text:
Maximilian II, Holy Roman Emperor

Maximilian II (31 July 1527 – 12 October 1576) was Holy Roman Emperor from 1564 until his death in 1576. A member of the Austrian House of Habsburg, he was crowned King of Bohemia in Prague on 14 May 1562 and elected King of Germany (King of the Romans) on 24 November 1562. On 8 September 1563 he was crowned King of Hungary and Croatia in the Hungarian capital Pressburg (Pozsony in Hungarian; now Bratislava, Slovakia). On 25 July 1564 he succeeded his father Ferdinand I as Holy Roman Emperor.

Maximilian's rule was shaped by the confessionalization process after the 1555 Peace of Augsburg. Though a Habsburg and a Catholic, he approached the Lutheran Imperial estates with a view to overcome the denominational schism, which ultimately failed. He also was faced with the ongoing Ottoman–Habsburg wars and rising conflicts with his Spanish Habsburg cousins.

According to Fichtner, Maximilian failed to achieve his three major aims: rationalizing the government structure, unifying Christianity, and evicting the Turks from Hungary. Peter Marshall opines that it is wrong to dismiss Maximilian as a failure. According to Marshall, through his religious tolerance as well as his encouragement of arts and sciences, he succeeded in maintaining a precarious peace.

Biography
Maximilian was born in Vienna, Austria, the second child and eldest son of the Habsburg King Ferdinand I, younger brother of Emperor Charles V, Holy Roman Emperor, and the Jagiellonian Princess Anne of Bohemia and Hungary (1503–1547). He was named after his great-grandfather, Emperor Maximilian I. At the time of his birth, his father Ferdinand succeeded his brother-in-law King Louis II in the Kingdom of Bohemia and the Kingdom of Hungary, greatly expanding the Habsburg monarchy.

Having spent his childhood years at his father's court in Innsbruck, Tyrol, Maximilian was educated principally in Italy. Among his teachers were humanist scholars like Kaspar Ursinus Velius and Georg Tannstetter. He also came in contact with the Lutheran teaching and early on corresponded with the Protestant prince Augustus of Saxony. From the age of 17, he gained some experience of warfare during the Italian War campaign of his uncle Charles V against King Francis I of France in 1544, and also during the Schmalkaldic War. Upon Charles' victory in the 1547 Battle of Mühlberg, Maximilian put in a good word for the Schmalkaldic leaders, Elector John Frederick I, Elector of Saxony and Philip I, Landgrave of Hesse, and soon began to take part in Imperial business.

Heir apparent
On 13 September 1548 Emperor Charles V married Maximilian to Charles's daughter (Maximilian's cousin) Maria of Spain in the Castile residence of Valladolid. By the marriage his uncle intended to strengthen the ties with the Spanish branch of the Habsburgs, but also to consolidate his nephew's Catholic faith. Maximilian temporarily acted as the emperor's representative in Spain, however not as stadtholder of the Habsburg Netherlands as he had hoped for. To his indignation, King Ferdinand appointed his younger brother Ferdinand II administrator in the Kingdom of Bohemia, nevertheless Maximilian's right of succession as the future king was recognised in 1549. He returned to Germany in December 1550 in order to take part in the discussion over the Imperial succession.

Maximilian's relations with his uncle worsened, as Charles V, again embattled by rebellious Protestant princes led by Elector Maurice of Saxony, wished his son Philip II of Spain to succeed him as emperor. However, Charles' brother Ferdinand, who had already been elected as the next occupant of the imperial throne, and his son Maximilian objected to this proposal. Maximilian sought the support of the German princes such as Albert V, Duke of Bavaria and even contacted Protestant leaders like Maurice of Saxony and Christoph, Duke of Württemberg. At length a compromise was reached: Philip was to succeed Ferdinand, but during the former's reign Maximilian, as King of the Romans, was to govern Germany. This arrangement was not carried out, and is only important because the insistence of the emperor seriously disturbed the harmonious relations that had hitherto existed between the two branches of the Habsburg family; an illness that befell Maximilian in 1552 was attributed to poison given to him in the interests of his cousin and brother-in-law, Philip II of Spain.

The relationship between the two cousins was uneasy. While Philip had been raised a Spaniard and barely travelled out of the kingdom during his life, Maximilian identified himself as the quintessential German prince and often displayed a strong dislike of Spaniards, whom he considered as intolerant and arrogant. While his cousin was reserved and shy, Maximilian was outgoing and charismatic. His adherence to humanism and religious tolerance put him at odds with Philip who was more committed to the defence of the Catholic faith. Also, he was considered a promising commander, while Philip disliked war and only once personally commanded an army. Nonetheless, the two remained committed to the unity of their dynasty.

In 1551 Maximilian attended the Council of Trent and the next year took up his residence at the Hofburg palace in Vienna, celebrated by a triumphal return into the city with a large entourage including the elephant Suleiman. While his father Ferdinand concluded the 1552 Treaty of Passau with the Protestant estates and finally reached the Peace of Augsburg in 1555, Maximilian was engaged mainly in the government of the Austrian hereditary lands and in defending them against Ottoman incursions. In Vienna, he had his Hofburg residence extended with the Renaissance Stallburg wing, the site of the later Spanish Riding School, and also ordered the construction of Neugebäude Palace in Simmering. In the 1550s, Vienna had more than 50,000 inhabitants, making it the largest city in Central Europe with Prague and before Nuremberg (40,000 inhabitants).

The religious views of the future King of Bohemia had always been somewhat uncertain, and he had probably learned something of Lutheranism in his youth; but his amicable relations with several Protestant princes, which began about the time of the discussion over the succession, were probably due more to political than to religious considerations. However, in Vienna he became very intimate with, a court preacher influenced by Heinrich Bullinger with strong leanings towards Lutheranism, and his religious attitude caused some uneasiness to his father. Fears were freely expressed that he would definitely leave the Catholic Church, and when his father Ferdinand became emperor in 1558 he was prepared to assure Pope Paul IV that his son should not succeed him if he took this step. Eventually Maximilian remained nominally an adherent of the older faith, although his views were tinged with Lutheranism until the end of his life. After several refusals he consented in 1560 to the banishment of Pfauser, and began again to attend the Masses of the Catholic Church.

Reign
In November 1562 Maximilian was chosen King of the Romans, or German king, by the electoral college at Frankfurt, where he was crowned a few days later, after assuring the Catholic electors of his fidelity to their faith, and promising the Protestant electors that he would publicly accept the confession of Augsburg when he became emperor. He also took the usual oath to protect the Church, and his election was afterwards confirmed by the papacy. He was the first King of the Romans not to be crowned in Aachen. In September 1563 he was crowned King of Hungary by the Archbishop of Esztergom, Nicolaus Olahus, and on his father's death, in July 1564, he succeeded to the empire and to the kingdoms of Hungary, Croatia and Bohemia.

The new emperor had already shown that he believed in the necessity for a thorough reform of the Church. He was unable, however, to obtain the consent of Pope Pius IV to the marriage of the clergy, and in 1568 the concession of communion in both kinds to the laity was withdrawn. On his part Maximilian granted religious liberty to the Lutheran nobles and knights in Austria, and refused to allow the publication of the decrees of the Council of Trent. Amidst general expectations on the part of the Protestants he met his first summoned Diet of Augsburg in March 1566. He refused to accede to the demands of the Lutheran princes; on the other hand, although the increase of sectarianism was discussed, no decisive steps were taken to suppress it, and the only result of the meeting was a grant of assistance for the war with the Turks, which had just been renewed. Maximilian gathered a large army and marched to fight the Ottomans. The Ottomans besieged and conquered Szigetvár in 1566, but their sultan, Suleiman the Magnificent, died of old age during the siege. With neither side winning a decisive engagement, Maximilian's ambassadors Antun Vrančić and Christoph Teuffenbach met with the Ottoman Grand Vizier Sokollu Mehmed Pasha in Adrianople to negotiate a truce in 1568. The terms of the Treaty of Adrianople required the emperor to recognise Ottoman suzerainty over Transylvania, Wallachia, and Moldavia.

Meanwhile, the relations between Maximilian and Philip of Spain had improved, and the emperor's increasingly cautious and moderate attitude in religious matters was doubtless because the death of Philip's son, Don Carlos, had opened the way for the succession of Maximilian, or of one of his sons, to the Spanish throne. Evidence of this friendly feeling was given in 1570, when the emperor's daughter, Anna, became the fourth wife of Philip; but Maximilian was unable to moderate the harsh proceedings of the Spanish king against the revolting inhabitants of the Netherlands. In 1570 the emperor met the Diet of Speyer and asked for aid to place his eastern borders in a state of defence, and also for power to repress the disorder caused by troops in the service of foreign powers passing through Germany. He proposed that his consent should be necessary before any soldiers for foreign service were recruited in the empire; but the estates were unwilling to strengthen the imperial authority, the Protestant princes regarded the suggestion as an attempt to prevent them from assisting their co-religionists in France and the Netherlands, and nothing was done in this direction, although some assistance was voted for the defense of Austria. The religious demands of the Protestants were still unsatisfied, while the policy of toleration had failed to give peace to Austria. Maximilian's power was very limited; it was inability rather than unwillingness that prevented him from yielding to the entreaties of Pope Pius V to join in an attack on the Turks both before and after the victory of Lepanto in 1571; and he remained inert while the authority of the empire in north-eastern Europe was threatened.

In 1576, Maximilian was elected by the part of Polish and Lithuanian magnates to be the King of Poland in opposition to Stephan IV Bathory, but he did not manage to become widely accepted there and was forced to leave Poland.

Maximilian died on 12 October 1576 in Regensburg while preparing to invade Poland. On his deathbed he refused to receive the last sacraments of the Church. He is buried in St. Vitus Cathedral in Prague.

By his wife Maria he had a family of ten sons and six daughters. He was succeeded by his eldest surviving son, Rudolf, who had been chosen king of the Romans in October 1575. Another of his sons, Matthias, also became emperor; three others, Ernest, Albert and Maximilian, took some part in the government of the Habsburg territories or of the Netherlands. His eldest daughter, Anna, married Philip II of Spain. Another daughter, Elizabeth, married Charles IX of France.

Religious policies
Maximilian's policies of religious neutrality and peace in the empire afforded its Roman Catholics and Protestants a breathing space after the first struggles of the Reformation. His reign also saw the high point of Protestantism in Austria and Bohemia and unlike his successors, Maximilian did not try to suppress it.

He disappointed the German Protestant princes by his refusal to invest Lutheran administrators of prince-bishoprics with their imperial fiefs. Yet on a personal basis he granted freedom of worship to the Protestant nobility and worked for reform in the Roman Catholic Church, including the right of priests to marry. This failed because of Spanish opposition.

Maximilian II was a member of the Order of the Golden Fleece.

