text:
User talk:Mennonot/archive1

Welcome to the Wikipedia
Here are some links I find useful

 * Policy Library
 * Cite your sources
 * Verifiability
 * Wikiquette
 * Conflict resolution
 * Brilliant prose
 * Neutral point of view
 * Pages needing attention
 * Peer review
 * Bad jokes and other deleted nonsense
 * Village pump
 * Boilerplate text

Feel free to ask me anything the links and talk pages don't answer. You can sign your name by typing 4 tildes, likes this: ~.

Cheers, Sam [Spade] 20:33, 14 Jun 2004 (UTC)

No, I really don't
I reviewed your edits just now, and they all seem fine. Mostly just minor stuff, but helpful (adding links, etc...). Nothing advice-wise occurs to me specific to your edits thusfar. If you have any particular questions feel free to ask, but you seem to be doing great. Glad to have you, Sam [Spade] 20:43, 14 Jun 2004 (UTC)

Be bold!
If you need any specific advice, I might be able to help, But I learn best by doing ;) Have you said anything in the article talk? I doubt you'd be answered, but if it were a more often used page it would be useful. In this case I'd just leave a note explaining after the fact, myself. Sam [Spade] 01:56, 15 Jun 2004 (UTC)

Current events
I assume you blanked the page accidentally?! Lupo 09:57, 30 Sep 2004 (UTC)
 * Yeah, sorry about that. I'm not sure how it happened. I think it had something to do with taking too long on a oft-edited page... mennonot 09:59, 30 Sep 2004 (UTC)

Is there a way to link to a category without joining it?
Yes, use category:Heretics for category:Heretics.

FLDS
Oops. Sorry. Thanks for explaining. If you haven't fixed, I will. Great to meet you. By the way, I have been trying to drum up some contributions from some FLDS members, but it is coming slowly. Tom Haws 17:36, Jun 20, 2005 (UTC)

Resistance and struggle
I don't know what part of nonviolent resistance concerns any other means of "achieving one's goals" than by defeating one's opponents - through means other than violence. A couple of the sections, in fact, were more about using violence.

I didn't do a point for point count, but roughly half to 3/4 or the 'resistance' article was about resisting and overcoming. Wouldn't you agree than was more specific than just "achieving one's goals"? I'm studying a foreign language and learning piano. What part of achieving these goals has any relation to nvr? Uncle Ed 03:00, July 11, 2005 (UTC)

Socialist church
The socialist church movement arose in late nineteenth century Britain. Although we don't yet have an article on it, I thought that it may be of interest to readers of the peace church article as another radical church-based movement. Warofdreams 09:28, 12 September 2005 (UTC)
 * There are several sources for socialist or labour churches. Krupskaya's description of a visit is very negative but gives somthing of their flavour, and the footnote of this article on the labour church has some more detail, but the best resource is probably the 1911 encyclopaedia article. Hope you can write something from these sources, Warofdreams talk 09:57, 14 September 2005 (UTC)

Bocholt meeting
Hi Tim. Thanks for the query on my talk page & blog mention. My source for the meeting is Jansma's book (see references at the foot of the page itself), pp.218-20 - his title, incidentally, translates as "Melchiorites, Münsterites and Batenburgers. A Sociological Analysis of a Millennial Movement from the 16th Century". It's a bit dry, but by far the most complete source on the Batenburgers and their kin; in fact Jansma is the only scholar to have made a thorough study of the movement. Unfortunately his work is only available in Dutch. I cannot say with any certainty whether his account is more correct than that of Williams. But, actually, I'm not surprised accounts differ, as quite possibly the sources themselves are in dispuite; the various sects had such different agendas to push. I'm going to update the Batenburgers article by qualifying my statement about lack of resolution. Mikedash 22:36, 15 September 2005 (UTC)

hi Tim,
i've been meaning to drop a line and say "hi" to you and was prompted by your recent edit to Mennonite. just FYI, i'm a mennonite "in exile" (i live to far from a Mennonite church to conveniently connect and my spouse is an Episcopalian). i'm still a member of Manhattan (NYC) Mennonite Fellowship. my other life is as an audio electrical engineer. r b-j 14:33, 1 November 2005 (UTC)

 * I don't think I've seen another regular editor who is Mennonite. It's nice to know there are others around. Perhaps some day we'll have enough to have a committee or something :-) mennonot 22:41, 1 November 2005 (UTC)

 * anyway, i have to admit that i discovered your existence here at WP from reading some example in the Arbitration help pages. i can't find it now.  looks like we both got into some disputed stuff that went to ArbCom.  for me it was Bogdanov Affair. anyway, nice to meet you.  if you're originally from North America, perhaps we can play the Mennonite game and find someone we both know.  i would start with a guy named Merv Horst (the only other Mennonite i know who's been to London).r b-j 02:46, 2 November 2005 (UTC)

 * That's really funny that you saw my name through arbcom. I had no idea my name was turning up on arbitration pages. After reading your comment I googled Mennonot and arbitration and got 79 results. After some digging I discovered that an edit by me was used as an example on the template that is stuck on people's page's when gathering evidence. After some digging I found the original template. The edit itself was a minor and random one and I've never personally been involved in arbitration. I guess it's completely random that I got used. I guess it's all in the spirit of open souce. :-)
 * As for the Mennonite game, I don't recognise the name Merv Horst, but I've only been here in London for two years or so. I'm originally from Goshen, Indiana. If you've got Manhattant ties, do you know Nekeisha who is now in Elkhart?mennonot 23:38, 2 November 2005 (UTC)

 * yeah, Nekeisha is married to Andy Baker and they came to MMF just after Phyllis and i and kids moved to VT. even though we're 5 hours away, we try to get down ("down" for us, it's upstate NY for the MMFers) to the retreats and keep in touch.  i can identify a little with Andy's and Nekeisha's theopolitics (i might be described as a middle-aged left-leaning long-haired hippie), but it seems to me that they take no prisoners and i would rather be taken more seriously so i'm a little more pragmatic.  but i still have some idealism, i was a Howard Dean volunteer (and even got to introduce the Guv to a town hall meeting during the NH primary).  there's a lot of stuff i would like to see different, but i'm not quite a Jesus-anarchist.  being in Elkhart/Goshen, have you met, or do you know John Rempel (former MMF pastor and MCC UN liason and now teaching at AMBS)?
 * also, tell me what's going on in London. it's a curiousity. r b-j 00:47, 3 November 2005 (UTC)

Athanasius
I still haven't had time to look into the Athanasius claims. Recognize however that the Mennonite views on the nature of Christ, as much as the Reformed (which I am), Catholic, Orthodox, or anyone else, come from Athanasius. Evan Donovan 03:29, 4 November 2005 (UTC)
 * I hear you. Problem is, some of the Christians I admire most have deeply problematic parts of their theology and practice (Augustine's urging of force against the Donatists, Bernard of Clairvaux's support of the Second Crusade, Luther's support of the nobles in the Peasants' War, not to mention his antisemitism or violent opposition to your theological predecessors, Calvin's tacit support of executions for heresy).  I try not to become a hero worshipper of anyone, recognizing that if I were to somehow become historically significant in the Church, people would be able to find similar inconsistencies and sins in my own life.

 * Lancaster County is a good place. I'm always glad to find others who were born there.  I don't really feel in some ways like a native though. Evan Donovan 05:49, 6 November 2005 (UTC)

Athanasius II
Just a typo. Thanks for noticing. Good luck w/ your Wiki and real life work. Kudos on the photos. By the way "emperor" may have been misspelled on your user page. God's peace, Dpr 05:20, 9 November 2005 (UTC)

Community
Thanks for joining the Community project, Tim. To answer you're note there, I suppose the best classification we have so far is a simple flat list that appears on the Community_(disambiguation) page. That's actually something we need to work on. Maybe a table of the diffierent types of communities like the list being used on the Community of practice article. At any rate, Welcome to the Community Builders Task Force! Just chime in on the discussion page there, and we'll see if we can get some things rolling :) -- CQ 16:58, 27 November 2005 (UTC)

Wikipedia Anti-war project, push to get a featured article b4 Xmass
February 15, 2003 anti-war protest, an article which is part of the WikiProject Anti-war of which you are listed as a member, has been recently rated A-class by the Version 1.0 Editorial team (see here) This means that it is considered to be of good quality. The Anti-war project has yet to achieve a featured article but with a little pushing I feel we could get this article up to FA standards. To this end I have put the article up for peer review, if you could help make this a brilliant article that would be much appreciated. Please give your comments at Peer review/February 15, 2003 anti-war protest/archive2 or on the article's talk page. Fingers crossed for a FA before Xmass.--JK the unwise 13:06, 30 November 2005 (UTC)

Andrés Manuel López Obrador
Thanks for your vandalism revert at this page. I just wanted to tell you that whehn you revert blatant vandalism (such as breaking the code, blanking text, or adding "hi mom!"-type comments) you don't need to explain yourself in the article's talk page. People will usually check the diffs so the edit would be enough. On the other hand when you make controversial changes to the content of an article then further explaining yourself in talk pages is highly appreciated.

I say this to save you time. Edit summaries are your friends! Let me know if you need help in anything around the wiki. Happy editing. -- Rune Welsh | ταλκ | Esperanza  16:34, 27 December 2005 (UTC)

title: User talk:Mennonot/archive1


text:
August Friedrich Gfrörer

August Friedrich Gfrörer (5 March 1803 – 6 July 1861) was a German historian.

Biography
He was born at Calw, in Württemberg. Obedient to the wishes of his parents, but against his own inclinations, he devoted himself to the study of theology; was a student at the "Little Evangelical Seminary" of Tübingen from 1817–21, and from 1821-25 continued his studies at the higher seminary of the same place. He completed his education by a series of scientific travels through Switzerland and Italy, during part of the time acting as companion and secretary to Charles de Bonstetten, after which he returned to his alma mater.

In 1829, he was appointed vicar in the city of Stuttgart. Having by this time lost all belief in revealed religion, he became convinced that to continue his pastoral duties would involve him in serious conflict; he therefore resigned his vicarage. At the recommendation of Victor von Bonstetten, a friend of his father, he was appointed third librarian of the public library of Stuttgart (1830) with the title of professor. During his numerous hours of leisure he applied himself with vigour and enthusiasm to the study of literature and history.

Around 1846, he was appointed professor of history at the Catholic University of Freiburg (Breisgau). In 1848, he was elected to the German Parliament at Frankfurt as representative of a district of Württemberg; he belonged to the greater German party, and was a fanatical opponent of Prussia. It is a notable fact that, while in Parliament, he proposed a motion for the reunion of Catholics and Protestants, but only on condition that the Holy See would promise never to permit the Jesuits or Redemptorists to settle on German soil.

