted. I once again humbly apologize for my stupidity.86.138.248.126 (talk) 18:38, 4 July 2008 (UTC)
replies: text: Chalk it up to the wiki process. It is easier to add a fact to an article than it is to organise a collection of facts into something readable. If you can give an example of an article on a chemistry topic (or any topic) which is of comparable difficulty but which is much more accessible, it would be appreciated. --EmbraceParadox (talk) 19:47, 4 July 2008 (UTC)

text: I think Russell's paradox should actually be easier to understand than the third law of thermodynamics, so the example is good. Not much should be required to at least get what it is and why people cared at the time, even if ZFC is too abstruse. --EmbraceParadox (talk) 18:20, 5 July 2008 (UTC)
thread_title: Huh?

message: I've always seen  this R set defined with an inverted R (the mirror image of it). Maybe the article should use the mirror image too. Albmont (talk) 14:33, 14 May 2009 (UTC)
thread_title:  R or its mirror image? 

message: We shall, therefore, have to say that statements about “all about “all propositions” are meaningless   (Whitehead and Russell 1910, 37)
This is a proposition about all propositions about all propositions. It declares itself to be meaningless.
No statement about all members of a group can be true.
The above statement is about all members of the group of statements about all members of a group. The statement itself is a statement about all members of a group.  It is a member of the group it is referring to.  It is a self-reference statement that declares itself to be untrue.Davidsstorm (talk) 16:14, 19 December 2009 (UTC)
replies: text: Ha! You sure? Let's see, "all members of the group of statements about all members of a group is equal to itself". That was all about "all members of the group of statements about all members of a group". It is obviously true. What do you think? voidnature 11:55, 14 May 2011 (UTC)
thread_title:  all propositions 

message: P = {all sets which contain themselves}
Q = {all sets which do not contain themselves}
A set is defined as a collection that contains all the elements of certain properties. Normally, the properties of an element can be written as an expression  just as (x + y + ...), when the expression is true the element belongs to a set, and when the expression is false the element not belongs to a set.
In Russell's paradox, P, Q are not existent sets. It is just as a question that in the conditions of Russell's paradox, whether there is a reasonable solution for P, Q. That is, Russell's paradox using a set of constraints to describe the set, a constraint can be written as a logical equation, so that multiple constraints can be written as a logical equations. Due to a logical equations may has no solution, when the constraints contains a description of whether an element belongs to a set, and the equations has no solution, then can not determine whether the element belongs to a set or not.
The direct cause of Russell's paradox is the definition of element properties conflict with the default rule of set theory, "an element has certain properties equal to the element belongs to a set". That is in the definition of element properties, it may different between "have some property" (the value of the expression x + y + ... ) and "belongs to a set" (a variable in the expression x + y + ... ). The value of the expression and a variable in the expression may not the same.
Qiuzhihong (talk) 17:16, 20 October 2010 (UTC)
thread_title:  The cause of Russell's paradox? 

message: All Russell's Paradox says is that defining {x|x∉x} is paradoxic. Since defining {x|x∉x} is paradoxic, {x|x∉x} cannot be defined. When people say "any definable collection is a set" and "Russell's Paradox showed that the naive set theory created by Georg Cantor leads to a contradiction" they should notice the paradox itself asserts that defining {x|x∉x} is paradoxic, therefore is not a definable collection, therefore is NOT a set. They should then notice the problem is NOT with the naive set theory, but with idioticy of people saying "any definable collection is a set" but defining {x|x∉x} is paradoxic and this is done in naive set theory so naive set theory is not consistent. So what do you think? voidnature 10:00, 14 May 2011 (UTC)
thread_title:  Russell's Paradox Only Asserts That {x|x∉x} Does Not Exist 

message: By definition, "any definable collection is a set", then, as the article and everyone above verbosely points out, the following turns out to not be definable: "Let R be the set of all sets that are not members of themselves", thus by definition, it's NOT a set, so where is the paradox?
It simply appears to me that simplistic "inverse" operations cannot be performed on sets, or that folks are trying to introduce incompatible things into sets - eg: having a "set" (i.e. some definition pertaining to elements) inside a set of elements, (e.g. mixing definitions and values together) is not unlike having imaginary and real numbers together - yeah, sure, do that, but you can't just ignore the fact that those beasts are different things (or different dimensions, if you think about this stuff spatially, like I do).
We all understand "number lines" - if you take any value on that line, and add something positive - you move right, or subtract, you move left.  Taking an "inverse" of a set, is like telling someone - here is my new position on the number-line - tell me what I added or subtracted to get here... when the "new position" is neither left nor right - but *up* (i.e. the spacial definition of an imaginary number - sqrt(-1)).  — Preceding unsigned comment added by 120.151.160.158 (talk) 07:58, 6 June 2013 (UTC)
thread_title:  Nitpicking - I cannot see any paradox here. 

message: This has been a problem for a long time, and I still don't know the best way to solve it.  But the recent change that an IP suggested, https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&type=revision&diff=677498532&oldid=677443163, is at least a start. Update:  It turns out that I had misinterpreted the history and an edit summary; the change was not by the IP.  It was my own change, from more than a year earlier. --Trovatore (talk) 19:51, 26 August 2015 (UTC)
thread_title:  Blaming RP on Cantor and/or informality 

message: This article needs a citation to Russell.  The article has a lot of discussion of the paradox, but does not cite the origin. Geoffrey.landis (talk) 17:28, 2 September 2018 (UTC)
thread_title:  Original Citation needed 

message: Is there a consensus on whether the Barber paradox is a variant of this paradox? As documented, Russell himself did not think it was. 37KZ (talk) 14:57, 13 November 2019 (UTC)
thread_title:  [[Barber paradox]] == Russell's paradox? 

message: An editor has asked for a discussion to address the redirect List of lists of lists that don't include themselves. Please participate in the redirect discussion if you wish to do so.  NineFiveSeven 17:36, 6 January 2020 (UTC)
thread_title:  "List of lists of lists that don't include themselves" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has asked for a discussion to address the redirect List of lists that don't include themselves. Please participate in the redirect discussion if you wish to do so.  NineFiveSeven 17:50, 6 January 2020 (UTC)
thread_title:  "List of lists that don't include themselves" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has asked for a discussion to address the redirect The set of all sets that do not contain themselves. Please participate in the redirect discussion if you wish to do so.  NineFiveSeven 18:25, 6 January 2020 (UTC)
thread_title:  "The set of all sets that do not contain themselves" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Its definition is like the like the set R in the article: i.e. x belongs to R if and only if x does not belong to x (however, determine whether a positive integer x is a Russell number may be very difficult, the smallest unknown x is 319) 2402:7500:917:8A69:2C6E:A04F:8752:A7E0 (talk) 05:09, 11 July 2022 (UTC)
thread_title:  Can {{OEIS|A053169}} be called “Russell numbers”? 

message: The "Formal presentation" section begin with a description of the Axiom of extensionality. However I don't see how this axiom is relevant nor that it is used anywhere in the rest of the section, which just uses Comprehension, Existential instantiation and Universal instantiation. Extentionality is also not mentioned in the source cited. Should the reference to extentionality be deleted? CodeTalker (talk) 20:11, 22 January 2023 (UTC)
thread_title:  Axiom of extensionality