Patronage of arts and sciences
Under Ferdinand I and Maximilian II, the imperial court itself became the centre of humanist scholarship. The court held close ties to the University of Vienna but the university, that reached its summit under Maximilian I, had been severely diminished due to wars and civil disturbances.

In his court, Catholic and Prostestant scholars equally thrived. Many artists and scholars came from Spain, Italy and Spanish Netherlands. Maximilian employed scholars like the botanist Carolus Clusius and the diplomat Ogier Ghiselin de Busbecq. Maximilian's library curated by Hugo Blotius later became the nucleus of the Austrian National Library. He implemented the Roman School of composition with his court orchestra, however, his plans to win Giovanni Pierluigi da Palestrina as Kapellmeister foundered on financial reasons.

Marriage and children
On 13 September 1548, Maximilian married his first cousin Maria of Spain, daughter of Emperor Charles V and Isabella of Portugal. Despite Maria's commitment to Habsburg Spain and her strong Catholic manners, the marriage was a happy one. The couple had sixteen children:

 * 1) Archduchess Anna of Austria (1 November 1549 – 26 October 1580). Married Philip II of Spain, her uncle. She became the mother of Philip III of Spain.
 * 2) Archduke Ferdinand of Austria (28 March 1551 – 25 June 1552).
 * 3) Rudolf II, Holy Roman Emperor (18 July 1552 – 20 January 1612).
 * 4) Archduke Ernest of Austria, (15 July 1553 – 12 February 1595). He served as Governor of the Low Countries.
 * 5) Archduchess Elisabeth of Austria (5 July 1554 – 22 January 1592). Married Charles IX of France.
 * 6) Archduchess Marie of Austria (27 July 1555 – 25 June 1556).
 * 7) Matthias, Holy Roman Emperor (24 February 1557 – 20 March 1619).
 * 8) A stillborn son (20 October 1557).
 * 9) Archduke Maximilian of Austria (12 October 1558 – 2 November 1618). Elected king of Poland, but never crowned. He served as grandmaster of the Teutonic Order and Administrator of Prussia.
 * 10) Archduke Albert of Austria (15 November 1559 – 13 July 1621). He served as Governor of the Low Countries.
 * 11) Archduke Wenceslaus of Austria (9 March 1561 – 22 September 1578).
 * 12) Archduke Frederick of Austria (21 June 1562 – 16 January 1563).
 * 13) Archduchess Marie of Austria (19 February 1564 – 26 March 1564). Named after her deceased older sister.
 * 14) Archduke Charles of Austria (26 September 1565 – 23 May 1566).
 * 15) Archduchess Margaret of Austria (25 January 1567 – 5 July 1633). A nun.
 * 16) Archduchess Eleanor of Austria (4 November 1568 – 12 March 1580).

In popular culture

 * Maximilian II figures in José Saramago's 2008 novel The Elephant's Journey.

title: Maximilian II, Holy Roman Emperor


text:
Talk:Scientific journal

Nature
Nature is more of a "general science" journal than a biology journal. A number of astronomical papers have been published there. -- April — Preceding undated comment added 15:51, 25 February 2002 (UTC)

template:JSTOR
Use template:JSTOR for archives of scientific journals. It takes the parameters, "no" and "name". e.g. for Biometrika:

Dunc|☺ 09:47, 14 Apr 2005 (UTC)

Astrophysical Journal
While I can see the distinction being made, saying that the Astrophysical Journal will take anything so long as it's not "hopelessly and fundamentally flawed" seems a bit of a slur. Not being an astronomer, I can't be entirely sure that it's not some bottom-feeding journal that really does fit this criterion, but either way it does seem harsh. And it gives the reader the impression that all journals other than Nature and Science will take practically anything. Oddly enough, since Nature and Science aim to be at the cutting-edge, they occasionally take onboard something that ultimately turns out to be "hopelessly and fundamentally flawed" (e.g. cold fusion). Anyway, unless anyone objects, can I alter the text around this subject? --Plumbago 09:30, 22 September 2005 (UTC)

 * I'm glad this was changed (long before I joined), for ApJ is not an example of a journal that will take anything so long as it's not "hopelessly and fundamentally flawed." It's the most prestigious journal in its field and will indeed take all articles from first-rate scientists at the research frontier of astrophysics, but that's not quite the same thing. There are plenty of other nominees for the "will take anything" category, but it would be invidious to mention only a few. Perhaps the comment was made because of its immense size,. but thats true of the top journals in some other fields. DGG 18:59, 25 September 2006 (UTC)

Journal covers
I've reverted 'cos the new image includes a journal (Phil. Trans.) that, while highly esteemed, isn't mentioned in the article. ''Phys. Rev.'' is mentioned in its place. Also, aesthetically, the previous version looked better (well, to me at any rate!). Fatter images (like that added) squash the text horizontally a bit much.

On an unrelated note, what's with the alterations to the journal ordering (Nature, Science, PNAS) that happens from time to time? Is an anonymous editor working for PNAS???

Cheers, --Plumbago 17:58, 27 January 2006 (UTC)

 * What about the new image? The loading time is reduced significantly and all three journal covers nicely fit into the first section. The other three images are very large (not everyone has a dsl connection, there is quite a difference...) The fact that PNAS appeared in the second section and could not be seen at the first glance was maybe the reason the anonymous editor tried to alter the ordering. Nobbie 13:14, 28 January 2006 (UTC)

 * I thought the new image was fine, but it included a journal not referenced in the article. Also, as I noted above, it's shape somewhat distorted the article, but that's a personal observation.  Another reason for keeping the single images is that periodically people update them with more recent journal covers.  That'd would make altering the new image somewhat complicated.  You're definitely right about the download time though - presumably smaller original images would be better?  As for the PNAS thing, the anonymous changes affected the journal ordering throughout the article - it wasn't just to bump it up the page so it could be seen.  Cheers, --Plumbago 15:27, 28 January 2006 (UTC)

 * Like the new image! Much better.  Still has the problem re: updating, but that's not a huge deal.  Nice work.  Cheers, --Plumbago 16:45, 29 January 2006 (UTC)

Academic vs. scientific
I am confused with the difference between this article (scientific journal) and the academic journal article. Academic journal refers to scientific journals as a subfield (in relation to the natural sciences, see scientific journal), wich is confirmed by that article: or a broader class of publications, which include scientific journals, see Academic journal. Therefore what leaps to mind is that scientific journals are for natural sciences only, and academic journal is for social sciences. If this is not a correct conclusion that those articles need to be redefined. Second I note that we have a List of scientific journals which lists journals both from natural and social sciences, and that the List of academic journals is a red link. Curiouser and curiouser, but not necessarily more logical. Finally, the difference between a scientific journal and a science magazine should probably be also explain in the lead, as this is yet another dimension of possible confusion.--Piotr Konieczny aka Prokonsul Piotrus Talk 16:54, 4 April 2006 (UTC)

 * Thanks for the note. I will work on this. The distinction is that the "hard" social sciences work like the sciences, with a reliance on journal articles and a citation network. In the humanities, it's altogether different, of course. Iask, though, whether it is appropriate to have an article on social science journals, or a refer to a discussion of them on the science journals page.    DGG 08:01, 19 September 2006 (UTC)

Volumes, issues and pages
Scientific journals seem to have their own rules for sorting editions of their magazines. For example, ACM SIGGRAPH's Computer Graphics  sorts by volumes (currently volume 39), in which there are issues (usually four per volume, always beginning with issue 1 when a new volume starts). Science Magazine on the other side has currently 312 volumes, and the issue numbers are consecutively adding up. Pages are also weirdly enumerated, with starting page number in one issue taking off where the previous issue left (for example Science mag's issue 5771 starting with page 155.

So to come up with my question: Why are scientific journals split in volumes and issues? --Abdull 14:59, 1 June 2006 (UTC)

 * Volumes are often annual or semi-annual, and are usually composed of several issues. Issues are the means by which papers are regularly published, volumes are a convenient way of grouping issues, usually into a single tome per year (or a few at most).  Issues, however, are usually not relevant when it comes to citing work.  While some journals still use the issue number, most simply refer to the volume and the page number (since the latter are continuous between issues in the same volume).  As for how we got here, I think this structuring is almost certainly a historical artifact of the paper publishing industry.  It wants regular output, hence frequent issues (as an aside, scientists want regular output too, but their concerns are usually secondary to those of publishers).  I suspect these were then bundled into annual volumes for simple convenience, although it may be so that one could tell a journal's age from its volume number.  However, if a historian of science could help us here ...  --Plumbago 15:25, 1 June 2006 (UTC)

 * It's tradition from print. The issue is what gets mailed, the volume is what gets bound. This is a useful distinction in print, for the two have to handled differently in a library--the uunbound issues go in somewhere from which they won't disappear, the bound volumes go the the stacks. In our e-journal period, they serveas convenient chunks--people usually want to look at a reasonable sized batch of articles at a time. But many journals now publish the individual articles on line as they come out. This should all be discussed, but it belongs with academic journal because its general.  DGG 08:01, 19 September 2006 (UTC)

No history
We need a section on the history of the journals, mentioning Philosophical Transactions, one of the first. — Preceding unsigned comment added by AaronSw (talk • contribs) 18:22, 5 August 2006 (UTC)

 * That's a very good point. Karol 09:34, 6 August 2006 (UTC)

 * we certainly do, but its an immense topic, and will take some planning. In the meantime we do have pages on the individual journals, most ofwhich are stubbs.
 * BTW, what's thecriterion for which ones get an article--historicaly important ones of course, but there are 6,000 current major ones --major enough for web of Knowledge. Now that all journals have websites, I ask how much is necessary. There's usually not much to add to the publisher's description. If we put them in, we have to keep them up to date. DGG 08:01, 19 September 2006 (UTC)

images
Do we have permission for the images shown? If we do, is it the policy to say so? if we don;t we could probably get, but I am not sure about GFDL. I am open to the position that thumbnails are fair use, .DGG 08:01, 19 September 2006 (UTC)

role in education
Expanded previous addition of Journal clubs to include role in scientific education more generally, and slight cleanupDGG 19:18, 27 September 2006 (UTC)

Cost and Copyright
Added mentions of free-access journals (PLoS, JHEP) and gave example of "friendly" copyright transfer policies. 72.57.79.40 01:31, 29 September 2006 (UTC)

 * we seem to beworking towards the same purpose, which is good. (pls e-mail) DGG 02:01, 29 September 2006 (UTC)

