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Common Era

Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the original Anno Domini (AD) and Before Christ (BC) notations used for the same calendar era. The two notation systems are numerically equivalent: "2024 CE" and "AD 2024" each describe the current year; "400 BCE" and "400 BC" are the same year.

The expression can be traced back to 1615, when it first appears in a book by Johannes Kepler as the annus aerae nostrae vulgaris, and to 1635 in English as "Vulgar Era". The term "Common Era" can be found in English as early as 1708, and became more widely used in the mid-19th century by Jewish religious scholars. Since the late 20th century, BCE and CE have become popular in academic and scientific publications on the grounds that BCE and CE are religiously neutral terms. They have been promoted as more sensitive to non-Christians by not referring to Jesus, the central figure of Christianity, especially via the religious terms "Christ" and Dominus ("Lord") utilized by the other abbreviations.

Origins
The idea of numbering years beginning from the date he believed to be the date of birth of Jesus, was conceived around the year 525 by the Christian monk Dionysius Exiguus. He did this to replace the then dominant Era of Martyrs system, because he did not wish to continue the memory of a tyrant who persecuted Christians. He numbered years from an initial reference date ("epoch"), an event he referred to as the Incarnation of Jesus. Dionysius labeled the column of the table in which he introduced the new era as "Anni Domini Nostri Jesu Christi" [Year of our Lord Jesus Christ].

This way of numbering years became more widespread in Europe with its use by Bede in England in 731. Bede also introduced the practice of dating years before what he supposed was the year of birth of Jesus, without a year zero. In 1422, Portugal became the last Western European country to switch to the system begun by Dionysius.

Vulgar Era
The term "Common Era" is traced back in English to its appearance as "Vulgar Era" to distinguish dates on the Gregorian calendar which was in popular use from dates of the regnal year (the year of the reign of a sovereign) typically used in national law. (The word 'vulgar' originally meant 'of the ordinary people', with no derogatory associations. )

The first use of the Latin term anno aerae nostrae vulgaris may be that in a 1615 book by Johannes Kepler. Kepler uses it again, as ab Anno vulgaris aerae, in a 1616 table of ephemerides, and again, as ab anno vulgaris aerae, in 1617. A 1635 English edition of that book has the title page in English that may be the earliest-found use of Vulgar Era in English. A 1701 book edited by John Le Clerc includes the phrase "Before Christ according to the Vulgar Æra,6".

The Merriam Webster Dictionary gives 1716 as being the date of first use of the term "vulgar era" (to mean Christian era).

The first published use of "Christian Era" may be the Latin phrase annus aerae christianae on the title page of a 1584 theology book, De Eucharistica controuersia. In 1649, the Latin phrase annus æræ Christianæ appeared in the title of an English almanac. A 1652 ephemeris may be the first instance found so far of the English use of "Christian Era".

The English phrase "Common Era" appears at least as early as 1708, and in a 1715 book on astronomy it is used interchangeably with "Christian Era" and "Vulgar Era". A 1759 history book uses common æra in a generic sense, to refer to "the common era of the Jews". The first use of the phrase "before the common era" may be that in a 1770 work that also uses common era and vulgar era as synonyms, in a translation of a book originally written in German. The 1797 edition of the Encyclopædia Britannica uses the terms vulgar era and common era synonymously. In 1835, in his book Living Oracles, Alexander Campbell, wrote: "The vulgar Era, or Anno Domini; the fourth year of Jesus Christ, the first of which was but eight days", and also refers to the common era as a synonym for vulgar era with "the fact that our Lord was born on the 4th year before the vulgar era, called Anno Domini, thus making (for example) the 42d year from his birth to correspond with the 38th of the common era". The Catholic Encyclopedia (1909) in at least one article reports all three terms (Christian, Vulgar, Common Era) being commonly understood by the early 20th century.

The phrase "common era", in lower case, also appeared in the 19th century in a 'generic' sense, not necessarily to refer to the Christian Era, but to any system of dates in common use throughout a civilization. Thus, "the common era of the Jews", "the common era of the Mahometans", "common era of the world", "the common era of the foundation of Rome". When it did refer to the Christian Era, it was sometimes qualified, e.g., "common era of the Incarnation", "common era of the Nativity", or "common era of the birth of Christ".