In 1853 he entered the Catholic Church, after all the other members of his family had taken the same step. He died at Karlsbad in 1861.

Works
The 1913 Catholic Encyclopedia describes Gfrörer as "bold" and "prolific", praising his "great acumen" and "unusual ability", but says that "his literary researches were sometimes lacking in method."

Gfrörer's first major publication was Philo und die judisch-alexandrinische Theosophie (2 vols., Stuttgart, 1831). This work was preparatory to his larger work entitled Kritische Geschichte des Urchristenthums (Stuttgart, 1838, in 5 vols.). In it Gfrörer, probably impelled by David Strauss's Leben Jesu, sought to conceive historically the life and teaching of Christ, and, although writing as a rationalist throughout, he strongly disclaims being "an adherent of the modern champion of negative truths", (i.e. of Strauss).

In the first part, with the sub-title Das Jahr des Heils, he investigates the time in which Christ lived; in the second, entitled Heilige Sage, he treats of the authenticity and literary character of the first three Gospels, and in the third, Das Heiligthum und die Wahrheit, he discusses the Gospel of John. The work, therefore, is a detailed investigation of the character and significance of the New Testament from an historical point of view, and is based on a wealth of materials. At the same time he studied the history of the Thirty Years' War, and in 1835 (in Stuttgart) published Gustav Adolf, König der Schweden und seine Zeit (4th ed., 1863), in which by emphasizing the political role of the Swedish king he took a position diametrically opposed to the views previously held by Protestants.

An equally profound impression, especially in Catholic circles, was produced by his Allgemeine Kirchengeschichte (4 vols., Stuttgart, 1841–46). Closing with the year 1305, it emphasises the part played by the Catholic Church in the development of the German Empire, and extols the policy of the popes.

His later publications are:

 * Geschichte der ost- und westfränkischen Karolinger (Freiburg, 1848, 2 vols.)
 * Die Urgeschichte des menschlichen Geschlechts (Schaffhausen, 1855, 2 vols., incomplete), which argues that neither critical history nor the natural sciences, in treating of the origin and earliest history of the human race, can lay claim to certainty, when opposed to the earliest traditions of mankind and especially to the Bible
 * Papst Gregorius VII und sein Zeitalter (Schaffhausen, 1859–61, in 7 vols.), a part of his Church History, notable for its brilliant scholarship and conscientious research

Many volumes of lectures were published posthumously:
 * Geschichte des 18. Jahrhunderts (Schaffhausen, 1862–73; Vols. I-IV by Johann Baptist Weiss; second part of the fourth vol. by Tiedemann, Basle, 1884)
 * Zur Geschichte deutscher Volksrechte im Mittelalter (Schaffhausen, 1865, 2 vols.)
 * Byzantinische Geschichten (Graz, 1872–74, 2 vols.)

His Prophetae veteres pseudepigraphi latine versi (Stuttgart, 1840), with translation, is critically unsatisfactory.

Gfrörer also translated and edited History of the Jewish War or the downfall of the Jewish people to its capital Jerusalem, by Flavius Josephus (Stuttgart, Leipzig: Rieger, 1836).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: August Friedrich Gfrörer


text:
Tender Buttons (album)

Tender Buttons is the third studio album by British indie electronic band Broadcast. Following the departure of several bandmembers, the album was recorded largely as the core duo of Trish Keenan and James Cargill, and as such is considered to have a rawer and more stripped back sound than previous Broadcast releases. It was released on 19 September 2005 by Warp. Upon its release, Tender Buttons received acclaim from critics but failed to place in international charts. "America's Boy", the lead and only single from the album, peaked at No. 139 in the UK Singles Chart.

Reception
Upon its release, Tender Buttons received critical acclaim. At Metacritic, which assigns a weighted average score out of 100 to reviews and ratings from mainstream critics, the album received a score of 76, based on 21 reviews, indicating "generally favorable reviews". AllMusic writer Heather Phares said that the album "strips [the band's] luminous electronic pop down to its barest essence" and "has a uniquely fresh, modern feel. Sparingly applied beats, intricate but subtle guitars, and hazy synths dominate the album, providing a restrained backdrop for Keenan's quietly commanding voice and crossword-puzzle lyrics." The Guardian's David Peschek wrote that "Broadcast's recent records have often seemed too cluttered with effects" but that on Tender Buttons the band "managed to find a halfway house between this always engaging but fussed-at sound and … resonant, muscular psychedelia". In a positive review, Paul Woloszyn of musicOMH said that the album "takes you to another planet with a sonic soundscape lent from Stereolab, but developed to be distinctly Broadcast", and referred to the album as "arguably their finest moment".

Writing for Stylus Magazine, Jeff Siegel said that "on its surface, [Tender Buttons] seems like such a simple little curlicue, all Mother Goose coos, descending-scale melodies, and no-wave screech over dinky drum-machine patters … no mucking around in different time signatures, no showy genre fusions, just a single idea … most acts would falter here, but Broadcast pull it off with an easy grace and breezy elegance". PopMatters reviewer Adrien Begrand wrote that "instead of finding a comfortable middle ground, there's more of a sense of tension to the proceedings, the vocal hooks lulling you, only to have electronic noise jolt you awake", further referring to Tender Buttons as "rewarding [and] their boldest album to date." Pitchfork's David Raposa was more reserved in his praise, saying that the band "bring the melodies, but then dress their poptastic efforts with whatever ruckus they can conjure" and "there's no … stand-out track on this album (and there's certainly no 'oh wow' moments)" but concluding that "this is still a Broadcast album, meaning it's one of the better things you'll put in your ear this year."

In 2018, Pitchfork ranked Tender Buttons at number seven on its list of the 30 best dream pop albums. In 2023, British GQ ranked it at number eight on its list of the 10 best electronic albums of all time.

Personnel
All personnel credits adapted from Tender Buttons' album notes.

 * Broadcast
 * Trish Keenan – vocals, production, engineering, recording, mixing
 * James Cargill – bass, production, recording, mixing
 * Roj Stevens – keyboards, effects (2)
 * Tim Felton – guitar (6)

 * Design personnel
 * Julian House – artwork

title: Tender Buttons (album)


text:
Wikipedia:Articles for deletion/Bangkatan

 This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was speedy deleted. Sjakkalle (Check!)  09:22, 21 July 2005 (UTC)

Bangkatan
Patent nonsense. This is vandalism by User:202.156.2.36. I think he refers to a street (Bangket Street) in Binjai Park, Singapore. Googling for "Bangkatan" reveals zero hits. Alex.tan 16:03, July 11, 2005 (UTC)
 * Speedy as article with little or no content. --Scimitar 16:38, 11 July 2005 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.


text:
User:Linzer2002

I am interested in Autism and Asperger syndrome.

title: User:Linzer2002


text:
Wikipedia:Articles for deletion/Betzefer

 This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was Delete --Allen3 talk 20:45, July 22, 2005 (UTC)

Betzefer
Unsure if band is notable or not (they are a group from Israel, supposedly), but their only release has come in 2005. Text is generally indicative of vanity, but I can't make a call on it. Can somebody please check the validity of this group? If not proven otherwise, the paucity of releases and meagre discography would call for a delete, I feel. jglc | t | c 16:05, 11 July 2005 (UTC)
 * Weak Keep - Tough call, no Allmusic page but 3,500 Google results for Betzefer "down low", among the results are interviews and reviews so at least some people find them notable, which is usually good enough for inclusion. I don't think they meet the criteria for WP:MUSIC, but that doesn't discount support for other pages, see Votes for deletion/Ampere (band). No big loss if it's deleted though, if they become more notable in the future a page can be created then. --TheMidnighters 17:53, 11 July 2005 (UTC)
 * Delete - After consideration, should go by the books regardless, doesn't pass WP:MUSIC, doesn't warrant inclusion yet. Sorry for the convoluted switching. --TheMidnighters 20:12, 11 July 2005 (UTC)

 * This band has just joined RoadRunner Records. If you check their website you should be able to find out more about them. — Preceding unsigned comment added by 80.42.254.150 (talk • contribs) 18:24, 11 July 2005
 * Comment: many bands are signed. Few go anywhere. Also, regarding Votes for deletion/Ampere (band), it seems as though the reason Ampere was kept was both for their being signed, as well as their inclusion of a well-known musician on the lineup. I'm still not judging Betzefer either way, but it seems that they do not - and being signed, in itself, does not fulfill the criteria for WP:MUSIC. jglc | t | c 18:59, 11 July 2005 (UTC)
 * Well known musician? The name of this well known musician isn't present in either the Orchid (band) page or the Ampere (band) page, so how can he be well known if we don't even know his name. My point is simply that Ampere does not satisfy WP:MUSIC but will probably be kept, therefore, the fact that this band does not satisfy WP:MUSIC does not necessarily justify a deletion. Either way I don't really care if it's deleted or not, I just think deletions should be consistent. --TheMidnighters 19:20, 11 July 2005 (UTC)
 * My bad. I was under the impression, after skimming over Votes for deletion/Ampere (band) was that this was a reason for the supporters to say that the band should be kept. I agree with the deletions being consistent, leaning towards noninclusionism. jglc | t | c 19:24, 11 July 2005 (UTC)
 * Simply put, neither pass WP:MUSIC, neither should stay. --TheMidnighters 20:19, 11 July 2005 (UTC)
 * I am in strong agreement. jglc | t | c 20:19, 11 July 2005 (UTC)

 * Delete per TheMidnighters. Dcarrano 21:09, July 11, 2005 (UTC)
 * Delete notability not established. JamesBurns 06:24, 12 July 2005 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.


text:
Bell v Lever Brothers Ltd

Bell v Lever Brothers Ltd [1931] UKHL 2 is an English contract law case decided by the House of Lords. Within the field of mistake in English law, it holds that common mistake does not lead to a void contract unless the mistake is fundamental to the identity of the contract.

Facts
Lever Brothers Ltd (which merged in 1930 to become Unilever) was a company which traded in West Africa, through a 99% owned subsidiary called the Niger Company (formerly the Royal Niger Company). The Niger trade was in trouble. Lord Leverhulme, the owner of Lever Bros, hired D'Arcy Cooper (a Quaker and senior partner of his uncle's accountant firm, Cooper Brothers) to be the chairman and manage the crisis. Cooper negotiated a loan from Barclays Bank, which insisted that a professional management run the Niger subsidiary. Cooper hired his friend, Ernest Hyslop Bell, a senior Barclays manager in 1923 as chairman of the subsidiary. Mr Snelling, a tax consultant that had successfully got Lever Bros a big tax refund in 1921, was appointed as vice chairman. They did well, and turned a profit. The company was then merged with a former competitor (African and Eastern Trade Corporation) to form the United Africa Company in 1929.