Do you think it makes sense to mention the Proceedings of Science here? It's an electronic "journal" for conference proceedings, not regular articles, but authors retain copyright to their contributions and the content is published under a Creative Commons licence. This is the first scientific publication I've seen that uses CC. HEL 16:15, 30 September 2006 (UTC)
 * Why askif you should do it, after you put it in a few hours previously? I happened to see your qy before I saw the new article. -- see talk there for some necessary changes. DGG 03:50, 1 October 2006 (UTC)
 * Sorry, I don't understand.... I meant, "does it make sense to mention PoS in the Cost and/or Copyright sections of the Scientific journals article?" (since it is a publishing forum for conference proceedings, not primary journal articles).  Thanks for the cleanups in the PoS article, BTW.  HEL 04:46, 1 October 2006 (UTC)

JHEP
why is there a lock symbol on JHEP? It's a journal worth its own article, but this is an external link not marked as such; how does one get it removed, so it can be replaced by a appropriate reference and link. Or does the symbol have some other meaning?DGG 04:53, 29 September 2006 (UTC)

 * I believe the lock is there just because it's an https (encrypted) link. I'm new at this and haven't figured out how to make new pages yet. 72.57.79.40 13:08, 29 September 2006 (UTC)
 * I made JHEP its own Wikipedia entry and changed the link. (Had to create an account first.) HEL 04:17, 30 September 2006 (UTC)

change in paragraph about Nature Science et al.
On what basis was the change made. Nature and Science do look for interest beyond their own specialty, and say so. PRL does not. ?? DGG (talk) 13:01, 11 October 2007 (UTC)

first paragraph
The first paragraph of the current version states: "they [= scientific journals] generally must supply enough details of an experiment that an independent researcher could repeat the experiment to verify the results". This articulates an extremely narrow and biassed view of what constitutes 'science'. It is not a necessary condition of science that a study is based on an "experiment" and that the experiment can be "repeated". This kind of definition simply strikes out such scientific fields as evolutionary biology from the definition of science - not to even mention many other well-established disciplines such as archaeology, linguistics, etc. Even many current theories in cosmology have not been tested and cannot be tested through an "experiment", but this does not mean that they are not science. Please rephrase this in an unbiassed manner. --213.139.161.102 (talk) 23:01, 13 December 2007 (UTC)
 * I have made some changes to reflect this and also to point out that if calculations are being described, enough information must be provided for others to repeat the calculation. I also edited the paragraph below that. The use of single articles in graduate education is common in the USA, but it less common in others countries where there is often more emphasis on getting students to review a whole area. --Bduke (talk) 23:26, 13 December 2007 (UTC)
 * I certainly agree with these more inclusive changes. DGG (talk) 04:34, 15 December 2007 (UTC)

Rating in scientific journals
Hi, how can one identify what authority a certain journal has in a specific field of interest? I'd like to classify a certain amount of articles in my possession, and heard rumours that there is a certain rating system on scientific journals, but I couldn't find anything on such a rating so far. 159.46.2.67 (talk) 12:24, 2 June 2009 (UTC)

 * You might be thinking of a journal's impact factor. This is a metric of how many times (on the average) articles that appear in a particular journal are cited by other articles.  Hope this helps.  --P LUMBAGO  12:36, 2 June 2009 (UTC)

 * Thanks for your help! I think it's just what I was looking for. 159.46.2.67 (talk) 12:56, 2 June 2009 (UTC)

First authorship
Can we have a section on first authorship? —Preceding unsigned comment added by 171.67.169.56 (talk) 19:23, 15 April 2011 (UTC)
 * Why? Doesn't seem to have anything to do with this article. --Crusio (talk) 20:52, 15 April 2011 (UTC)
 * Back when I was in biology research, the tradition was that the graduate or post-doc student who did most of the work, and wrote the first draft of the article was first author, the senior scientist in who's lab the work was being done and who had provided the funding for the work was last author. The names in between either had something to do with the study (statistical analysis, specialty lab work, etc.) or sometimes just people the senior scientist owed a favor. If the study was industry funded, some companies insist that at least one of their in-house scientists be a co-author, but other companies have policy of no authorship. Nowadays, some journals insist that each authors' contribution is described. David notMD (talk) 13:12, 24 August 2017 (UTC)

RFC: Representative article image
The image below, of a Nature Physics journal cover was originally placed in the introduction to represent a scientific journal: File:Nature physics nov 2010.gif (deleted as WP:CSD F5; Orphaned non-free media)

It has just been replaced by the current image:

It appears to me that the second image (Nautilus) is inferior to the first image (Nature Physics cover). I would like to keep the Nature Physics image in the introduction. Comments please (below)--- Steve Quinn (talk) 04:48, 21 April 2011 (UTC)

Rfc comments section

 * The Nature Physics one seems on the face of it to violate Non-free content: it is a copyrighted image, used not in any irreplaceable way but merely as a representative. And the fact that it has been replaced by a free image demonstrates conclusively that it can be so replaced. That said, the replacement is a bit plain; maybe we can find something else that is appropriately free but also a bit more decorative? —David Eppstein (talk) 05:12, 21 April 2011 (UTC)
 * I absolutely agree that the Nautilus cover is not very representative and that the Nature cover is vastly preferable. However, I think that the Nature cover was replaced because it is a fair use image and our copyright tag for these images states that they can only be used to illustrate the article on the journal in question, so its use here may be a copyright infringement (I don't know much about these things, so I just say what's in the copyright tag...) If the Nature cover cannot be used, I'd prefer a free image of another high-profile journal, or if that is not available, not an image at all might be better than this. Perhaps somebody could make a picture like this one: File:Research Journals.jpg (but with sci journals instead of the economics journals in that pic)? --Crusio (talk) 05:20, 21 April 2011 (UTC)
 * As mentioned, the Nature Physics image is not usable under fair-use in this article and should probably be deleted. Why the Physics-specific journal cover was included when a primary nature cover is available (or that of science) is also strange... but anyway none of them can be used here. I'll search for a free alternative but I find it unlikely that even open-access journals won't copyright their front covers. Potentially a cover of Science or Nature from a long time ago (whose copyright has expired) could be used, it's worth looking into  Je b us 9 8 9  ✰ 16:16, 24 April 2011 (UTC)
 * Actually PloS Biology covers have been uploaded to commons, e.g. PLoS Biol., but it's pretty uninspiring. Better options are a Nature Materials cover (That's been OTRSd) or something a bit quirkier?  Je b us 9 8 9  ✰ 18:16, 24 April 2011 (UTC)

 * To add another to the mix (although I'm biased toward AmJSci - thanks for throwing that out there), how about the title page of the first ever issue of Nature. Kind of cool, huh? And also already in Commons. Awickert (talk) 18:44, 24 April 2011 (UTC)

 * Thanks for suggesting both of these covers. I didn't even think of the ORTS idea, or realize that the first "Nature" cover would be availble at Wikicommons. Hopefully both of these can be used in the first part of the article. This is certainly better than the idea I had in mind. And yes it's kind of cool. Just to be clear - I am not attached to the "Nature Physics" cover above. Furthermore, it will have to be deleted anyway because it is a non-free image.  Steve Quinn (talk) 22:12, 24 April 2011 (UTC)
 * The Nature Physics cover is certainly superior to the Natilus cover, for the same reason we wouldn't want to use a childhood picture as the main image for a living adult. However, if there are copyright issues we should avoid it. Certainly there is an open-access journal like PLoS Biology that would have a modern-looking cover but wouldn't have the same copyright issues, isn't there? –CWenger ( ^ •  @ ) 02:18, 25 April 2011 (UTC)
 * I linked to a PLoS Biol. cover above, but it's pretty bland. The majority of their readerbase is online, I've never even seen a print issue, though I know they exist  Jebus989 ✰ 08:26, 3 May 2011 (UTC)

 * This discussion has stalled, but it seems that the consensus is to change the picture. I am therefore, without endorsing it as a permanent solution, changing the picture to the 1st issue of Nature, just because it seems more acceptable than the status quo. Awickert (talk) 08:11, 3 May 2011 (UTC)
 * I support that move. A historic journal which is presumably out of copyright by now. Martin Hogbin (talk) 17:58, 7 May 2011 (UTC)
 * Good outcome. John Vandenberg (chat) 21:53, 20 May 2011 (UTC)

 * Clearly the freely licensed and out-of-copyright images can and should in this case be used instead of the non-free images (which by the way, responding to what Jebus989 said, don't have to be deleted if their use in other articles is OK, they only have to be removed from the articles where their use is not justified). But the fundamental misunderstanding here seems to be the idea that such a thing as a "representative image" exists or should be used at all. There is no requirement for articles to have a lead image at all. For an article such as this, I would expect there to be either an 'example' image (no one image can really be truly representative, but you can have an example image), or no lead image at all and appropriate images throughout the article and maybe a small gallery at the end, with a link to a larger gallery on Commons, plus links to whatever resources exist on the internet for galleries of images related to scientific journals (which is not, of course, limited to images of the covers). These galleries, though they would have to license the images in question, would be truly representative of the topic, as they would not be limited to just freely licensed images. I'll say more on this below. Carcharoth (talk) 10:22, 21 May 2011 (UTC)
 * You seem to not understand non-free image use, which is concerning for an administrator. Images uploaded with fair-use rationale which are not used in any articles must be deleted (as the image was after it was removed here), see WP:FUC  Jebus989 ✰ 11:24, 21 May 2011 (UTC)
 * I'm aware of how non-free image use works. I had presumed that the image in question had been in use on the article on the journal in question. It should never really have been used here in the first place, as any rationale for its use here should have been contested much earlier. May I suggest that if you want to continue this, you raise any concerns at my talk page and we can discuss things there, and I can then point you to the previous work I have done on non-free images, which will hopefully allay your concerns. Carcharoth (talk) 11:56, 21 May 2011 (UTC)