An adapted translation of Common Era into Latin as Era Vulgaris was adopted in the 20th century by some followers of Aleister Crowley, and thus the abbreviation "e.v." or "EV" may sometimes be seen as a replacement for AD.

History of the use of the CE/BCE abbreviation
Although Jews have their own Hebrew calendar, they often use the Gregorian calendar without the AD prefix. As early as 1825, the abbreviation VE (for Vulgar Era) was in use among Jews to denote years in the Western calendar. , Common Era notation has also been in use for Hebrew lessons for more than a century. Jews have also used the term Current Era.

Contemporary usage
Some academics in the fields of theology, education, archaeology and history have adopted CE and BCE notation despite some disagreement. Several style guides now prefer or mandate its use. A study conducted in 2014 found that the BCE/CE notation is not growing at the expense of BC and AD notation in the scholarly literature, and that both notations are used in a relatively stable fashion.

United Kingdom
In 2002, an advisory panel for the religious education syllabus for England and Wales recommended introducing BCE/CE dates to schools, and by 2018 some local education authorities were using them.

In 2018, the National Trust said it would continue to use BC/AD as its house style. English Heritage explains its era policy thus: "It might seem strange to use a Christian calendar system when referring to British prehistory, but the BC/AD labels are widely used and understood." Some parts of the BBC use BCE/CE, but some presenters have said they will not. As of October 2019, the BBC News style guide has entries for AD and BC, but not for CE or BCE. The style guide for The Guardian says, under the entry for CE/BCE: "some people prefer CE (common era, current era, or Christian era) and BCE (before common era, etc.) to AD and BC, which, however, remain our style".

United States
In the United States, the use of the BCE/CE notation in textbooks was reported in 2005 to be growing. Some publications have transitioned to using it exclusively. For example, the 2007 World Almanac was the first edition to switch to BCE/CE, ending a period of 138 years in which the traditional BC/AD dating notation was used. BCE/CE is used by the College Board in its history tests, and by the Norton Anthology of English Literature. Others have taken a different approach. The US-based History Channel uses BCE/CE notation in articles on non-Christian religious topics such as Jerusalem and Judaism. The 2006 style guide for the Episcopal Diocese Maryland Church News says that BCE and CE should be used.

In June 2006, in the United States, the Kentucky State School Board reversed its decision to use BCE and CE in the state's new Program of Studies, leaving education of students about these concepts a matter of local discretion.

Australia
In 2011, media reports suggested that the BC/AD notation in Australian school textbooks would be replaced by BCE/CE notation. The change drew opposition from some politicians and church leaders. Weeks after the story broke, the Australian Curriculum, Assessment and Reporting Authority denied the rumours and stated that the BC/AD notation would remain, with CE and BCE as an optional suggested learning activity.

Canada
In 2013, the Canadian Museum of Civilization (now the Canadian Museum of History) in Gatineau (opposite Ottawa), which had previously switched to BCE/CE, decided to change back to BC/AD in material intended for the public while retaining BCE/CE in academic content.

Support
The use of CE in Jewish scholarship was historically motivated by the desire to avoid the implicit "Our Lord" in the abbreviation AD. Although other aspects of dating systems are based in Christian origins, AD is a direct reference to Jesus as Lord.

Proponents of the Common Era notation assert that the use of BCE/CE shows sensitivity to those who use the same year numbering system as the one that originated with and is currently used by Christians, but who are not themselves Christian.

Former United Nations Secretary-General Kofi Annan has argued:

"[T]he Christian calendar no longer belongs exclusively to Christians. People of all faiths have taken to using it simply as a matter of convenience. There is so much interaction between people of different faiths and cultures – different civilizations, if you like – that some shared way of reckoning time is a necessity. And so the Christian Era has become the Common Era."