Bell had wanted to run the new United Africa Company, because he was too old at 54 to have a job in the City, and he had left his Barclays position. At lunch in the Savoy Grill he agreed with Cooper that he would get a big compensation package (£30,000) and retire. A similar "golden parachute" of £20,000 was given to Mr Snelling. However, shortly after, it was revealed that Bell and Snelling had been part of a regional cocoa cartel, and used information on future price reductions to sell cocoa from their personal accounts. Lever Brothers Ltd therefore brought a claim for rescission of the compensation package on grounds of mistake of fact.

Trial
The initial trial was held before Wright J and a City of London Special Jury. The jury found that Bell and Snelling's illicit dealings breached the employment contract and that if the Lever Brothers had known they would not have entered into the agreement. Furthermore, the jury found that at the time of the agreement Bell and Snelling did not have in mind their illicit acts. Wright J therefore held the compensation agreements were void.

House of Lords
On appeal, the House of Lords found that there was no mistake and the contract could not be rescinded nor was it void on mistake. Lord Atkin was writing for the majority. Dissent was written by Warrington and held that the mistaken assumption was fundamental to the contract, and thus the contract is voidable.

The Court identified the mistake as a common mistake.

A mutual mistake as to some fact which, by the common intention of the parties to a contract, whether expressed or implied, constitutes the underlying assumption without which the parties would not have made the contract they did, and which, therefore, affects the substance of the whole consideration, is sufficient to render the contract void.

Effectively, the mistake must nullify or negative consent of the parties in order for the agreement to be void.

In order for the contract to be void by common mistake the mistake must involve the actual subject-matter of the agreement and must be of such a "fundamental character as to constitute an underlying assumption without which the parties would not have entered into the agreements".

From the facts the Court found that the mistake was not sufficiently close to the actual subject-matter of the agreement. The parties got exactly what they had bargained for.

The MacMillan article explains that the ratio was in part the result of media attention at the time, and socio-economic context of the trial.

Discussions
In an article by JC Smith, "Contracts- mistake, frustration and implied terms", it is suggested that Bell v. Lever Brothers can be analysed into cases of res sua and res extincta.

Lever Brothers in substance was buying the right to 'extinguish' Bell and Snelling. Both parties were under the common mistake that Lever Brothers should pay the "Golden Parachutes" to Bell and Snelling. Lever Brothers did not know Bell and Snelling were speculating while Bell and Snelling did not know their speculation would entitle Lever Brothers to dismiss them without paying anything.

In the point of view of Lever Brothers, they are in substance buying a right they already had, that is extinguishing Bell and Snelling without paying a cent. This would be a case of res sua, since you cannot buy something you already have.

In the point of view of Bell and Snelling, it is the right of entitling the "Golden Parachutes" they are selling. This right does not exist since they speculated. The subject-matter they tried to sell, their right, no longer exist before they enter into the contract. This would be a case of res extincta, the disappearance of the subject-matter of the contract.

In either way, the contract would be void for mistake, though the House of Lords held that the mistake is not fundamental enough.

Significance
The case put a high standard on the finding of common mistake. This was criticized in the later cases written by Lord Denning such as in Solle v Butcher where Denning LJ reduced the standard by enumerating an equitable remedy for a shared common mistake, which rendered the agreement voidable. Subsequently, in Great Peace Shipping Ltd v Tsavliris Salvage (International) Ltd (2002) the Court of Appeal purported to overturn Solle v Butcher and set the standard for common mistake in line with the original Bell v Lever Brothers standard.

Also in Scottish Co-operative Wholesale Society Ltd v Meyer, Lord Denning remarked the following, in the context to the equivalent of an unfair prejudice action under UK company law. "Your Lordships were referred to Bell v Lever Brothers Ltd where Lord Blanesburgh said that a director of one company was at liberty to become a director also of a rival company. That may have been so at that time. But it is at the risk now of an application under section 210 if he subordinates the interests of the one company to those of the other."

title: Bell v Lever Brothers Ltd


text:
Generic filter

In the mathematical field of set theory, a generic filter is a kind of object used in the theory of forcing, a technique used for many purposes, but especially to establish the independence of certain propositions from certain formal theories, such as ZFC. For example, Paul Cohen used forcing to establish that ZFC, if consistent, cannot prove the continuum hypothesis, which states that there are exactly aleph-one real numbers. In the contemporary re-interpretation of Cohen's proof, it proceeds by constructing a generic filter that codes more than $$\aleph_1$$ reals, without changing the value of $$\aleph_1$$.

Formally, let P be a partially ordered set, and let F be a filter on P; that is, F is a subset of P such that:
 * 1) F is nonempty
 * 2) If p, q ∈ P and p ≤ q and p is an element of F, then q is an element of F (F is closed upward)
 * 3) If p and q are elements of F, then there is an element r of F such that r ≤ p and r ≤ q (F is downward directed)

Now if D is a collection of dense open subsets of P, in the topology whose basic open sets are all sets of the form {q | q ≤ p} for particular p in P, then F is said to be D-generic if F meets all sets in D; that is,

 * $$F\cap E \ne \varnothing,\,$$ for all E ∈ D.

Similarly, if M is a transitive model of ZFC (or some sufficient fragment thereof), with P an element of M, then F is said to be M-generic, or sometimes generic over M, if F meets all dense open subsets of P that are elements of M.

title: Generic filter


text:
Talk:Black May (1992)

I have some "unconfirmed" details, the people leading this brutal intermezzo was fired the near days after or degraded to desktop-work.

Government counts 50 dead
The actual death toll of Black may was much higher some say as much as 10,000. The bodies were quickly removed and disposed of by the military and were never found. This article fails to convey the travesty that was this MASSACRE, it was not simple altercation. Thousands lost their lives and that should be recognized. —Preceding unsigned comment added by 144.91.51.253 (talk) 06:21, 21 February 2008 (UTC)

What a crap and false article. 50 deads. I myself saw in front of my eyes, 560 young people being cut in pieces and thrown into a canal in Banglamphoo near the Chao Praya River and these liars (paid by some of these genocidal government) say us there were 50 deads. This is complicity in genocide. Real deat toll was DOZENS OF THOUSANDS. —Preceding unsigned comment added by 58.11.37.146 (talk) 17:28, 25 August 2010 (UTC)
 * I am finding the sources of this claim too, but I found nothing. If anyone know the source, please update.--Polyesterchips (talk) 03:41, 19 December 2021 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on Black May (1992). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added tag to http://www6.cityu.edu.hk/searc/Data/FileUpload/212/WP25_02_Choi.pdf
 * Added archive https://web.archive.org/web/20070927141226/http://www.seameo.org/vl/92may/92may1.htm to http://www.seameo.org/vl/92may/92may1.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 10:21, 21 July 2017 (UTC)

title: Talk:Black May (1992)


text:
Category talk:Political parties of minorities

Untitled
There seems to be a confusion between ethnic/minority parties and regionalist/separatist parties, shouldn't only the first be characterized as "political parties of minorities" ? --Pylambert 16:07, 11 July 2005 (UTC)


text:
Winkler

Winkler may refer to:

 * Winkler (surname), people with the surname Winkler or Winckler
 * Winkler scale, also known as the heat summation scale for classifying climates
 * Winkler (crater), a crater on the Moon
 * 6473 Winkler, an asteroid
 * Winkler method, a test to determine dissolved oxygen concentration in water
 * Winkler vine, an example of large-vine grape culture
 * Winkler (novel), by Giles Coren
 * Winkler + Dünnebier, German machine building company

 * Places
 * Winkler, Manitoba, a Canadian city
 * Winkler, Kansas, an unincorporated community
 * Winkler, Missouri, an unincorporated community
 * Winkler County, Texas, a county in the state of Texas

title: Winkler


text:
Cold Water Music

Cold Water Music is the debut studio album by British musician Aim, released on 11 October 1999 by Grand Central Records. The album was re-issued in 2007 by ATIC Records.

Song information
The first track, "Intro", contains a sample from the documentary Hoop Dreams (1994) of William Gates, one of the basketball players followed in the film, speaking from his recovery room after surgery. The commentary forms the lyrics to the track. The track "Cold Water Music" contains a sample of "Maureen in the Desert", written by Carter Burwell and taken from the soundtrack to the film Psycho III (1986). The extended dialogue in the track "Demonique" was sampled from the John Carpenter horror films, Halloween (1978) and Halloween II (1981). It features (primarily) the exchanges between the characters of Dr. Sam Loomis (Donald Pleasence) and Sheriff Leigh Brackett (Charles Cyphers). The track "Ain't Got Time to Waste" is featured on the soundtrack of the European version of the video game Tony Hawk's Pro Skater. The track “Force” includes a sample of Spirit's “Mr. Skin.”

Personnel
Credits for Cold Water Music adapted from album liner notes.

 * Aim – arrangement, production, scratching, sleeve design

Additional musicians
 * A.G. – performance
 * Q'n'C – performance
 * Kate Rogers – performance
 * Josef Ward – horns
 * YZ – performance

Production
 * Mike Ball – engineering (assistant)
 * Steve Christian – engineering, mixing
 * Nilesh Patel – mastering

Design
 * Nick Fry – artwork, design
 * Benge Newman – liner notes
 * Tony Stone – photography
 * Phil Turner – photography

title: Cold Water Music


text: User talk:196.202.144.3

title: User talk:196.202.144.3


text:
User talk:JakeWalley

Welcome!

Hello,, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~); this will automatically produce your name and the date. If you need help, check out Where to ask a question, ask me on my talk page, or place  on your talk page and someone will show up shortly to answer your questions. Again, welcome! Gamaliel 16:10, 11 July 2005 (UTC)
 * The five pillars of Wikipedia
 * How to edit a page
 * Help pages
 * Tutorial
 * How to write a great article
 * Manual of Style

title: User talk:JakeWalley


text:
Wikipedia:Collaboration of the week/Learning

Learning (July 25)

 * Nominated on 16:10, 11 July 2005 (UTC); needs 10 votes by July 25.

A topic that concerns everybody and it is just a stub.