Other images
The lead image now currently used is (as Awickert said above) a title page image, which shows that you don't have to limit yourself to cover page images. If I was thinking outside the box here, I would suggest the following as other possibilities for images to be used in this article: (i) a montage of early scientific journal editors; (ii) a picture of an early meeting of a scientific society that resulted in a 'proceedings' that was published as a journal; (iii) some pictures related to the journal production process; (iv) a screenshot of some sort to illustrate electronic publishing. Such extra images would eventually be expected as this article develops. Indeed, the idea that general articles on the topic of journals (rather than on specific journals) can only be illustrated by cover images is a bit quaint. It seems what is needed is to illustrate the whole article more, rather than focusing on whether a lead image is strictly needed. Another example of how to illustrate the topic of journals is showing how they are used: e.g. an academic reading a journal (it sounds corny, yes, but it is standard to show in general topic articles how the subject of that article is used), or a series of journals on library shelves, and individual issues versus bound issues, and a meeting of an editorial board (if they still have physical meetings), and so on. Some of these ideas are more suited to the academic journal article, and it is possible to go too far and illustrate merely for the sake of it, but I do think there should be more than just images of journal covers being considered. I'll try and see if we have any such images already. Carcharoth (talk) 10:22, 21 May 2011 (UTC)
 * While I agree that images of editors and meetings could have a place in the article, common sense requires the lead image to be a picture of a scientific journal. I don't think anyone has suggested the only images to be allowed on this page are covers, just that the lead image of the 'scientific journal' article would be of a 'scientific journal'. The distinction you make between title page and cover page is trivial; it appears that in the first issue of Nature they are one and the same. Some of the image suggestions you make could be useful, but others add nothing to the text. A photo of a meeting, which personally I would find interesting, aids the reader little in understanding the concept of a scientific journal  Jebus989 ✰ 11:15, 21 May 2011 (UTC)
 * I sometimes work with title pages and frontispieces in old books (15th to 19th centuries), so forgive my pedantry there in contrasting those with book cover (the closest equivalent we have to journal covers). Not sure what they were for the first issue of Nature. There is also a technical term for a piece of artwork used at the top of an initial chapter page, which is similar to what we are seeing on that Nature title page, but I forget what that term is. I agree that some of my suggestions would add nothing to the text, but that takes us in the direction of a discussion of decorative images versus illustrative images vs encyclopedic images. I'd be happy to have that discussion, but this is probably not the best place for it. I still think that other images, if carefully considered, would enhance this article (once it is expanded), and that no lead image is required. The obvious one, if a lead image is needed, would be a montage or picture of journals on a library shelf, rather than a single journal. Example images of specific journals would come later in the article. But that leads on to a discussion of montage images and when to use those. Carcharoth (talk) 11:38, 21 May 2011 (UTC)
 * I agree a montage would be nice and (as suggested by Crusio above) a fanned selection of prominent scientific journals could be near ideal (similar to this). I would certainly not want to remove any image similar to those you suggest, even if purely illustrative, as it is not suffering from an excess  Jebus989 ✰ 11:53, 21 May 2011 (UTC)
 * If the journals covers are individually copyrighted, that impacts on the licensing and non-free use rationales needed for montages. It has been discussed at WT:NFC before. I disagree with some of the restrictions on montages of individually copyrighted items, but things may have changed since the last time I saw a discussion there. See older discussions here for examples. Carcharoth (talk) 12:06, 21 May 2011 (UTC)

External link
"The cost of publishing in a scientific journal, some examples and recommended reading from OpenWetWare life scientists' wiki" - Look like WP:PROMOTION? Shouldn't be delete or expanded? --Karlaz1 (talk) 14:44, 17 February 2022 (UTC)

Content paragraph
I spent a couple of hours completely revising and reworking the "Content" section, including finding citations for each of the statements in it, adding context where it seemed appropriate, and breaking up that long paragraph into two subsections (with several paragraphs for each section). So, if the section seems satisfactory, would someone else remove the tag at the top indicating that it doesn't cite any sources? Thanks. Mateo Tembo (talk) 06:15, 26 January 2023 (UTC)

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

title: Talk:Scientific journal


text:
Infimum and supremum

In mathematics, the infimum (abbreviated inf; plural infima) of a subset $$S$$ of a partially ordered set $$P$$ is the greatest element in $$P$$ that is less than or equal to each element of $$S,$$ if such an element exists. If the infimum of $$S$$ exists, it is unique, and if b is a lower bound of $$S$$, then b is less than or equal to the infimum of $$S$$. Consequently, the term greatest lower bound (abbreviated as ) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset $$S$$ of a partially ordered set $$P$$ is the least element in $$P$$ that is greater than or equal to each element of $$S,$$ if such an element exists. If the supremum of $$S$$ exists, it is unique, and if b is an upper bound of $$S$$, then the supremum of $$S$$ is less than or equal to b. Consequently, the supremum is also referred to as the least upper bound (or ).

The infimum is in a precise sense dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration. However, the general definitions remain valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.

The concepts of infimum and supremum are close to minimum and maximum, but are more useful in analysis because they better characterize special sets which may have. For instance, the set of positive real numbers $$\R^+$$ (not including $$0$$) does not have a minimum, because any given element of $$\R^+$$ could simply be divided in half resulting in a smaller number that is still in $$\R^+.$$ There is, however, exactly one infimum of the positive real numbers relative to the real numbers: $$0,$$ which is smaller than all the positive real numbers and greater than any other real number which could be used as a lower bound. An infimum of a set is always and only defined relative to a superset of the set in question. For example, there is no infimum of the positive real numbers inside the positive real numbers (as their own superset), nor any infimum of the positive real numbers inside the complex numbers with positive real part.

Formal definition
A of a subset $$S$$ of a partially ordered set $$(P, \leq)$$ is an element $$a$$ of $$P$$ such that A lower bound $$a$$ of $$S$$ is called an (or, or Join and meet) of $$S$$ if
 * $$a \leq x$$ for all $$x \in S.$$
 * for all lower bounds $$y$$ of $$S$$ in $$P,$$ $$y \leq a$$ ($$a$$ is larger than any other lower bound).

Similarly, an of a subset $$S$$ of a partially ordered set $$(P, \leq)$$ is an element $$b$$ of $$P$$ such that An upper bound $$b$$ of $$S$$ is called a (or, or Join and meet) of $$S$$ if
 * $$b \geq x$$ for all $$x \in S.$$
 * for all upper bounds $$z$$ of $$S$$ in $$P,$$ $$z \geq b$$ ($$b$$ is less than any other upper bound).

Existence and uniqueness
Infima and suprema do not necessarily exist. Existence of an infimum of a subset $$S$$ of $$P$$ can fail if $$S$$ has no lower bound at all, or if the set of lower bounds does not contain a greatest element. (An example of this is the subset $$\{ x \in \mathbb{Q} : x^2 < 2 \}$$ of $$\mathbb{Q}$$. It has upper bounds, such as 1.5, but no supremum in $$\mathbb{Q}$$.)

Consequently, partially ordered sets for which certain infima are known to exist become especially interesting. For instance, a lattice is a partially ordered set in which all subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which  subsets have both a supremum and an infimum. More information on the various classes of partially ordered sets that arise from such considerations are found in the article on completeness properties.

If the supremum of a subset $$S$$ exists, it is unique. If $$S$$ contains a greatest element, then that element is the supremum; otherwise, the supremum does not belong to $$S$$ (or does not exist). Likewise, if the infimum exists, it is unique. If $$S$$ contains a least element, then that element is the infimum; otherwise, the infimum does not belong to $$S$$ (or does not exist).

Relation to maximum and minimum elements
The infimum of a subset $$S$$ of a partially ordered set $$P,$$ assuming it exists, does not necessarily belong to $$S.$$ If it does, it is a minimum or least element of $$S.$$ Similarly, if the supremum of $$S$$ belongs to $$S,$$ it is a maximum or greatest element of $$S.$$

For example, consider the set of negative real numbers (excluding zero). This set has no greatest element, since for every element of the set, there is another, larger, element. For instance, for any negative real number $$x,$$ there is another negative real number $$\tfrac{x}{2},$$ which is greater. On the other hand, every real number greater than or equal to zero is certainly an upper bound on this set. Hence, $$0$$ is the least upper bound of the negative reals, so the supremum is 0. This set has a supremum but no greatest element.

However, the definition of maximal and minimal elements is more general. In particular, a set can have many maximal and minimal elements, whereas infima and suprema are unique.

Whereas maxima and minima must be members of the subset that is under consideration, the infimum and supremum of a subset need not be members of that subset themselves.

Minimal upper bounds
Finally, a partially ordered set may have many minimal upper bounds without having a least upper bound. Minimal upper bounds are those upper bounds for which there is no strictly smaller element that also is an upper bound. This does not say that each minimal upper bound is smaller than all other upper bounds, it merely is not greater. The distinction between "minimal" and "least" is only possible when the given order is not a total one. In a totally ordered set, like the real numbers, the concepts are the same.

As an example, let $$S$$ be the set of all finite subsets of natural numbers and consider the partially ordered set obtained by taking all sets from $$S$$ together with the set of integers $$\Z$$ and the set of positive real numbers $$\R^+,$$ ordered by subset inclusion as above. Then clearly both $$\Z$$ and $$\R^+$$ are greater than all finite sets of natural numbers. Yet, neither is $$\R^+$$ smaller than $$\Z$$ nor is the converse true: both sets are minimal upper bounds but none is a supremum.

Least-upper-bound property
The is an example of the aforementioned completeness properties which is typical for the set of real numbers. This property is sometimes called.

If an ordered set $$S$$ has the property that every nonempty subset of $$S$$ having an upper bound also has a least upper bound, then $$S$$ is said to have the least-upper-bound property. As noted above, the set $$\R$$ of all real numbers has the least-upper-bound property. Similarly, the set $$\Z$$ of integers has the least-upper-bound property; if $$S$$ is a nonempty subset of $$\Z$$ and there is some number $$n$$ such that every element $$s$$ of $$S$$ is less than or equal to $$n,$$ then there is a least upper bound $$u$$ for $$S,$$ an integer that is an upper bound for $$S$$ and is less than or equal to every other upper bound for $$S.$$ A well-ordered set also has the least-upper-bound property, and the empty subset has also a least upper bound: the minimum of the whole set.

An example of a set that the least-upper-bound property is $$\Q,$$ the set of rational numbers. Let $$S$$ be the set of all rational numbers $$q$$ such that $$q^2 < 2.$$ Then $$S$$ has an upper bound ($$1000,$$ for example, or $$6$$) but no least upper bound in $$\Q$$: If we suppose $$p \in \Q$$ is the least upper bound, a contradiction is immediately deduced because between any two reals $$x$$ and $$y$$ (including $\sqrt{2}$ and $$p$$) there exists some rational $$r,$$ which itself would have to be the least upper bound (if $$p > \sqrt{2}$$) or a member of $$S$$ greater than $$p$$ (if $$p < \sqrt{2}$$). Another example is the hyperreals; there is no least upper bound of the set of positive infinitesimals.

There is a corresponding ; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least-upper-bound of the set.

If in a partially ordered set $$P$$ every bounded subset has a supremum, this applies also, for any set $$X,$$ in the function space containing all functions from $$X$$ to $$P,$$ where $$f \leq g$$ if and only if $$f(x) \leq g(x)$$ for all $$x \in X.$$ For example, it applies for real functions, and, since these can be considered special cases of functions, for real $$n$$-tuples and sequences of real numbers.

The least-upper-bound property is an indicator of the suprema.