Support:
 * 1) Fenice 16:10, 11 July 2005 (UTC)
 * 2) ZeWrestler 16:24, 11 July 2005 (UTC)
 * 3) Wackymacs 17:03, 11 July 2005 (UTC)
 * 4) Poli 19:46, 2005 July 11 (UTC)
 * 5) Newbie222 20:32, 11 July 2005 (UTC)
 * 6) Matthew kokai 07:49, 13 July 2005 (UTC)
 * 7) McCart42 (talk) 14:46, 13 July 2005 (UTC)
 * 8) Steven McCrary 19:17, July 13, 2005 (UTC)
 * 9) bjwebb 18:52, 15 July 2005 (UTC)
 * 10) Fallstorm 18:09, 16 July 2005 (UTC)


text:
User talk:Fonzie Fann

User:Fonzie Fan was not blocked; User:Wikipedia Vandalism Warning Bot was just fucking with you. Keep the Fonzie coming. --SPUI (talk) 16:11, 11 July 2005 (UTC)

title: User talk:Fonzie Fann


text:
User:Nrets

Please leave messages on my Talk Page.

title: User:Nrets


text:
Portuguese language in Africa

Portuguese is spoken in a number of African countries and is the official language in six African countries: Angola, Cape Verde, Equatorial Guinea, Guinea-Bissau, Mozambique and São Tomé and Príncipe. There are Portuguese-speaking communities in most countries of Southern Africa, a mixture of Portuguese settlers and Angolans and Mozambicans who left their countries during the civil wars. A rough estimate has it that there are about 14 million people who use Portuguese as their sole mother tongue across Africa, but depending on the criteria applied, the number might be considerably higher, since many Africans speak Portuguese as a second language, in countries like Angola and Mozambique, where Portuguese is an official language, but also in countries like South Africa and Senegal, thanks to migrants coming from Portuguese-speaking countries. Some statistics claim that there are over 60 million Portuguese speakers in the continent. Africa is, therefore, the continent with the second-most Portuguese speakers in the world, only behind the Americas. Like French and English, Portuguese has become a post-colonial language in Africa and one of the working languages of the African Union (AU) and the Southern African Development Community (SADC). Portuguese co-exists in Guinea-Bissau, Cape Verde, and São Tomé and Principe with Portuguese-based creoles (Upper Guinea and Gulf of Guinea Creoles), but Portuguese continues to be the official language of these countries.

Portuguese has become the national language of Angola, as it is so widely spoken in every segment of society, and serves as the home language of the majority of the Angolan population, particularly in the big towns and cities. A few native African languages continue to be spoken, but are losing ground to Portuguese. In Mozambique, in addition to Portuguese as the official language, it is fast becoming the lingua franca. And as in Angola, Portuguese is the dominant spoken language in the urban areas of the country. In the five former African Portuguese colonies, Portuguese is the language of: commerce, the government, courts, schools and mass media.

In Africa, the Portuguese language experiences pressure and possibly competition from French and English. Cape Verde, Guinea-Bissau and São Tomé and Príncipe are all members of La Francophonie and Mozambique is a member of the Commonwealth of Nations and has observer status at La Francophonie. Conversely, Equatorial Guinea has announced its decision to introduce Portuguese as its third official language, in addition to Spanish and French, and has been accepted as a member CPLP. Mauritius and Senegal have also joined the CPLP as associate observer members.

Geographic distribution
The nation-states with Portuguese as an official language in Africa are referred to by the acronym PALOP (Países Africanos de Língua Oficial Portuguesa) and include the following: Angola, Cape Verde, Guinea-Bissau, Mozambique, São Tomé and Príncipe and Equatorial Guinea. Portuguese is a primarily urban language having a reduced presence in rural areas, except for in Angola and São Tomé and Príncipe, where the language is more widespread on a national level.

South Africa also has approximately 300,000 speakers of Portuguese, primarily settlers from Madeira and white Angolans and Mozambicans who emigrated from 1975 onwards, following the independence of the former colonies. The civil wars in Angola and Mozambique also resulted in more recent migrations of refugees (some of whom speak Portuguese) to neighbouring countries such as Democratic Republic of Congo, Namibia, Zambia and South Africa. Other migrations involved returning Afro-Brazilian ex-slaves to places such as Nigeria, Benin, Togo, Angola and Mozambique. There are also some returning white Portuguese African refugees and their descendants from Brazil, Portugal, and South Africa to their former African controlled territories, mostly to Angola (up to 500,000) and Mozambique (350,000), and most importantly, there is the arrival of Portuguese post-colonial expatriates in Angola in the recent years, because of Portugal's economic interests and the Angolan economic boom.

Senegal has its own Lusophone connection with a significant community of Cape Verdeans in Dakar and speakers of Guinea-Bissau Creole in its southern region of Casamance, which was once part of the Portuguese colonial empire. Portuguese is taught as a foreign language throughout the country. In 2008, Senegal became an observer nation in the CPLP.

Equatorial Guinea, at one point a Portuguese colony, is home to a Portuguese-based Creole and is a member nation in the CPLP. Portuguese is now an official language in Equatorial Guinea, although it is practically not used.

Mauritius, a multilingual island in the Indian Ocean, has strong cultural ties with Mozambique. The Portuguese were the first Europeans to encounter the island. In 2006, Mauritius joined the CPLP as an associate member.

As a fellow member of the SADC, Zambia has introduced Portuguese language instruction in its primary school system, partially due to the presence of a large Angolan population there.

The role of Portuguese in Africa
As an official language, Portuguese serves in the realms of administration, education, law, politics and media. Given the existing linguistic diversity of the PALOPs, Portuguese also serves the purpose of lingua franca allowing communication between fellow citizens of different ethno-linguistic backgrounds. The standard Portuguese used in education, media and legal documents is based on European Portuguese vocabulary used in Lisbon, but African Portuguese dialects differ from standard European Portuguese both in terms of pronunciation and colloquial vocabulary.

Additionally, Portuguese connects the PALOP countries to one another, to Portugal and to East Timor, Macau and Brazil, which were also once Portuguese colonies.

Music is one way in which the linguistic profiles of PALOP have increased. Many recording artists from PALOP, in addition to singing in their maternal languages, sing in Portuguese to one degree or another. The success of these artists in the world music industry increases international awareness of Portuguese as an African language.

As a literary language, Portuguese has a strong role in the PALOP. Authors such as Francisco José Tenreiro, Luandino Vieira, Mia Couto, Pepetela, Lopito Feijóo, Rui Knopfli, Luis Kandjimbo, Manuel Rui or Ondjaki have made valuable contributions to lusophone literature, prompting an African scent and ideas to the language and creating a place for the Portuguese language in the African imaginary.

Sub-Saharan Africa is the region where the Portuguese language is most likely to expand, because of the expansion of education and rapid population growth. It is also where the language has evolved the most in recent years. It is estimated that for 2100, Africa will have the majority of Portuguese speakers in the world, surpassing Brazil. The Portuguese-speaking African nations together with Brazil, have turned Portuguese into a formidable world language, also making it an important language of the global economy.

Media
Portuguese is the language of journalism, which serves as a vehicle for the dissemination of the language. Literacy being an issue, radio serves as an important source of information for Lusophone Africans.

Voice of America, BBC Para África, RFI and RTP África have regular services in Portuguese for listeners in Africa.

Creoles
Any discussion of the role of the Portuguese language in Africa must take into account the various Portuguese creoles that have developed there. These creole languages co-exist with Portuguese and, in the countries where they are spoken, form a continuum with the lexifying language.

In Cape Verde, crioulo levinho refers to a variety of Cape Verdean Creole which takes on various features of Portuguese and is a result of processes of decreolization in the archipelago. In São Tome e Principe, Santomense Portuguese is a variety of Portuguese strongly influenced by Forro in syntax and vocabulary. Since the lexicons of those languages are derived from Portuguese, even creole-speakers who do not speak Portuguese have a passive knowledge of it.

In addition, Portuguese creoles have often been (and often continue to be) written using Portuguese orthography. An important issue in discussions of standardization of creoles is whether it is better to devise a truly phonetic orthography or to choose an etymological one based on Portuguese.

title: Portuguese language in Africa


text:
Karl Abraham

Karl Abraham (3 May 1877 – 25 December 1925) was an influential German psychoanalyst, and a collaborator of Sigmund Freud, who called him his 'best pupil'.

Life
Abraham was born in Bremen, Germany. His parents were Nathan Abraham, a Jewish religion teacher (1842–1915), and his wife (and cousin) Ida (1847–1929). His studies in medicine enabled him to take a position at the Burghölzli Swiss Mental Hospital, where Eugen Bleuler practiced. The setting of this hospital initially introduced him to the psychoanalysis of Carl Gustav Jung.

Collaborations
In 1907, he had his first contact with Sigmund Freud, with whom he developed a lifetime relationship. Returning to Germany, he founded the Berliner Society of Psychoanalysis in 1910. He was the president of the International Psychoanalytical Association from 1914 to 1918 and again in 1925.

Karl Abraham collaborated with Freud on the understanding of manic-depressive illness, leading to Freud's paper on 'Mourning and Melancholia' in 1917. He was the analyst of Melanie Klein during the years 1924–1925, and of a number of other British psychoanalysts, including Edward Glover and Alix Strachey. He was a mentor for an influential group of German analysts, including Karen Horney, Helene Deutsch, and Franz Alexander.

Karl Abraham studied the role of infant sexuality in character development and mental illness and, like Freud, suggested that if psychosexual development is fixated at some point, mental disorders will likely emerge. He described the personality traits and psychopathology that result from the oral and anal stages of development (1921).

Abraham observed his only daughter, Hilda, reporting on her reaction to enemas and infantile masturbation by her brother. He asked that secrets be shared with him but he was careful to respect her privacy and some reports were not published until after Hilda's death. Hilda was later to become a psychoanalyst.

In the oral stage of development, the first relationships children have with objects (caretakers) determine their subsequent relationship to reality. Oral satisfaction can result in self-assurance and optimism, whereas oral fixation can lead to pessimism and depression. Moreover, a person with an oral fixation will present a disinclination to take care of themself and will require others to look after them. This may be expressed through extreme passivity (corresponding to the oral benign suckling substage) or through a highly active oral-sadistic behaviour (corresponding to the later sadistic biting substage).

In the anal stage, when the training in cleanliness starts too early, conflicts may result between a conscious attitude of obedience and an unconscious desire for resistance. This can lead to traits such as frugality, orderliness and obstinacy, as well as to obsessional neurosis as a result of anal fixation (Abraham, 1921). In addition, Abraham based his understanding of manic-depressive illness on the study of the painter Segantini: an actual event of loss is not itself sufficient to bring the psychological disturbance involved in melancholic depression. This disturbance is linked with disappointing incidents of early childhood; in the case of men always with the mother (Abraham, 1911). This concept of the prooedipal “bad” mother was a new development in contrast to Freud’s oedipal mother and paved the way for the theories of Melanie Klein.

Another important contribution is his work “A short study of the Development of the Libido”, where he elaborated on Freud’s “Mourning and Melancholia” (1917) and demonstrated the vicissitudes of normal and pathological object relations and reactions to object loss.