Infima and suprema of real numbers
In analysis, infima and suprema of subsets $$S$$ of the real numbers are particularly important. For instance, the negative real numbers do not have a greatest element, and their supremum is $$0$$ (which is not a negative real number). The completeness of the real numbers implies (and is equivalent to) that any bounded nonempty subset $$S$$ of the real numbers has an infimum and a supremum. If $$S$$ is not bounded below, one often formally writes $$\inf_{} S = -\infty.$$ If $$S$$ is empty, one writes $$\inf_{} S = +\infty.$$

Properties
If $$A$$ is any set of real numbers then $$A \neq \varnothing$$ if and only if $$\sup A \geq \inf A,$$ and otherwise $$-\infty = \sup \varnothing < \inf \varnothing = \infty.$$

If $$A \subseteq B$$ are sets of real numbers then $$\inf A \geq \inf B$$ (unless $$A = \varnothing \neq B$$) and $$\sup A \leq \sup B.$$

Identifying infima and suprema

If the infimum of $$A$$ exists (that is, $$\inf A$$ is a real number) and if $$p$$ is any real number then $$p = \inf A$$ if and only if $$p$$ is a lower bound and for every $$\epsilon > 0$$ there is an $$a_\epsilon \in A$$ with $$a_\epsilon < p + \epsilon.$$ Similarly, if $$\sup A$$ is a real number and if $$p$$ is any real number then $$p = \sup A$$ if and only if $$p$$ is an upper bound and if for every $$\epsilon > 0$$ there is an $$a_\epsilon \in A$$ with $$a_\epsilon > p - \epsilon.$$

Relation to limits of sequences

If $$S \neq \varnothing$$ is any non-empty set of real numbers then there always exists a non-decreasing sequence $$s_1 \leq s_2 \leq \cdots$$ in $$S$$ such that $$\lim_{n \to \infty} s_n = \sup S.$$ Similarly, there will exist a (possibly different) non-increasing sequence $$s_1 \geq s_2 \geq \cdots$$ in $$S$$ such that $$\lim_{n \to \infty} s_n = \inf S.$$

Expressing the infimum and supremum as a limit of a such a sequence allows theorems from various branches of mathematics to be applied. Consider for example the well-known fact from topology that if $$f$$ is a continuous function and $$s_1, s_2, \ldots$$ is a sequence of points in its domain that converges to a point $$p,$$ then $$f\left(s_1\right), f\left(s_2\right), \ldots$$ necessarily converges to $$f(p).$$ It implies that if $$\lim_{n \to \infty} s_n = \sup S$$ is a real number (where all $$s_1, s_2, \ldots$$ are in $$S$$) and if $$f$$ is a continuous function whose domain contains $$S$$ and $$\sup S,$$ then $$f(\sup S) = f\left(\lim_{n \to \infty} s_n\right) = \lim_{n \to \infty} f\left(s_n\right),$$ which (for instance) guarantees that $$f(\sup S)$$ is an adherent point of the set $$f(S) \,\stackrel{\scriptscriptstyle\text{def}}{=}\, \{f(s) : s \in S\}.$$ If in addition to what has been assumed, the continuous function $$f$$ is also an increasing or non-decreasing function, then it is even possible to conclude that $$\sup f(S) = f(\sup S).$$ This may be applied, for instance, to conclude that whenever $$g$$ is a real (or complex) valued function with domain $$\Omega \neq \varnothing$$ whose sup norm $$\|g\|_\infty \,\stackrel{\scriptscriptstyle\text{def}}{=}\, \sup_{x \in \Omega} |g(x)|$$ is finite, then for every non-negative real number $$q,$$ $$\|g\|_\infty^q ~\stackrel{\scriptscriptstyle\text{def}}{=}~ \left(\sup_{x \in \Omega} |g(x)|\right)^q = \sup_{x \in \Omega} \left(|g(x)|^q\right)$$ since the map $$f : [0, \infty) \to \R$$ defined by $$f(x) = x^q$$ is a continuous non-decreasing function whose domain $$[0, \infty)$$ always contains $$S := \{|g(x)| : x \in \Omega\}$$ and $$\sup S \,\stackrel{\scriptscriptstyle\text{def}}{=}\, \|g\|_\infty.$$

Although this discussion focused on $$\sup,$$ similar conclusions can be reached for $$\inf$$ with appropriate changes (such as requiring that $$f$$ be non-increasing rather than non-decreasing). Other norms defined in terms of $$\sup$$ or $$\inf$$ include the weak $L^{p,w}$ space norms (for $$1 \leq p < \infty$$), the norm on Lebesgue space $$L^\infty(\Omega, \mu),$$ and operator norms. Monotone sequences in $$S$$ that converge to $$\sup S$$ (or to $$\inf S$$) can also be used to help prove many of the formula given below, since addition and multiplication of real numbers are continuous operations.

Arithmetic operations on sets
The following formulas depend on a notation that conveniently generalizes arithmetic operations on sets. Throughout, $$A, B \subseteq \R$$ are sets of real numbers.

Sum of sets

The Minkowski sum of two sets $$A$$ and $$B$$ of real numbers is the set $$A + B ~:=~ \{a + b : a \in A, b \in B\}$$ consisting of all possible arithmetic sums of pairs of numbers, one from each set. The infimum and supremum of the Minkowski sum satisfies $$\inf (A + B) = (\inf A) + (\inf B)$$ and $$\sup (A + B) = (\sup A) + (\sup B).$$

Product of sets

The multiplication of two sets $$A$$ and $$B$$ of real numbers is defined similarly to their Minkowski sum: $$A \cdot B ~:=~ \{a \cdot b : a \in A, b \in B\}.$$

If $$A$$ and $$B$$ are nonempty sets of positive real numbers then $$\inf (A \cdot B) = (\inf A) \cdot (\inf B)$$ and similarly for suprema $$\sup (A \cdot B) = (\sup A) \cdot (\sup B).$$

Scalar product of a set

The product of a real number $$r$$ and a set $$B$$ of real numbers is the set $$r B ~:=~ \{r \cdot b : b \in B\}.$$

If $$r \geq 0$$ then $$\inf (r \cdot A) = r (\inf A) \quad \text{ and } \quad \sup (r \cdot A) = r (\sup A),$$ while if $$r \leq 0$$ then $$\inf (r \cdot A) = r (\sup A) \quad \text{ and } \quad \sup (r \cdot A) = r (\inf A).$$ Using $$r = -1$$ and the notation $-A := (-1) A = \{- a : a \in A\},$ it follows that $$\inf (- A) = - \sup A \quad \text{ and } \quad \sup (- A) = - \inf A.$$

Multiplicative inverse of a set

For any set $$S$$ that does not contain $$0,$$ let $$\frac{1}{S} ~:=\; \left\{\tfrac{1}{s} : s \in S\right\}.$$

If $$S \subseteq (0, \infty)$$ is non-empty then $$\frac{1}{\sup_{} S} ~=~ \inf_{} \frac{1}{S}$$ where this equation also holds when $$\sup_{} S = \infty$$ if the definition $$\frac{1}{\infty} := 0$$ is used. This equality may alternatively be written as $$\frac{1}{\displaystyle\sup_{s \in S} s} = \inf_{s \in S} \tfrac{1}{s}.$$ Moreover, $$\inf_{} S = 0$$ if and only if $$\sup_{} \tfrac{1}{S} = \infty,$$ where if $$\inf_{} S > 0,$$ then $$\tfrac{1}{\inf_{} S} = \sup_{} \tfrac{1}{S}.$$

Duality
If one denotes by $$P^{\operatorname{op}}$$ the partially-ordered set $$P$$ with the opposite order relation; that is, for all $$x \text{ and } y,$$ declare: $$x \leq y \text{ in } P^{\operatorname{op}} \quad \text{ if and only if } \quad x \geq y \text{ in } P,$$ then infimum of a subset $$S$$ in $$P$$ equals the supremum of $$S$$ in $$P^{\operatorname{op}}$$ and vice versa.

For subsets of the real numbers, another kind of duality holds: $$\inf S = - \sup (- S),$$ where $$-S := \{ -s ~:~ s \in S \}.$$

Infima

 * The infimum of the set of numbers $$\{2, 3, 4\}$$ is $$2.$$ The number $$1$$ is a lower bound, but not the greatest lower bound, and hence not the infimum.
 * More generally, if a set has a smallest element, then the smallest element is the infimum for the set. In this case, it is also called the minimum of the set.
 * $$\inf \{ 1, 2, 3, \ldots \} = 1.$$
 * $$\inf \{ x \in \R : 0 < x < 1 \} = 0.$$
 * $$\inf \left\{ x \in \Q : x^3 > 2 \right\} = \sqrt[3]{2}.$$
 * $$\inf \left\{ (-1)^n + \tfrac{1}{n} : n = 1, 2, 3, \ldots \right\} = -1.$$
 * If $$\left(x_n\right)_{n=1}^{\infty}$$ is a decreasing sequence with limit $$x,$$ then $$\inf x_n = x.$$

Suprema

 * The supremum of the set of numbers $$\{1, 2, 3\}$$ is $$3.$$ The number $$4$$ is an upper bound, but it is not the least upper bound, and hence is not the supremum.
 * $$\sup \{ x \in \R : 0 < x < 1\} = \sup \{ x \in \R : 0 \leq x \leq 1\} = 1.$$
 * $$\sup \left\{ (-1)^n - \tfrac{1}{n} : n = 1, 2, 3, \ldots \right\} = 1.$$
 * $$\sup \{ a + b : a \in A, b \in B \} = \sup A + \sup B.$$
 * $$\sup \left\{ x \in \Q : x^2 < 2 \right\} = \sqrt{2}.$$

In the last example, the supremum of a set of rationals is irrational, which means that the rationals are incomplete.

One basic property of the supremum is $$\sup \{ f(t) + g(t) : t \in A \} ~\leq~ \sup \{ f(t) : t \in A \} + \sup \{ g(t) : t \in A \}$$ for any functionals $$f$$ and $$g.$$

The supremum of a subset $$S$$ of $$(\N, \mid\,)$$ where $$\,\mid\,$$ denotes "divides", is the lowest common multiple of the elements of $$S.$$

The supremum of a set $$S$$ containing subsets of some set $$X$$ is the union of the subsets when considering the partially ordered set $$(P(X), \subseteq)$$, where $$P$$ is the power set of $$X$$ and $$\,\subseteq\,$$ is subset.

title: Infimum and supremum


text:
Talk:Distance

(old)
Could somebody who knows how please write out the distance formula in symbols, too, just for clarity? I read the last paragraph a couple of times before I realized that it was talking about the formula I know :) Dreamyshade

I split proxemics and propinquity into separate articles. When people are looking for 'proxemics' they will likely be surprised to see a page about geometrical distance. Ditto for 'propinquity' -- I study both mathematics and psychology, and propinquity is a major topic in social psychology, but I have never heard it used in geometry.

--Johnkarp 11:11, 9 Oct 2004 (UTC)

removed not well-explained and unhelpful paragraph
I removed the following text from distance
 * Distance is one sort of interval between things or events, Time being the other.