Moreover, Abraham investigated child sexual trauma and, like Freud, proposed that sexual abuse was common among psychotic and neurotic patients. Furthermore, he argued (1907) that dementia praecox is associated with child sexual trauma, based on the relationship between hysteria and child sexual trauma demonstrated by Freud.

Abraham (1920) also showed interest in cultural issues. He analyzed various myths suggesting their relation to dreams (1909) and wrote an interpretation of the spiritual activities of the Egyptian monotheistic Pharaoh Amenhotep IV (1912).

Death

Abraham died prematurely on December 25, 1925, from complications of a lung infection and may have suffered from lung cancer.

Works and publications

 * Normentafel zur Entwicklungsgeschichte des Huhnes (with Prof. Keibel). (1900) Normentafeln zur Entwicklungsgeschichte der Wirbeltiere, Heft 2. Jena.
 * Beiträge zur Entwicklungsgeschichte des Wellensittichs. (inaugural dissertation.) (1901) Anatomische Blätter (Anatomical Institute, Freiburg), Heft LVI/LVII. (Wiesbaden, I. F. Bergmann.)
 * Beiträge zur Kenntnis des Delirium tremens der Morphinisten. (1902) C., Jahrg. XXV, June, S. 369–80.
 * ber Versuche mit 'Veronal' bei Erregungszuständen der Paralytiker. (1904) C., Jahrg.
 * Abraham, K.(1907). On the significance of Sexual Trauma in Childhood for the Symptomatology of Dementia Praecox. In Hilda, C., Abraham, M.D.(Ed) (1955). Clinical Papers and Essays on Psycho-Analysis. London : The Hogarth Press and the Institute of Psychoanalysis.
 * Abraham, K.(1909). Dreams and Myths : A study in folk-Psychology. In Hilda, C., Abraham, M.D.(Ed) (1955). Clinical Papers and Essays on Psycho-Analysis. London : The Hogarth Press and the Institute of Psychoanalysis.
 * Abraham, K.(1911). Giovanni Segantini : A Psycho-analytical Study. In Hilda, C., Abraham, M.D.(Ed) (1955). Clinical Papers and Essays on Psycho-Analysis. London : The Hogarth Press and the Institute of Psychoanalysis.
 * Abraham, K. (1912). Amenhotep IV. Psycho-analytical Contributions Towards the understanding of his Personality and of the Monotheistic Cult of Aton. .  In Hilda, C., Abraham, M.D.(Ed) (1955). Clinical Papers and Essays on Psycho-Analysis. London : The Hogarth Press and the Institute of Psychoanalysis.
 * Abraham, K. (1920). The Cultural Significance of Psycho-analysis. In Hilda, C., Abraham, M.D.(Ed) (1955). Clinical Papers and Essays on Psycho-Analysis. London : The Hogarth Press and the Institute of Psychoanalysis.
 * Abraham, K (1921). Contributions to the theory of the anal character. In Stein, D.J, Stone, M. H. (Ed) (1997). Essential papers on obsessive-compulsive disorders. New York: New York University Press.
 * Abraham, K The influence of oral erotism on character-formation. In Perzow, S. M., Kets de Vries, M.F.R. (Ed) (1991). Handbook of character studies: Psychoanalytic explorations. Madison, CT: International Universities Press.
 * Abraham, K. A short study of the development of the libido. In Frankiel, R.V. (Ed) (1994). Essential papers on object loss, New York: New York University Press.

title: Karl Abraham


text:
Talk:Tree (set theory)

Untitled
Why is this page called infinite tree, when the given definition does not require the tree to be infinite? A better name might be "Tree (set theory)" or "Rooted tree (graph theory)" -- the latter to distinguish from the existing article "Tree (graph theory)", which refers to trees without distinguished roots.

Once a final name is picked, the link should be placed on "Tree (disambiguation)" as well.--Trovatore 16:15, 11 July 2005 (UTC)

On reflection I think my vote is "Tree (set theory)", as long as the "See also" to "Tree (descriptive set theory)" is kept. "Rooted tree (graph theory)" is kind of ugly and, more to the point, is not what people usually say, except in the unusual circumstance that they have to make the distinction with unrooted trees.

An alternative possibility would be a merge with Tree (graph theory), but the uses of the two sorts of trees are so distinct that I doubt that's a good idea. Also, while I don't know much about graph theory, I don't really think graph theorists are all that interested in infinite rooted trees; it's really more of a set theory concept, which my proposed name reflects. --Trovatore 16:45, 11 July 2005 (UTC)

Oops. Set-theoretic trees don't have to be graph-theoretic trees at all. My comments about rooted and unrooted were more appropriate to descriptive-set-theoretic trees, which do have a graph-theoretic tree structure plus a distinguished root. I'll have to think about how/whether to say that on the tree (descriptive set theory) page.

Still, this is if anything a better reason than before for the move to "Tree (set theory)", since "Infinite tree (graph theory)" is even more clearly an inaccurate description. --Trovatore 06:29, 12 July 2005 (UTC)

(Formerly) Disputed
Well, "disputed" might be too strong a word, but that's what the template wants. I'm concerned that the given definition for "branch" doesn't require it to be downward-closed, which I would think is intuitively a requirement. Of course I'm more used to descriptive-set-theoretic trees. Are there any infinitary combinitorists who can weigh in on whether a "branch" is necessarily downward-closed? --Trovatore 23:58, 12 July 2005 (UTC)

Actually, more than downward closed. I think a branch should be a maximal totally ordered chain -- that is, it should not be possible to add another element of the tree to the branch without violating total orderedness. But I'm not sure--Kunen doesn't actually define "branch" in this context, as far as I can tell. --Trovatore 00:11, 13 July 2005 (UTC)

OK, I found the def in Jech. A branch is a maximal totally ordered subset of the tree. Removed tag. --Trovatore 02:32, 13 July 2005 (UTC)

Definition of "height"
The page says
 * The height of a tree is the least ordinal α such that any branch has length at most α. If we have an element x of our tree and the well ordered section of the tree smaller than it is order isomorphic to α then we say x has height α.

This is equivalent to the definition in Kunen, but it takes a little thought to be sure of that. I think I'd prefer the following:

 * The height of an element x of a tree T is the ordinal isomorphic to the collection of all elements of T that are less than x in the tree ordering. The height of a tree is the least ordinal α such that no element of the tree has height α

I'll look at it here and reflect before making the edit in the actual article. --Trovatore 00:58, 14 July 2005 (UTC)

The use of greek ε for set membership
Is there a reason the introduction for the article uses ε instead of $$\in$$? This way, the text is very hard to read and understand. Since I'm a newbie here on Wikipedia, I don't know if there is any precendent regarding the use of set membership operator in introductory text, but I would definitely vote for a change.

Avakar 13:43, 7 December 2006 (UTC)

Complex math deserves a hug
Yes, I hug ALL types of trees.Notorious Tree Hugger Phinneas J. Hippy 01:54, 7 October 2007 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 3 one external links on Tree (set theory). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit User:Cyberpower678/FaQs for additional information. I made the following changes:
 * Added archive http://web.archive.org/web/20070930230404/http://planetmath.org/encyclopedia/TreeSetTheoretic.html to http://planetmath.org/encyclopedia/TreeSetTheoretic.html
 * Added archive http://web.archive.org/web/20070712031425/http://planetmath.org/encyclopedia/Branch.html to http://planetmath.org/encyclopedia/Branch.html
 * Added archive http://web.archive.org/web/20070930231713/http://planetmath.org/encyclopedia/ExampleOfTreeSetTheoretic.htm to http://planetmath.org/encyclopedia/ExampleOfTreeSetTheoretic.htm

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.—cyberbot II  Talk to my owner :Online 19:40, 2 June 2016 (UTC)

Contrary to the merging with Tree_(descriptive_set_theory).
Of course, parts of the pages overlap, but the notion of a tree in general set theory bears significance also in other contexts, eg, a definition of weakly compact cardinals. Paolo Lipparini (talk) 23:22, 24 August 2017 (UTC)

Infinite binary tree
@User:David Eppstein, about File:Infinite Binary Tree.gif The elements are all the nodes of the tree. They are partially ordered. For two nodes x and y, x<y if x and y are on the same branch and x is below y. Isn't it right? (I'm not an expert in this field). TD (talk) 01:11, 27 August 2023 (UTC)

 * Is it a picture of a set-theoretic tree? Does it accurately depict the important distinction between set-theoretic trees and graph-theoretic infinite trees, that the nodes are related by ancestor-descendant and not by edges (because edge-to-edge connection may not be possible when the total orderings of ancestors and descendants are more complicated than the ordering of an integer sequence)? What is the significance of being "binary", in the context of a set-theoretic tree? How is a binary set-theoretic tree even defined, and is it studied in the literature? And what are "nodes" in the context of the picture? I see only line segments; there are no nodes depicted. —David Eppstein (talk) 01:19, 27 August 2023 (UTC)
 * The nodes are the points where two branches begin. Binary means that there are always two branches from a node. I'm sorry but I'm not familiar with this field, and its terminology. It looks like a tree. That's all I know. If you think this example should be elsewhere in Wikipedia, please inform me.TD (talk) 01:33, 27 August 2023 (UTC)
 * Your new caption makes it clear that you have failed to understand the point of this article. Your caption describes two nodes as being one less than the other only when they "are on the same branch", and the earlier text of the caption makes clear that you intend "branch" to mean the line segment between two nodes. That is a graph-theoretic tree. In set-theoretic trees, there are no edges and is not always possible to reach the root by stepping from elements to their parents; indeed, an element might not have a parent. For instance, the set of numbers $$x-\tfrac1y$$ for positive integer $$x$$ and $$y$$, ordered numerically, forms a set-theoretic tree (rooted at $$0=1-\tfrac11$$, with a single linear order of its elements) but $$1$$ has no parent: all the numbers $$1-\tfrac12,1-\tfrac13,1-\tfrac14,\dots$$ are ancestors but none of them is directly connected to $$1$$.
 * By using an illustration that does not depict this crucial aspect of this topic, the primary difference between this kind of trees from graph-theoretic trees, you mislead the readers.
 * Further, the less-than relation you describe is not a total order, because a total order should obey the transitive law and the relation you describe does not. Further, you have failed to properly address my question: is there a definition of "binary tree" that applies to set theoretic trees that are not graphs? What does "two branches from each node" mean in a structure that is not based on direct connections between nodes? For instance, if I linearly ordered the positive integers, and then added countably many "leaf" elements, each of which is above all the integers but incomparable to all the other leaves, would that obey your definition? It is not very binary but each non-leaf element has only one other element for which it is the parent. —David Eppstein (talk) 04:27, 27 August 2023 (UTC)
 * A branch is not only a line between two successive nodes, but also any succession of nodes such that one is always below the next. With this interpretation, x<y is transitive. This tree is only a simple example. It doesn't pretend to do the impossible, illustrate the definition of a tree in its full generality. Of course there are partial well-orderings such that the order can't be defined by a connected line. Your last example is a binary tree. TD (talk) 09:01, 27 August 2023 (UTC)
 * For now, it should easily be possible to obtain a fairly nontrivial example by stacking two copies of the current image one upon the other, connecting the root of the upper tree to e.g. the end of the leftmost branch of the lower tree. The leftmost branch of the composed tree would correspond to order type $$\omega+\omega$$. By stacking $$\omega$$ trees one upon the other in a similar way, an example with the leftmost branch corresponding to order type $$\omega \cdot \omega$$ could be generated. However, I feel that a precise mathematical definition of the depicted tree should be given in the caption, or at least somewhere in the article. - Jochen Burghardt (talk) 11:32, 27 August 2023 (UTC)
 * Thanks for your examples. A precise mathematical definition can't be given in the caption, because it would be too long. I think about giving it in the article, but since I'm not an expert in this field, it's a difficult task for me. I will try.TD (talk) 12:01, 27 August 2023 (UTC)
 * The Python file which generated this image is here.TD (talk) 12:35, 27 August 2023 (UTC)
 * The point is, this image DOES NOT ILLUSTRATE THE CONCEPT OF A SET-THEORETIC TREE. It illustrates the concept of a graph-theoretic tree. As such it is a bad image for this article. Please remove it. —David Eppstein (talk) 15:03, 27 August 2023 (UTC)
 * An ordered tree in graph theory is also a set-theoretic tree. Set-theoretic trees are more general than ordered trees in graph theory, but this is not a reason to exclude this example from this page. It's only a simple example, it gives insight into the concept of a set-theoretic tree. TD (talk) 15:31, 27 August 2023 (UTC)
 * It misleads readers into a false understanding of the concept. —David Eppstein (talk) 15:36, 27 August 2023 (UTC)
 * Why? TD (talk) 15:38, 27 August 2023 (UTC)
 * By analogy: In the article real number, you wouldn't write "For example, 1, 2, 3, ... are real numbers". The sentence is true, but is far from illustrating the whole extension of the concept. - Jochen Burghardt (talk) 16:11, 27 August 2023 (UTC)
 * This tree is a clear illustration of the concept of partial ordering, which is essential to the concept of tree. I agree that its well-ordering is trivial. So we need more examples, not less. Your examples are very good ones. TD (talk) 16:55, 27 August 2023 (UTC)
 * It is not clear even as an example of a partial ordering, first because of the same issue (partial orders do not require any concept of edges; consider the partial order on the real numbers) and second because the illustration is not drawn in a way that makes clear what the elements being ordered are. Also what are the colors supposed to mean? —David Eppstein (talk) 19:55, 27 August 2023 (UTC)
 * The colors mean nothing. I don't understand why you think this illustration is not clear. We see the branches, hence we see the order. The tree shows clearly the difference between a partial order and a total one: for nodes x and y, x y or x=y is not always true. The ordinary order on the real line is total, what is the partial order you mention?
 * I have a reason to make use of two colors. There is a bijection between the set of infinite branches from the root in this tree and the set of sets of natural numbers. Without the two colors, or the left-right relation, I need the axiom of choice to explain this point.TD (talk) 20:53, 27 August 2023 (UTC)
 * A total order is an example of a partial order. It is equally good and equally bad as an example of a partial order to your examples: it illustrates some aspects of the subject but misses its generality. (The positive real number line is not however a tree in the sense described here because it is not a well order.)
 * Also, you keep talking about "branches". This is not a concept that has meaning for set-theoretic trees. —David Eppstein (talk) 21:21, 27 August 2023 (UTC)
 * Read the present article (Tree(set theory)): "a branch of a tree is a maximal chain in the tree" in the definition section. My intuitive use of the concept of branch was not in agreement with this definition.TD (talk) 21:58, 27 August 2023 (UTC)
 * I uploaded at File:2 Stacked infinite binary trees.png an experimental version with 2 stacked copies of TD's tree, aligned along the rightmost path. The resulting set-theoretic tree has a rightmost branch of length $$\omega \cdot 2$$. (File:6 Stacked infinite binary trees.png shows 6 similarly stacked trees, but the image is too large for an article.)  If this example would be acceptable for now, I'd try to come up with a mathematical definition for it. - Jochen Burghardt (talk) 16:51, 27 August 2023 (UTC)

A precise mathematical definition of this tree: an initial segment of the set of natural numbers is the set of all natural numbers n such that n<N for a natural number N. A finite sequence of binary digits is a map from an initial segment of natural numbers to the set {0,1}. An ordering can be defined on the set T of all finite sequences of binary digits: x<=y if and only if x(n)=y(n) for all n in the domain of x. T is a (set-theoretic) tree for this ordering. The root of the tree is the map [] whose domain is the null set {}. [0] (the map x whose domain is {0} such that x(0)=0) and [1] are the next nodes. [00] (the map y whose domain is {0,1} such that y(0)=0 and y(1)=0), [01], [10] and [11] follow, and so on. My image is a visualization of T. TD (talk) 00:46, 28 August 2023 (UTC)

 * I reverted your addition of the above since (1) your definition of <= seems flawed, (2) disallowing infinite sequences make your example even more trivial as an example of set-theoretic tree, and (3) I'd prefer to settle the dispute here before adding new material. - Jochen Burghardt (talk) 08:05, 28 August 2023 (UTC)

@Jochen Burghardt where is the flaw? if the domain of y is larger then the domain of x we can't have both x<=y and y<=x because there is at least an n such that y(n) exists and x(n) doesn't exist.TD (talk) 08:03, 28 August 2023 (UTC)

 * You didn't require the domain of y to be larger than that of x. - Jochen Burghardt (talk) 08:07, 28 August 2023 (UTC)
 * I didn't have to. If the domain of y is larger than the domain of x, we can't have y<=x with the present definition. TD (talk) 08:09, 28 August 2023 (UTC)
 * Why not first construct a good example on the talk page, and then publish it? - Jochen Burghardt (talk) 08:08, 28 August 2023 (UTC)
 * I did it. I wrote the example on the talk page last night and published later. I'm sorry that I didn't wait for your answer. TD (talk) 08:14, 28 August 2023 (UTC)
 * About your point (2): you asked for a precise definition of this tree, not of another tree.TD (talk) 08:26, 28 August 2023 (UTC)
 * What about showing File:2 Stacked infinite binary trees.png, and giving the following definition:
 * Let $U$ be the set of all real numbers in the interval $[0,1)$ such that their decimal representation (omitting the leading zero) contains no other digits than $1$ and $2$. For $u,v \in U$ define $u < v$ if the decimal representation of $u$ is a proper prefix of that of $v$. (This should formalize TD's intention from the definition above.) Let $T = U \times U$ with the lexicographic order, i.e. define $(u_1,u_2) < (v_1, v_2)$ if $ u_1 < u_2$ or $u_1=u_2 \text{ and } v_1 < v_2$. Then $T$ is a fairly nontrivial set-theoretic tree, but is hard to depict. However, the subset $T' = (\{ 0.111111... \} \times U) \cup ( U \times \{ 0. \})$ can be depicted, viz. by File:2 Stacked infinite binary trees.png.
 * This definition is admittedly still clumsy. I thought by referring to real numbers it could shortened (compared to speaking about sequences over $$\mathbb{N}$$ or an initial segment thereof), but I didn't succeed. An alternative might be to use the set of mappings from the ordinal $$\omega \cdot 2$$, or initial segments thereof, to $$\{0,1\}$$. This could avoid Cartesian product and lexicographic order; however, reals are better known than ordinals.
 * In any case, we'll still have to explain that in the image only line junctions represent set members. This seems unavoidable, since in any kind of fractal figure, we don't have space to draw e.g. circles for nodes. Jochen Burghardt (talk) 09:09, 28 August 2023 (UTC)
 * My definitions (see below) seem to me to be simpler than yours. And it can easily be extended to many kinds of non-trivial infinite trees. TD (talk) 09:18, 28 August 2023 (UTC)
 * In an article about trees, the concept of ordinal can be supposed to be known, because the definition of a tree require the concept of well-ordering, and an ordinal is essentially a well-ordered set.TD (talk) 09:31, 28 August 2023 (UTC)
 * In an article about trees, the concept of ordinal can be supposed to be known, because the definition of a tree require the concept of well-ordering, and an ordinal is essentially a well-ordered set.TD (talk) 09:31, 28 August 2023 (UTC)

Can someone clarify what the list of features are that need to be depicted to get across the concept of a set-theoretic tree? The current image to me looks like a demonstration of the way to fill an isosceles right triangle by (tilted) squares in a fractal pattern, and doesn't really convey much about trees per se. I could also see it as a representation of infinite binary fractions, though I think for that the image could be made substantially clearer with some design changes. –jacobolus (t) 16:58, 28 August 2023 (UTC)

 * Read the definition: "a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <." TD (talk) 17:59, 28 August 2023 (UTC)
 * Yes, I can read the definition. But what I don't really understand from the article is, e.g.: what are some non-trivial examples of set theoretic trees? Which partially ordered sets are usually studied as trees per se rather than for some other structural prooerties?
 * Why is it called a "tree"? Why are the chains called "branches"? Can particular elements be members of more than one branch? Are people interested in finite set theoretic trees or only infinite ones? What theorems or problems does the structure of "tree" help solve that other structures don't suffice for? ...
 * Reading the definition (and the rest of the article) gives me a few bits of trivia and some pointers to other places to look for answers, but doesn't really give me enough context to know why anyone should care about this. As a newcomer to set theoretic trees I can't really make meaningful sense of the figures you made here. –jacobolus (t) 20:02, 28 August 2023 (UTC)
 * One kind of of diagram that might be helpful to newcomers would be a finite tree with a relatively small number of elements involving a fairly obvious (but not entirely trivial) order, where all of the branches could be clearly labeled. –jacobolus (t) 20:19, 28 August 2023 (UTC)
 * You seem to be honest so I'd like to help you. But I'm not an expert in this field. I'm a newcomer too. Here are a few tentative answers to your interesting questions:
 * Trivial examples are finite trees (but trivial doesn't mean they are not interesting). They look like real trees in the air. A root (the trunk), branches which start from the trunk, and more branches which start at nodes from preceding branches.
 * Usually (but not necessarily) an element of a tree (a node) is an element of many branches. More precisely, the concept of branch in this theory is defined as a maximal chain. This means that it starts from the root and ends with a 'leaf'.
 * The concept of well-ordering is essential here. An ordered set is well-ordered if and only if all its subsets have a minimal element. $$\N$$ is well-ordered, but $$\Z$$ and $$\R ^+$$ aren't. All the branches of a tree shall be well ordered, else the partial order doesn't define a tree. If you want to know more about well-orderings, study the theory of ordinal numbers. A trivial well-ordering is finite or is the order of natural numbers, but there are many more infinite well-orderings (Cantor theory and after).TD (talk) 20:33, 28 August 2023 (UTC)