I found it unclear. Oleg Alexandrov 22:20, 31 May 2005 (UTC)

 * But see Time. Banno 21:39, May 31, 2005 (UTC)

OK, you are writing at the very beginning of the time article:

 * Time is one sort of interval between things or events, distance being the other..

I am not sure this is a proper characterisation of time. I am not sure time and distance can be compared in that way. I am not sure you what you mean by interval in this sentence. I cannot even say that what you wrote is incorrect, I think it is ambiguous and confusing. Would you clarify me please? Oleg Alexandrov 22:14, 31 May 2005 (UTC)
 * An excellent point - I see the circularity in interval. I had just retained the word from a previous edit. Try:
 * Time is one sort of separation between things or events, distance being the other..
 * Failing that, I'm open to your suggestions. Banno 22:48, May 31, 2005 (UTC)

 * This sentence is true. But I do not think it is so important or so releveant as to be the very first sentence in either the distance article or in the time article. Oleg Alexandrov 23:37, 31 May 2005 (UTC)
 * If you wish to demote it, be my guest. But then, what is your suggestion for an introduction to time? The advantage of this sentence is that it draws attention to the link between time and distance; it is also succinct. Banno 23:48, May 31, 2005 (UTC)

 * "This sentence is true." - AFAIK in a classical Newtonian universe - yes, in an Einstein-Minkowski universe - no. Physicists nowadays know that time and space are not independent, consequently causing things like e.g. the Twin paradox. Furthermore I understand that extreme accurate measuring and comparing of horizontal and vertical distances in a gravitational field is not trivial and therefore might warrant its own page (but my current knowledge about physics isn't enough for that). Stevemiller (talk) 17:47, 22 January 2008 (UTC)

 * In the most general sense: Distance is a description or gauge of the expected strength of interaction of between two reference entities A and B. Strength of interaction also being the basis for ease of observability. Distance is a transitive property in that proposed interaction between A and C may be described in terms of AB and BC interactions. In general physics and the common realm of human perception, distance is normally referenced to gravity and EM fields, the macroscopic long forces.

 * One trivial result of this definition is that the universe will remain finite in size despite the "infinite" numerical space upon which it could be mapped. Given a finite number of elementary particles, all systems in which a given particle is separated beyond measurable interaction of forces with all other particles are essentially identical. Thus meaningful and recognizable definitions of the universe require that all elementary particles remain within limits of interaction with at least one other particle in the universe. Given a rough estimate of the number of particles in the universe an theoretical upper limit can be set on the size of a meaningful universe.
 * Alternatively, we could expect that the number of particles and mass of the universe can randomly change through "disappearance" and "appearance" of particles from beyond meaningful distance at the edge of the universe. The old philosophical issue of observability: "just because you can't see it or measure it doesn't mean it isn't there -- only that you are at the limits of your ability to measure via interactions". Of course at the quantum level where distance is a measure of interaction via dominant short forces, the edge of the universe might be at your very feet, if very rare. What happens when a given particle finds a position beyond the limits of short force interaction with any other particle? Essentially it meets the criteria for being unobservable and can fall into a crack and disappear "perpendicular" to our universe with its reappearance only a statistical probability. 69.23.124.142 (talk) 20:11, 9 January 2008 (UTC)

Reworked Article
I’ve made some rather significant changes to this article. In the course of doing so, I deleted the following material. Wherever possible, I’ve attempted to reincorporate this information elsewhere in the text, but some of it didn’t seem particularly pertinent to the discussion. As this is one of my first attempts, I would appreciate feedback from more experienced users. It would be nice if someone could help with the page layout or say something more about physics and informal treatments. I wasn't sure what to do with the "Euclidean spaces" section either, but it seems a like it might be a bit excessive for this article.

 *  The distance between two points is the length of a straight line segment between them.

 * Sometimes a distance thus indicated is ambiguous because the means of transport is neither mentioned nor obvious.

 * In the study of complicated geometries, we call the most common type of distance Euclidean distance, as we define it from the Pythagorean theorem.

 * ===The distance formula===
 * The (Euclidean) distance, d, between two points expressed in Cartesian coordinates equals the square root of the sum of the squares of the changes of each coordinate.
 * Thus, in a two-dimensional space

 * $$d = \sqrt{(\Delta x)^2 + (\Delta y)^2},$$

 * and in a three-dimensional space:

 * $$d = \sqrt{(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2}.$$

 * Here, "Δ" (delta) refers to the change in a variable. Thus, Δx is the change in x, pronounced as such, or as "delta-x". In mathematical terms, $$\Delta x = \left|x_1 - x_0\right|$$, and so $$(\Delta x)^2 = (x_1 - x_0)^2$$.

 * This distance formula can be seen as a specialized form of the Pythagorean theorem; it can also be expanded into the arc-length formula.

 * == Formal definition ==
 * A distance between two points P and Q in a metric space is d(P,Q), where d is the distance function that defines the given metric space.

 * We can also define the distance between two sets A and B in a metric space as being the minimum (or infimum) of distances between any two points P in A and Q in B.

 * Alternatively, the distance between sets may indicate "how different they are", by taking the supremum over one set of the distance from a point in that set to the other set, and conversely, and taking the larger of the two values (Hausdorff distance).

 * ===Generalized distance in arbitrary dimensions: Norms===
 * == Distances in other spaces ==
 * ==Distance covered==

--Fell Collar 06:39, 10 March 2006 (UTC)

 * Headers should have sentence-style capitalization (i.e. only one capital).

 * Also you made some odd deletions, e.g. in the section on the distance between sets.

 * Please do not start a line with a blank space, even on the talk page, it makes lines wider than the screen.--Patrick 14:38, 10 March 2006 (UTC)

 * I've put back the material about the Hausdorff metric in the section on distance between sets and fixed the headers. Are there any other deletions that struck you as inappropriate?  I had read that it is considered polite to move deleted material to the talk page, but I wasn't sure how to format it.  What is the convention?  --Fell Collar 16:51, 10 March 2006 (UTC)

 * Aw, I see it right above: indent and italicize.  I've restored a great deal more of the material I'd deleted.  In retrospect, I'm not sure why I got rid of a lot of it.  The remainder is either
 * paraphrased elsewhere in the article
 * a now-defunct header, or
 * superfluous (e.g. the bit about "delta x", which should be fairly obvious from the way I've formatted the equation)
 * Fell Collar

 * Thanks!--Patrick 00:32, 11 March 2006 (UTC)

Negative Distance?
Someone (81.207.214.244) indicated that one could have negative distance if it was "predefined". I wonder if they (or someone else) could elaborate. If distance was negative, it certainly wouldn't be a metric, so it seems odd to me that we would call it "distance" in a formal setting. Can someone give an example? --Fell Collar 18:03, 13 March 2006 (UTC)
 * I'm moving the sentence here for now. It seems very suspect, and at any rate distance certainly won't be negative in Euclidean space (the section it was placed in).  If someone could elaborate and put this where it belongs, that would be nice.
 * There is no such thing as a negative distance (unless it is predefined).
 * --Fell Collar 03:41, 16 March 2006 (UTC)

Ive changed the heading of what was the physics section, because, it appeared to have nothing much to do with physics! I made a new physics description, and put it at the top, but I think it generally covers what most people know of as distance. I deleted the "distinctions" of distance that had been written, that said things like "the distance formula is not true for curved surfaces", which cant be true, because the distance formula is part of the law of physics and is always true! they were true in a general sense, but i didnt see how they had any useful meaning.

if someone understands the special theory of reletivity better than i do, can they please give some information on how distance applies generally in physics.

ive been thinking that it might be overkill to seperate this topic into physics/geometry/maths, because distance is all of them at once, and it doesnt need to be explained over and over in slightly different senses.

(Comment)Isn't it impossible to have a negative distance, as it would just be a positive distance in another direction. Somebody, correct me if I'm wrong.24.22.22.113 (talk) 00:39, 16 September 2009 (UTC)
 * There's no such thing as negative distance, distance uses absolute values therefore it is positive no matter what direction. Planet  Star  01:21, 28 April 2017 (UTC)

Content syncronizing
Please see Talk:Metric (mathematics). `'Míkka 17:52, 8 October 2007 (UTC)

Distance between functions
I am of the opinion that a section on distance between functions be added:

For e.g. In the fourier series representation of a simple periodic function f(t) with time 't' as the independent variable, the fourier coefficients are so adjusted that the distance between the finite fourier sum and the function f(t) is minimized.

Here the distance between f(t) and g(t) is given by : {(1/2pi integral((f(t)-g(t))sqrd.dt}sq. root.

It would be infromative if this is discussed in the article. Sridhar10chitta (talk) 08:48, 27 November 2007 (UTC)

distance of a function
It would probably be appropriate if a section describing the distance of a time dependent function maybe f(t) = at^sq + bt +c is added as well before discussing the distance between functions. Sridhar10chitta (talk) 16:56, 28 November 2007 (UTC)

minkowski unit circles
Here's an image I made that might be helpful for explaining Minkowski distances:

Purpose of this article
This article mainly talks about distance in mathematics. Most of that material is in Metric (mathematics), or could be moved there. There is little mention of distance in physics, and no mention of distance in everyday use. Why do we have this article? --Taeshadow (talk) 15:49, 11 March 2009 (UTC)

Removed section
The following seciton is removed since it is absolutely incomprehensible. While it may be OK for an expert in the field, who can read between lines, it is absolutely inadmissible in encuclopedia due to its lack of context, lack of explanation of notation and unclear opinions. Whoever can fix it, they are welcome. - Altenmann >t 15:33, 24 September 2009 (UTC)

Generalization of Euclidean distance to higher-dimensional manifolds
The Euclidean distance between two objects may also be generalized to the case where the objects are no longer points but are higher-dimensional manifolds, such as space curves. Additional concepts such as non-extensibility, curvature constraints, and non-local interactions that enforce noncrossing then become central to the notion of distance. The distance between the two manifolds is the scalar quantity that results from minimizing the generalized distance functional, which represents a transformation between the two manifolds:

\mathcal {D} = \int_0^L\int_0^T \, ds \, dt \left \{ \sqrt{\left({\partial \vec{r}(s,t) \over \partial t}\right)^2} + \lambda \left[\sqrt{\left({\partial \vec{r}(s,t) \over \partial s}\right)^2} - 1\right] \right\} $$

If two discrete polymers are inextensible, then the minimal-distance transformation between them no longer involves purely straight-line motion, even on a Euclidean metric. There is a potential application of such generalized distance to the problem of protein folding This generalized distance is analogous to the Nambu–Goto action in string theory, however there is no exact correspondence because the Euclidean distance in 3-space is inequivalent to the space-time distance minimized for the classical relativistic string.
 * OK. I added a section on variational formulation of distance. This will make the above text much more accessible to an non-expert user. Nocompletechaos (talk) 07:42, 26 September 2009 (UTC)

Definition
Currently the article begins:
 * Distance is a numerical description of how far apart objects are.