Okay, is this an example of a set theoretic tree then? (Where the dots are elements, the arrows indicate order, and elements not on any branch with each-other are not comparable.) –jacobolus (t) 23:19, 28 August 2023 (UTC)
 * Consider the third point (from bottom to top). The set of its ascendants (the two points at the bottom) is not ordered. Therefore it is not a tree. TD (talk) 23:29, 28 August 2023 (UTC)
 * Okay, great. That's what I thought. So I think what the lead section should show is a small handful of such finite posets, highlighting which ones are or aren't 'trees' and clearly explaining why or why not. Then a reader can get a quick visual concept of what "tree" means in this context. –jacobolus (t) 23:32, 28 August 2023 (UTC)
 * I added a figure to the article. Does that seem helpful? –jacobolus (t) 16:40, 29 August 2023 (UTC)
 * It does. But why did you delete my figure? TD (talk) 16:55, 29 August 2023 (UTC)
 * Why do you find this image confusing? TD (talk) 17:06, 29 August 2023 (UTC)
 * Okay, I put it back in the 'infinite trees' section.
 * I find this image confusing because the elements are not pictured but only implied, the order relations (which are depicted as line segments) use two unrelated colors and have dramatically different lengths from half the diagram down to invisibly small, distinct elements from different branches of the tree are infinitely close together at the top of the diagram, and many aspects of the particular tree are arbitrary (i.e. not essential to the concept of trees).
 * I think your example would work better if you found a concrete poset matching the picture (e.g. strings of arbitrary length over a 2-letter alphabet, ordered by a "starts with" relationship), and then explicitly described it in text (in body copy, not a caption). Otherwise readers have to make a lot of inferences about the picture. –jacobolus (t) 17:40, 29 August 2023 (UTC)
 * I guess there is an example in the text. I wonder if it can be copyedited a bit to make it more accessible to a broader audience. –jacobolus (t) 17:44, 29 August 2023 (UTC)
 * What's the purpose of the zooming picture? –jacobolus (t) 17:45, 29 August 2023 (UTC)
 * It's obvious. The purpose of a zoom is to see details which would be otherwise unseen. TD (talk) 21:58, 30 August 2023 (UTC)
 * Sure, but the zooming picture doesn't actually show any visual data that isn't already in the static picture, and the infinite repetition is already implied. I'm not sure whatever benefit is intended is worth the extra space and added visual distraction of a moving picture. YMMV. –jacobolus (t) 22:33, 30 August 2023 (UTC)
 * Without the zoom, would the viewer understand that the details are already in the whole picture? See File:Cantor Set Expansion.gif for another example. Please stop disturbing me with such requests, which are near nonsense.TD (talk) 22:49, 30 August 2023 (UTC)
 * Perhaps other readers find it useful, but I personally don't find this zooming cantor set image very helpful or easy to interpret. I think File:Cantor_set_in_seven_iterations.svg is much clearer. –jacobolus (t) 22:55, 30 August 2023 (UTC)
 * Also, nobody here is forcibly "disturbing you" or forcing you to work on or otherwise engage with any particular Wikipedia page. Whatever notifications you have set about talk page discussions are in your own personal settings, which nobody else has control over. As always on this entirely volunteer driven project, anyone is free to just go away and do something else whenever they feel like. –jacobolus (t) 23:01, 30 August 2023 (UTC)
 * This page is on my watchlist because I'm interested in it. And if someone asks for something I feel obliged to answer. TD (talk) 23:40, 30 August 2023 (UTC)
 * The reason of the zoom is to show scale invariance.TD (talk) 23:52, 30 August 2023 (UTC)
 * This image would fit better to Tree_(data_structure) where a collection of similar examples and non-examples of finite trees is already shown. in tree (set theory), a much more general concept is explained, allowing branches that are not just "infinitely long" (like e.g. rational trees in unification theory), but have lengths corresponding to arbitrary ordinal numbers. Jochen Burghardt (talk) 17:29, 30 August 2023 (UTC)

 * Someone reading this particular article should be able to have some kind of picture for what "tree" means that doesn't involve interpreting 3 layers of advanced mathematical jargon. These kinds of simple finite examples give a basic pictorial impression that readers can subsequently embellish by imagining the generalization to infinite cases. If there are better images elsewhere feel free to copy them here. For a similar example from a different field, look at the pictorial representation of "neighborhood" in topology. Clearly a dotted-line circle around a point within a blobby shape in a plane does not represent the full range of possible topological neighborhoods. But the point is only to give readers something basic to get them started understanding what the definition says, not to provide a comprehensive representation of the subject. –jacobolus (t) 17:34, 30 August 2023 (UTC)
 * With that said though, if you like we could also try to make some more schematic / abstract top-of-page drawing, not necessarily showing a specific concrete tree or collection of trees. If you can sketch out on paper how you think a more abstracted drawing could look (with little bundles of lines representing infinite branches, or whatever), I'd be happy to try to make a legible and "pretty" version. –jacobolus (t) 18:11, 30 August 2023 (UTC)

@Jochen Burghardt and @David Eppstein I added a new "infinite" top image. Does this one properly demonstrate the features needed here? –jacobolus (t) 06:59, 31 August 2023 (UTC)

 * It seems significantly better to me, after already having some idea what this topic is supposed to be about and how it differs from other kinds of trees. Whether it would be informative to someone coming to the article for the first time is a different question. —David Eppstein (talk) 07:02, 31 August 2023 (UTC)
 * I think it would have helped me at least. I tried to attach a picture to several features that are somewhat abstractly described (which always takes more effort for me to make sense of): "root", "branch", "height", ... But I can't answer for whether it will help anyone else. If nothing else, I tried to make it look tree-like. :-) –jacobolus (t) 07:27, 31 August 2023 (UTC)

Examples of infinite trees
I would like to add the following section to this article. Are there objections against it?

A proper initial segment of the set $$\N$$ of natural numbers is the set of all natural numbers $$n$$ such that $$n<N$$ for a natural number $$N$$. A finite sequence of binary digits is a map from an initial segment of natural numbers to the set $$\{ 0, 1 \}$$. An ordering can be defined on the set $$T$$ of all finite sequences of binary digits: $$f \leq g$$ if and only if $$f(n)=g(n)$$ for all $$n$$ in the domain of $$f$$. $$T$$ is a tree for this ordering. The root of the tree is the map $$\langle \rangle$$ whose domain is the null set $$\varnothing$$. $$\langle 0 \rangle$$ (the map $$f$$ whose domain is $$\{ 0 \}$$ such that $$f(0)=0$$ ) and $$\langle 1 \rangle$$ are the next nodes. $$\langle 00 \rangle$$ (the map $$g$$ whose domain is $$\{ 0, 1 \}$$ such that $$g(0)=0$$ and $$g(1)=0$$ ), $$\langle 01 \rangle$$, $$\langle 10 \rangle$$ and $$\langle 11 \rangle$$ follow, and so on. The image at the top of this page is a visualization of $$T$$.

The well-ordering of branches of $$T$$ is trivial. It is the well-ordering of the set $$\N$$ of natural numbers. We can obtain less trivial well-orderings if we replace in the above definition $$\N$$ by any ordinal greater than $$\omega$$ (when considered as an ordinal $$\N$$ is usually noted $$\omega$$). TD (talk) 08:53, 28 August 2023 (UTC) We can also replace the set {0,1} by any other set.TD (talk) 09:22, 28 August 2023 (UTC)

Another example:

TD (talk) 10:10, 28 August 2023 (UTC)

 * A better example, that would actually get at the concept of a set-theoretic tree: Let the elements of the tree be functions $$f:\alpha\mapsto\Z$$ where $$\alpha$$ is a countable ordinal, and let the predecessors of any such function $$f$$ be all functions $$g:\beta\mapsto\Z$$ where $$\beta<\alpha$$ and $$g$$ agrees with $$f$$ on all arguments they have in common. The root is the (unique) function on the empty set. —David Eppstein (talk) 18:19, 28 August 2023 (UTC)
 * I already mentioned this kind of example. Replace {0,1} by $$\Z$$ and $$\N$$ by the first uncountable ordinal in the definition of $$T$$, and you get your example.TD (talk) 18:26, 28 August 2023 (UTC) modifiedTD (talk) 15:21, 30 August 2023 (UTC)
 * Thanks, that is much more concise than my above attempt. In order that a particular tree remains a set, $$\alpha$$ would have to be restricted to be less or equal to some fixed ordinal, say $$\kappa$$. I suggest we include this example in the corresponding section, show the above picture File:An infinite tree with a non-trivial well-ordering.gif, and refer from its caption to the example, adding
 * that only junction points represent tree nodes,
 * that the range set is $$\{0,1\}$$ (corresponding to red and green; larger sets can hardly be depicted),
 * that $$\kappa = \omega \cdot 2$$, and
 * that only branches with an initial segment of $$(0,0,0,...)$$ or $$(1,1,1,...)$$ are shown in full length, due to space restrictions.
 * I'd suggest to add more examples in the section, establishing the relation to
 * tree (graph theory),
 * tree (data structure) (always finite),
 * tree (automata theory) (apparently may be infinite, up to $$\omega$$),
 * which I guess are all subsumed here (maybe with a grain of salt, such as different choices of root node in graph theory). I'm less sure about
 * tree (descriptive set theory) (didn't yet read the article).
 * Jochen Burghardt (talk) 14:51, 29 August 2023 (UTC)
 * Your plan looks good to me. Re "In order that a particular tree remains a set": that is why I implicitly restricted $$\alpha$$ to $$\alpha<\omega_1$$ by asking for it to be countable. —David Eppstein (talk) 18:03, 29 August 2023 (UTC)
 * [Oops, I'd overlooked that. In my suggestion below, I stuck with $$\kappa$$ rather than "countable" or $$\omega_1$$ in order to have some variable that can be instantiated in the picture caption.]
 * Meanwhile, I came up, at User:Jochen_Burghardt/sandbox, with a suggestion for the examples section. If, after some improvements and corrections, it is acceptable as a consensus, I'd like to ask to revert his image to the original colored version, since I referred to the colors. I marked some sentences with  to indicate that I'm particularly unsure whether they are right; please check and fix them where necessary. - Jochen Burghardt (talk) 20:25, 30 August 2023 (UTC)
 * I won't change my images for your pleasure. TD (talk) 21:23, 30 August 2023 (UTC)
 * No objection for 4 days - installing the suggestion now. - Jochen Burghardt (talk) 06:34, 4 September 2023 (UTC)

title: Talk:Tree (set theory)


text:
Jim Bohlen

Jim Bohlen (July 4, 1926 – July 5, 2010) was an American engineer and activist who worked as part of the Atlas ICBM missile program and went on to be one of the founders of Greenpeace.

title: Jim Bohlen


text: Template:Porgy and Bess

title: Template:Porgy and Bess


text: File:Aim ColdWaterMusic albumcover.jpg

title: File:Aim ColdWaterMusic albumcover.jpg


text:
Talk:DMZ (computing)

Update
I have updated the article and removed the stub. If you have any comments, please let me know. Jasonlfunk 15:45, 11 October 2007 (UTC).

Illustrations
The picture does not show a proper DMZ. It should look like (in ascii art): | [internet][Firewall/router]- | --[Firewall]-[Internal network] |                                   [DMZ]

What is shown here is a three-legged firewall concept.

Greg Rojas

I am confused as to the way a DMZ is laid out. The pictures are showing two different methods, which I understand are differences in topography. But, how is the ascii art dipiction laid out with the actual machines, is there a router between the firewalls? There should maybe be an illustration in the article or more detailed discriptions. 12:08 CDT, 02 June 2006

Software used to make them?
Unrelated query, but, anyone know what software was used to make the illustrations in this article? I doubt it was Visio. Thanks! —S3BST3R (talk) 22:49, 28 June 2011 (UTC)

 * The SVG files contain the following comment: "Created with Inkscape (http://www.inkscape.org/)". 149.32.224.39 (talk) 18:44, 20 October 2023 (UTC)

The boundary between
The term DMZ has been used to describe the boundary between autonomous networks, likely predating the adoption of the term by firewall vendors.

Cjcoleman 20060121

it was used for computation purposes too. —Preceding unsigned comment added by 59.177.41.244 (talk) 09:50, 24 December 2010 (UTC)

Whether DMZ can be one of the NIC of the firewall
Is it possible to configure one of the network card IP of the firewall(With 3 Network Card) as DMZ. One NIC to Internal network One NIC to external network

Response to above
I believe that many people do this: configure the one Firewall to be the connection between DMZ and LAN and External. However, if the Firewall is breached from the outside then there is the potential to get to the LAN as easily as they get to the DMZ. It is a more secure solution to use 2 Firewalls.

82.211.102.231 10:09, 1 December 2006 (UTC)Helen

Article title wrong?
Everyone understands that the term "DMZ" in computing is short for "demilitarized zone", but no one in computing ever actually says "demilitarized zone" (except in answer to the question "what does DMZ stand for?"). And the article reflects this; the full term is never used again after the first sentence.

So I think the article should be renamed to "DMZ (computing)", and the first paragraph updated accordingly. Or maybe even renamed to just "DMZ", with a disambiguation link to "Demilitarized zone" (since, eg, googling for "DMZ" turns up this article first and the military article second). —Preceding unsigned comment added by 24.99.22.247 (talk) 18:13, 30 May 2008 (UTC)

 * Done --h2g2bob (talk) 21:13, 28 October 2008 (UTC)

Article title wrong!
Better to call this a 'Data Management Zone'. —Preceding unsigned comment added by 194.110.215.6 (talk) 12:40, 10 March 2009 (UTC)

I'd like some source info on this. As a 13 year IT veteran and many other people I communicate with just as much if not more IT experience have NEVER heard of 'Data Management Zone' and would prefer this is removed. A DMZ in terms of computing does root from Demilitarized Zone and is best described as that or a Perimeter Network. My re-wording of that in the first sentence could be helped by someone more elegant in their writing skills. thanks. Turnpike420 (talk) 18:42, 14 December 2009 (UTC)

Dual Firewalls and security through obscurity
The Dual Firewalls section mentions that using two firewalls is either "defense in depth" or "security through obscurity" as if they are opposite viewpoints. However, using two firewalls is not considered pejorative in this case (the security through obscurity wikipedia entry specifically states it is a pejorative term). It's goal is not to simply hide the internal network by obscure means (the goal of a single or dual firewall with DMZ is to "obscure" the LAN from access by design), but would provide real extra protection in the case of a security hole being found in the first firewall that didn't exist in the one from a second vendor. Thus, it is defense in depth (if the first measure fails the second may stand), but does not rise to the level of security through obscurity because even if you told the world the brand of both firewalls in use (and even the configuration, assuming both are properly configured), a vulnerability in the first wouldn't necessarily allow access through the second. Davidszp (talk) 17:42, 5 April 2011 (UTC)

There is no documented case of the compromise of a correctly-configured firewall. The dual-skinned architecture began to be popular as a result of the discovery that a certain firewall vendor incorporated a backdoor into their platform, so any discussion of two brands of firewalls is based on a misconception. Gregmal (talk) 9:13, 6 May 2013 (UTC)

Industry advice is that there is no merit to having firewalls from two vendors and in fact the support overhead increases the risk of mis-configuration. See Gartner 'Debunking the Myth of the Single-Vendor Network' G00208758 from 17 November 2010. — Preceding unsigned comment added by 137.191.247.20 (talk) 15:17, 4 August 2015 (UTC)

Accidental misconfiguration is more likely to occur in one or more ways across the configuration interfaces of two different vendors, which now require competency for two (potentially very) different configurations. — Preceding unsigned comment added by 72.200.196.17 (talk) 22:08, 31 August 2015 (UTC)

Gartner G00208758 study actually finds that two vendors is beneficial: "Our findings show that most organizations should consider a dual-vendor or multivendor solution as a viable approach to building their network, as significant cost savings are achievable with no increase in network complexity, while improving the focus on meeting business requirements." Telempe (talk) 09:33, 4 July 2017 (UTC)

Propose merge
There is so much overlap between this article and its synonym, Screened subnet, that I think we should consider merging these two articles. Let's discuss. Stephen Charles Thompson (talk) 08:09, 17 October 2018 (UTC)

Which article should we keep?
I am not sure which article title would best encapsulate the merged content. Wikipedia manual of style probably suggests using the most authoritative or popular term. Let's add our findings in the sub-sections below. Stephen Charles Thompson (talk) 08:40, 17 October 2018 (UTC)

Screened subnet references: Screened subnet may be the original term.
 * NIST, 1994, SP 800-10: "two routers are used to create an inner, screened subnet. This subnet (sometimes referred to in other literature as the "DMZ")..."
 * O'Reilly & Associates, 1995: "The screened subnet architecture adds an extra layer of security to the screened host architecture by adding a perimeter network that further isolates the internal network from the Internet." Stephen Charles Thompson (talk) 08:40, 17 October 2018 (UTC)

 * I doubt there's a significant difference in age, as a Google Books search for DMZ firewall for 20th century also gives several books from the mid-1990s using the term, often without a sense of novelty. --Joy [shallot] (talk) 20:03, 17 October 2018 (UTC)

 * The 1994 ref uses both. 😊 All the best: Rich Farmbrough, 20:20, 17 October 2018 (UTC).

This SANS Institute GIAC paper in 2000 acknowledges the confusion in terms:
 * "There are a number of terms that are used, such as bastion hosts, screened subnets, DMZ, or perimeter networks that can be confusing, especially when used together." ... "Another term that may often causes confusion is the DMZ (demilitarized zone), as opposed to a screened subnet. A true DMZ is a network that contains hosts accessible from the internet with only the exterior, or border, router between them. These hosts are not protected by a screening router." ... "A screened subnet may also be a collection of hosts on a subnet, but these are located behind a screening router. The term DMZ may be used by a vendor to mean either, so it is best to verify which they mean." Stephen Charles Thompson (talk) 08:55, 17 October 2018 (UTC)

DMZ (computing) references:
 * Who coined the term "DMZ" and when? Stephen Charles Thompson (talk) 08:40, 17 October 2018 (UTC)

 * T|he earliest refs I can find on Googlebooks are 1994 (earlier matches ones were due to mis-dated items). It's not clear where the term comes from. All the best: Rich Farmbrough, 14:27, 18 October 2018 (UTC).

 * The term DMZ is by far more common than screened subnet. This is immediately apparent by Google search: network DMZ yields 10.4 million hits versus screened subnet which yields only 64 thousand hits.

Conclusion: I think that what has happened is that the first generation of firewalls were little more than screened routers, routers with packet filter capability (OSI Layer 3), such as ipchains. Firewalls became more advanced including features like stateful inspection operating at OSI Layer 4 and OSI Layer 5. The next generation of firewalls including application firewalls now operate at even higher layers in the OSI model. The term "screened" lost some relevance as layer 3 firewalls became obsolete. The apparent synonym, DMZ, did not become obsolete because the term was not linked to a specific functionality but rather to a desired effect. What do you think? Stephen Charles Thompson (talk)

Call for vote

 * I vote in favor of merging the contents of screened subnet to the article DMZ (computing) for the reasons listed above. Stephen Charles Thompson (talk) 21:54, 18 October 2018 (UTC)

 * Oppose. A DMZ is always located outside of the internal network and is a "middleground" where data can pass between the internal network and another one (most often the Internet). As the screened subnet article states..it can be entirely inside a network (ie: a sensitive R&D area or Human Resources Department, etc). They are similar concepts but they're not necessarily the same thing. Markvs88 (talk) 22:00, 18 October 2018 (UTC)
 * I'm not seeing that wording or getting that interpretation from the screened subnet article. What you are describing sounds more like Multitier architecture. If you have a good references for this, I think we should update the screened subnet article to reflect this. Stephen Charles Thompson (talk) 22:48, 18 October 2018 (UTC)

 * Oppose for now: some people define a screened subnet as 'triple-homed firewall'. This is a particular implementation of DMZ, and indeed be used for different purposes.  All the best: Rich Farmbrough, 10:26, 22 October 2018 (UTC).

title: Talk:DMZ (computing)


text:
Oceanside Union Free School District

Oceanside School District is a school district in Oceanside, New York. There are 10 schools with 854 full-time employees, of which 440 are teachers.

Schools

 * Florence A. Smith Elementary School
 * Oaks Elementary School #3
 * South Oceanside Road Elementary School #4
 * North Oceanside Road Elementary School #5
 * Fulton Avenue Elementary School #8
 * Boardman Elementary School #9E
 * Oceanside Middle School
 * Oceanside High School (New York)
 * Oceanside High School Castleton
 * School #6 Early Learning Center

title: Oceanside Union Free School District


text: File:Aim Hinterland albumcover.jpg

title: File:Aim Hinterland albumcover.jpg