Sometimes distance is not expressed numerically, but rather quantitatively as in "A is further away than B". Also, sometimes it is not about how far apart objectS are, but about how extensive a single object is - either numerically as "A is 3 metres long", or non-numerically (but still quantitatively) as "A is taller than B". It can aso be the distance travelled in a period of time, like "The Earth travels further in one orbit than Mercury does"  JimWae (talk) 09:28, 12 July 2010 (UTC)

Prudent distance
What's the definition of prudent distance? I saw it in an article about Cassini's final days and said 'Cassini is orbiting Saturn at the same inclination it will have during the Grand Finale, but at a more prudent distance.' I learned the definition of prudence but how that relates to distance? Planet Star  00:32, 28 April 2017 (UTC)
 * This is not a technical term, which is probably why no one has responded to your query. Some editor was just waxing eloquently when what was meant was a "safer" distance, that is, not so close as to spiral into Saturn as it will during the Grand Finale.--Bill Cherowitzo (talk) 04:26, 13 May 2017 (UTC)

Splitting Distance (mathematics)
I noticed you recently made some edits to distance and split out distance (mathematics). Do you have a vision for what should be on these pages? I've tried to think coherently about the "distance" page but I don't have a clear idea of its intended audience or purpose, either now or ideally in the future. What sort of person visits the Wikipedia page on "distance" and what do they hope to find there? (My angle here is that I'm a mathematician and recently thoroughly rewrote metric space, which has some overlap with both these pages but probably a different intended audience.) --platypeanArchcow (talk) 00:46, 14 September 2022 (UTC)

 * If you're interested in a broader discussion we can also move this to Wikipedia talk:WikiProject Mathematics. --platypeanArchcow (talk) 00:47, 14 September 2022 (UTC)
 * I wanted to give more space for Distance (mathematics) to grow and flourish. Then Distance would remain as a WP:broad-concept article. A successful example is Surface and Surface (mathematics). fgnievinski (talk) 00:53, 14 September 2022 (UTC)
 * Thanks for the links, that's helpful. In the case of surfaces, there really is a well-defined mathematical idea of a surface which can be thought of as the mathematical formalization of the broad concept.  This is not so clear in the case of distance.  Thinking aloud:
 * The mathematical formalization of the colloquial notion of distance (whether literal or metaphorical) is the metric in a metric space. Note that distance function already redirects to metric space.  Moreover, the ideas described in the sections "In physics and geography", "In computer science", as well as some of those in "In statistics", can be formalized as metrics.  (In particular, they are all mathematical concepts, so separating distance (mathematics) from them seems perverse.)
 * Not everyone who comes to Wikipedia to understand the mathematics of distance is well-served by the article "metric space". If they are interested in distances in Euclidean geometry or something like distance between two skew lines, then it will be needlessly intimidating for them.  However, these elementary topics are fairly well-summarized in Euclidean distance.
 * Not every concept described in distance (mathematics) is a metric. Specifically, Distance (mathematics) describes something that's not a metric.  Perhaps distance between sets deserves to be a separate article.
 * The current distance (mathematics) is a random collection of topics that doesn't serve anyone particularly well. Most of these topics are covered in depth in the articles "Euclidean distance", "metric space", and "geodesic".
 * In summary, I'm not convinced that distance (mathematics) needs to exist, but there does need to be some sort of disambiguation/launching point for anyone who is looking for information on the various topics that could be there. IMO this could easily fit within the main broad-topic article (which itself needs a lot of improvement).
 * --platypeanArchcow (talk) 04:22, 14 September 2022 (UTC)
 * Thanks for your input. Your first and second points illustrate well the challenge: "distance function" may suffice for a mathematician, but it doesn't seve well for a layperson. But blanking Distance (mathematics) and redirecting it to Euclidean distance would not do justice to the richness of mathematical concepts related to "distance". Ideally, Distance (mathematics) would be a either summary style article (possibly with automatic excerpts from other articles) or an introduction to metric space (as in ). fgnievinski (talk) 03:03, 15 September 2022 (UTC)
 * @Fgnievinski I find unnecessary -- and, frankly, a bit weird -- to have two articles. I agree with @PlatypeanArchcow that it isn't clear there is a need for Distance (mathematics), and that the content of this article could easily fit in a subsection of Distance.
 * I think that the fact that there isn't a need for two separate articles is well illustrated by the fact that Distance (mathematics) currently starts with "In mathematics, a metric space is a set for which distances between all members of the set are defined." and that Metric space starts with "In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points."
 * I would also like add another point against keeping Distance (mathematics): I think it can hide Metric space for some users (or at least make it a bit less direct to find the right article). One of the main reasons why I use math articles such as Metric space is to quickly check a specific technical point that I have forgotten or -- as a non-native English speaker having studied math outside of the English-speaking world -- to remind myself of the correct way to name some objects in English (e.g, "is there a standard name for that axiom saying that d(x, y) = 0 iff x = y?" or "is that axiom called the 'triangular' inequality, or just the 'triangle' inequality"; etc). I think those are fairly common use cases.
 * With the new article, I land by default on Distance (mathematics), which is not the article I need. Since the name suggests to me that I'm on the right article, I don't even bother looking around for Metric space: I just assume that what I'm looking for is not on Wikipedia, and I leave.
 * So, for all these reasons: personally not a big fan of the split. Malparti (talk) 13:11, 16 September 2022 (UTC)
 * @Malparti, thanks for the comments. With your implied blessing I reorganized the article in a way that hopefully demonstrates that a separate "(mathematics)" sub-article is unnecesssary :)  --platypeanArchcow (talk) 00:59, 18 September 2022 (UTC)

See also Length. fgnievinski (talk) 06:51, 21 September 2022 (UTC)

Definition source
Is there any source for the definition given?131.114.35.40 (talk) 14:11, 26 October 2022 (UTC)

Science
Distance 2001:4456:1C3:4A00:FCE1:8FD8:B7B4:7564 (talk) 10:48, 1 February 2023 (UTC)

Science
What is Distance 122.52.249.56 (talk) 12:44, 8 January 2024 (UTC)

title: Talk:Distance


text:
Pope Lando

Lando (also known as Landus) was the pope from c. September 913 to his death c.  March 914. His short pontificate fell during an obscure period in papal and Roman history, the so-called Saeculum obscurum (904–964).

According to the Liber pontificalis, Lando was born in the Sabina (Papal States), and his father was a wealthy Lombard count named Taino from Fornovo. The Liber also claims that his pontificate lasted only four months and twenty-two days. A different list of popes, appended to a continuation of the Liber pontificalis at the Abbey of Farfa and quoted by Gregory of Catino in his Chronicon Farfense in the twelfth century, gives Lando a pontificate of six months and twenty-six days. This is closer to the duration recorded by Flodoard of Reims, writing in the tenth century, of six months and ten days. The end of his pontificate can be dated to between 5 February 914, when he is mentioned in a document of Ravenna, and late March or early April, when his successor, John X, was elected.

Lando is thought to have been the candidate of Count Theophylact I of Tusculum and Senatrix Theodora, who were the most powerful couple in Rome at the time. The Theophylacti controlled papal finances through their monopoly of the office of vestararius, and also controlled the Roman militia and Senate. During Lando's reign, Arab raiders, operating from their stronghold on the Garigliano river, destroyed the cathedral of San Salvatore in Vescovio in his native diocese. No document of Lando's chancery has survived. The only act of his reign that is recorded is a donation to the diocese of Sabina mentioned in a judicial act of 1431. Lando made the large personal gift in order to restore the cathedral of San Salvatore so that the clergy who were then living at Toffia could return.

Lando was the last pope with a unique name and without regnal number until Pope Francis in 2013.

title: Pope Lando


text:
Engagement

An engagement or betrothal is the period of time between the declaration of acceptance of a marriage proposal and the marriage itself (which is typically but not always commenced with a wedding). During this period, a couple is said to be fiancés (from the French), 'betrothed', 'intended', 'affianced', 'engaged to be married', or simply 'engaged'. Future brides and grooms may be called fiancée (feminine) or fiancé (masculine), 'the betrothed', a 'wife-to-be' or 'husband-to-be', respectively. The duration of the courtship varies vastly, and is largely dependent on cultural norms or upon the agreement of the parties involved.

Long engagements were once common in formal arranged marriages, and it was not uncommon for parents betrothing children to arrange marriages many years before the engaged couple were old enough. This is still done in some countries.

Many traditional Christian denominations have optional rites for Christian betrothal (also known as 'blessing an engaged couple' or 'declaration of intention') that bless and ratify the intent of a couple to marry before God and the Church.

Origin
The origins of European engagement in marriage practice are found in the Jewish law (Torah), first exemplified by Abraham, and outlined in the last Talmudic tractate of the Nashim (Women) order, where marriage consists of two separate acts, called erusin (or kiddushin, meaning sanctification), which is the betrothal ceremony, and nissu'in or chupah, the actual ceremony for the marriage. Erusin changes the couple's interpersonal status, while nissu'in brings about the legal consequences of the change of status. (However, in the Talmud and other sources of Jewish law there is also a process, called shiduchin, corresponding to what today is called engagement. Marrying without such an agreement is considered immoral. To complicate matters, erusin in modern Hebrew means engagement, not betrothal.)

This was later adopted in Ancient Greece as the gamos and engeysis rituals, although unlike in Judaism, the contract made in front of witness was only verbal. The giving of a ring was eventually borrowed from Judaism by Roman marriage law, with the fiancé presenting it after swearing the oath of marriage intent, and presenting of the gifts at the engagement party.

Betrothal

Betrothal (also called 'espousal') is a formal state of engagement to be married.

Typical steps of a match were the following:
 * Negotiation of a match, usually done by the couple's families with bride and groom having varying levels of input, from no input, to veto power, to a fuller voice in the selection of marriage partner.
 * This is not as widely practiced as it was historically, although it is still common in culturally conservative communities in Israel, India, Africa, and Arab states of the Persian Gulf, although most of these have a requirement that the bride be at least allowed veto power.
 * Negotiation of bride price or dowry
 * In most cultures evolved from Europe, bride prices or dowries have been reduced to the engagement ring accompanying the marriage contract, while in other cultures, such as those on the Arabian Peninsula, they are still part of negotiating a marriage contract.
 * Blessing by the parents and clergy
 * Exchange of vows and signing of contracts
 * Often one of these is omitted
 * Celebration

The exact duration of a betrothal varies according to culture and the participants’ needs and wishes. For adults, it may be anywhere from several hours (when the betrothal is incorporated into the wedding day itself) to a period of several years. A year and a day are common in neo-pagan groups today. In the case of child marriage, betrothal might last from infancy until the age of marriage.

The responsibilities and privileges of betrothal vary. In most cultures, the betrothed couple is expected to spend much time together, learning about each other. In some historical cultures (including colonial North America), the betrothal was essentially a trial marriage, with marriage only being required in cases of conception of a child. Almost all cultures are loosening restrictions against physical contact between partners, even in cultures that normally had strong prohibitions against it. The betrothal period was also considered to be a preparatory time, in which the groom built a house, started a business or otherwise proved his readiness to enter adult society.

In medieval Europe, in canon law, a betrothal could be formed by the exchange of vows in the future tense ("I will take you as my wife/husband," instead of "I take you as my wife/husband"), but sexual intercourse consummated the vows, making a binding marriage rather than a betrothal. Although these betrothals could be concluded with only the vows spoken by the couple, they had legal implications: Richard III of England had his older brother's children declared illegitimate on the grounds their father had been betrothed to another woman when he married their mother.

A betrothal is considered to be a 'semi-binding' contract. Normal reasons for invalidation of a betrothal include:
 * Revelation of a prior commitment or marriage
 * Evidence of infidelity
 * Failure to conceive (in 'trial marriage' cultures)
 * Failure of either party to meet the financial and property stipulations of the betrothal contract

Normally, either party can break a betrothal, though in certain traditions, a financial penalty (such as forfeit of the bride price) applies. In some common law countries, including England and Wales and many US states, it was once possible for the spurned partner (often only the woman) to sue the other for breach of promise or "heart-balm". This provided some protection in an age where virginity at marriage was considered important and having a failed engagement could damage one's reputation, but this tort has become obsolete in most jurisdictions as attitudes to premarital sex have softened and emphasis shifted to allowing people to leave loveless relationships.

Judaism
In Jewish weddings during Talmudic times (c.1st century BC – 6th century AD), the two ceremonies of betrothal (erusin) and wedding usually took place up to a year apart; the bride lived with her parents until the actual marriage ceremony (nissuin), which would take place in a room or tent that the groom had set up for her. Since the Middle Ages the two ceremonies have taken place as a combined ceremony performed in public. The betrothal is now generally part of the Jewish wedding ceremony, accomplished when the groom gives the bride the ring or another object of at least nominal value. As mentioned above, betrothal in Judaism is separate from engagement; breaking a betrothal requires a formal divorce, and violation of betrothal is considered adultery.

Christianity
In most localities, the Rite of Betrothal (also known as 'blessing an engaged couple' or 'declaration of intention') as a precursor to Holy Matrimony is an optional practice in traditional forms of Christianity today that blesses and ratifies the intention of two Christians to marry one another. Many Christian denominations provide liturgies for Christian betrothal, which often feature prayer, Bible readings, a blessing of the engagement rings (in cultures in which rings are used), and a blessing of the couple. A betrothal makes what a couple promises to one another sanctified by God and the Church. A Christian engagement (betrothal) ceremony, which may be followed with a party, is normative in certain parts of the world, as with the Christians of India and Pakistan.

Catholic Church
Historically, betrothal in Roman Catholicism is a formal contract considered as binding as marriage, and a divorce is necessary to terminate a betrothal. Betrothed couples are regarded legally as husband and wife – even before their wedding and physical union. The concept of an official engagement period in Western European culture may have begun in 1215 at the Fourth Lateran Council, headed by Pope Innocent III, which decreed that "marriages are to be ... announced publicly in the churches by the priests during a suitable and fixed time so that, if legitimate impediments exist, they may be made known." Such a formal church announcement of the intent to marry is known as banns. In some jurisdictions, reading the banns may be part of one type of legal marriage.

Protestant Churches
The Lutheran book of Liturgical Forms includes the "Form and Manner of Betrothal in Church", which can take place in the church or alternatively, in the house of the bride. This rite can be found throughout history, such as in early Lutheran liturgical texts, the Stasbourg C.O. 1604 being an example. Liturgical Forms states that The Rite of Betrothal is seen as an "admirable practice of plighting one's troth in church, so in keeping with the holiness and importance of marital betrothal as the incipient marital life."

The 2019 Book of Common Prayer, used by Anglican Christian denominations such as the Anglican Church in North America, includes a Christian rite of betrothal called "A Brief Liturgy for the Signing of the Declaration of Intention" in which a Christian couple ratifies their intention before God and the Church to marry. During this liturgy, the following is signed and dated by the engaged couple after the sign of peace: "“We, N.N. and N.N., desiring to receive the blessing of Holy Matrimony in the Church, do solemnly declare that we hold marriage to be a lifelong union of husband and wife as it is set forth in the Book of Common Prayer. We believe it is established by God for the procreation of children, and their nurture in the knowledge and love of the Lord; for mutual joy, and for the help and comfort given one another in prosperity and adversity; to maintain purity, so that husbands and wives, with all the household of God, might serve as holy and undefiled members of the Body of Christ; and for the upbuilding of Christ’s kingdom in family, church, and society, to the praise of his holy Name. We do engage ourselves, so far as in us lies, to make our utmost effort to establish this relationship and to seek God’s help thereto.”" Following the signing of the declaration of intention, the couple is blessed by the priest: "Now that N. and N. have declared their intention for a Holy Marriage, and have begun the process of pre-marital preparation, let us pray for their relationship [and for their families]. Almighty God, we thank you for the love of N. and N., and we ask your blessing upon them [and their families] during this time of preparation. Open their minds and hearts to one another, enable them faithfully to receive your Word and Sacrament, and help us to support them, that they may rightly prepare for their marriage. And, we pray, give us wisdom to uphold and encourage all who have been united in Holy Matrimony; through Jesus Christ our Lord. Amen." The Lutheran Churches, the Anglican Communion, the Methodist Churches and the Presbyterian Churches have questions and responses for family members in its Rite of Betrothal, which is sometimes incorporated into the Service of Holy Matrimony itself.

Orthodox Churches
In the Eastern Orthodox and Oriental Orthodox Churches, the Rite of Betrothal is traditionally performed in the narthex (entranceway) of the church, to indicate the couple's first entrance into the married estate. The priest blesses the couple and gives them lit candles to hold. Then, after a litany, and a prayer at which everyone bows, he places the bride's ring on the ring finger of the groom's right hand, and the groom's ring on the bride's finger. The rings are subsequently exchanged three times, either by the priest or by the best man, after which the priest says a final prayer. Traditionally, the betrothal service takes place at the time the engagement is announced, though in certain localities it may performed immediately before the wedding ceremony itself. The exchange of rings is not a part of the wedding service in the Eastern Churches, but only occurs at the betrothal ceremony. Traditionally, the groom's ring is gold and the bride's ring is silver.

Engagement rings

Customs for engagement rings vary according to time, place, and culture. An engagement ring has historically been uncommon, and when such a gift was given, it was separate from the wedding ring.

The first instance of the tradition of giving a ring for marriage in the Hebrew Bible is in, when a golden nose ring (Chayei Sarah 24:22) was given by Eliezer of Damascus to Rebecca, with Saadiah Gaon also citing as a possible source of the practice in the phrase in be’nei tabbaot (children of the rings). The latter case refers to betrothal (see above) rather than engagement; one of the three ways in which betrothal may be effected in Judaism is by the husband giving the bride money or an object of at least nominal value. In fact, it is a long-standing practice within Judaism to contract the betrothal with a ring.

The practice of Marriage ring in Byzantine Empire date back to 3rd century CE.

Romantic rings from the time of the Roman Empire sometimes bore clasped hands symbolizing contract, from which the later Celtic Claddagh symbol (two hands clasping a heart) may have evolved as a symbol of love and commitment between two people. Romans believed the circle was a bond between the two people who were to be married and signified eternity, but was first practiced on the fourth finger/ring finger by the Romans, who believed this finger to be the beginning of the vena amoris ("vein of love"), the vein that leads to the heart. In cultures with European origin, and many other countries, an engagement ring is worn following the practice of the Romans who "...wore the ring either on the right middle finger or the left ring [4th] finger, from which, according to ancient Egyptian physicians, a nerve led directly to the heart." The custom in Continental Europe and other countries is to wear it on the right hand. One historical exception arose in monarchical regimes, in which a nobleman entering into morganatic marriage, a marriage in which the person, usually the woman, of lower rank stayed at the same rank instead of rising ranks, would present their left hand to receive the ring, hence the alternative term 'marriage with the left hand' (Ger. Ehe zur linken Hand), the offspring of such marriages considered to be disinherited from birth.

The modern Western form of the practice of giving or exchanging engagement rings is traditionally thought to have begun in 1477 when Maximilian I, Holy Roman Emperor, gave Mary of Burgundy a diamond ring as an engagement present.

In other countries like Argentina, men and women each wear a ring similar to wedding bands. They are made of silver ("alianza de plata") when manifesting an informal "boyfriend-girlfriend" relationship, though this first step might not always happen; howbeit depending on finances, this may be the only ring given at all. The gold band ("anillo de compromiso" or "alianza de oro") is given to the bride when the commitment is formal and the [optional] diamond ring ("cintillo") is reserved for the wedding ceremony when the groom gives it to the bride. The gold band that the groom wore during the engagement – or a new one, as some men choose not to wear them during engagement – is then given to the groom by the bride; and the bride receives both the original gold band and the new diamond at the ceremony. The bride's diamond ring is worn on top of the engagement band at the wedding and thereafter, especially at formal occasions or parties; otherwise the engagement band suffices for daily wear for both parties. At the wedding, the rings are swapped from the right to the left hand. In Brazil, they are always made of gold, and there is no tradition for the engagement ring. Both men and women wear the wedding band on their right hand while engaged, and, after they marry, they shift the rings to their left hands.

In the modern era, some women's wedding rings are made into two separate pieces. One part is given to her to wear as an engagement ring when she accepts the marriage proposal and the other during the wedding ceremony. When worn together, the two rings look like one piece of jewelry. The engagement ring is not worn during the wedding ceremony, when the wedding ring is put by the groom on the finger of the bride, and sometimes by the bride onto the groom's finger. After the wedding, the engagement ring is put back on, and is usually worn on the outside of the wedding ring.

Engagement parties

In contemporary American culture some engagements are announced at an engagement party, traditionally hosted by the bride's parents. These parties help introduce both the bride and groom's friends and family to each other in one place prior to the wedding. Often contemporary engagement parties are either cocktail parties or dinners with décor kept to a minimum. Gifts are not often given until either the wedding itself or a bridal shower.

In ancient Greece, engagement parties were held without the bride and took place to discuss the legal and economic aspects of the marriage. Later, engagement parties were when both sides announced a legal union prior to marriage where if one side broke the agreement they would have to pay the wronged side. Engagements became non-legally bending and by the early 20th century some couples would announce their engagement in the local paper.

title: Engagement