Adena K. Berkowitz, in her application to argue before the United States Supreme Court, opted to use BCE and CE because "Given the multicultural society that we live in, the traditional Jewish designations – B.C.E. and C.E. – cast a wider net of inclusion".

"Non-Christian scholars, especially, embraced [CE and BCE] because they could now communicate more easily with the Christian community. Jewish, Islamic, Hindu and Buddhist scholars could retain their [own] calendar but refer to events using the Gregorian Calendar as BCE and CE without compromising their own beliefs about the divinity of Jesus of Nazareth".

Opposition
Some critics often note the fact that there is no difference in the epoch of the two systems, a moment about four to seven years after the date of birth of Jesus of Nazareth. BCE and CE are still aligned with BC and AD, which denote the periods before and after Jesus was born.

Some Christians are offended by the removal of the reference to Jesus in the Common Era notation. The Southern Baptist Convention supports retaining the BC/AD abbreviations.

Roman Catholic priest and writer on interfaith issues Raimon Panikkar argued that the BCE/CE usage is the less inclusive option, since they are still using the Christian calendar numbers, forcing it on other nations. In 1993, the English-language expert Kenneth G. Wilson speculated a slippery slope scenario in his style guide that "if we do end by casting aside the AD/BC convention, almost certainly some will argue that we ought to cast aside as well the conventional numbering system [that is, the method of numbering years] itself, given its Christian basis."

Conventions in style guides
The abbreviation BCE, just as with BC, always follows the year number. Unlike AD, which still often precedes the year number, CE always follows the year number (if context requires that it be written at all). Thus, the current year is written as 2024 in both notations (or, if further clarity is needed, as 2024 CE, or as AD 2024), and the year that Socrates died is represented as 399 BCE (the same year that is represented by 399 BC in the BC/AD notation). The abbreviations are sometimes written with small capital letters, or with periods (e.g., " B.C.E. " or "C.E."). The US-based Society of Biblical Literature style guide for academic texts on religion prefers BCE/CE to BC/AD.

Similar conventions in other languages

 * In Germany, Jews in Berlin seem to have already been using words translating to "(before the) common era" in the 18th century, while others like Moses Mendelssohn opposed this usage as it would hinder the integration of Jews into German society. The formulation seems to have persisted among German Jews in the 19th century in forms like vor der gewöhnlichen Zeitrechnung (before the common chronology). In 1938 Nazi Germany the use of this convention was also prescribed by the National Socialist Teachers League. However, it was soon discovered that many German Jews had been using the convention ever since the 18th century, and Time magazine found it ironic to see "Aryans following Jewish example nearly 200 years later".
 * In Spanish, common forms used for "BC" are a. C. and a. de C. (for "antes de Cristo", "before Christ"), with variations in punctuation and sometimes the use of J. C. (Jesucristo) instead of C. The Real Academia Española also acknowledges the use of a. n. e. (antes de nuestra era) and d. n. e. (después de nuestra era). In scholarly writing, a. e. c. is the equivalent of the English "BCE", "antes de la era común" or "Before the Common Era".
 * In Welsh, OC can be expanded to equivalents of both AD (Oed Crist) and CE (Oes Cyffredin); for dates before the Common Era, CC (traditionally, Cyn Crist) is used exclusively, as Cyn yr Oes Cyffredin would abbreviate to a mild obscenity.
 * In Russian since the October Revolution (1917) до н.э. (до нашей эры, lit. before our era) and н.э. (нашей эры, lit. of our era) are used almost universally. Within Christian churches до Р.Х./от Р.Х. (до/от Рождества Христова, i.e. before/after the birth of Christ, equivalent to Ante Christum natum) remains in use.
 * In Polish, "p.n.e." (przed naszą erą, lit. before our era) and "n.e." (naszej ery, lit. of our era) are commonly used in historical and scientific literature. Przed Chrystusem (before Christ) and po Chrystusie (after Christ) see sporadic usage, mostly in religious publications.
 * In China, upon the foundation of the Republic of China, the Government in Nanking adopted the Republic of China calendar with 1912 designated as year 1, but used the Western calendar for international purposes. The translated term was 西元 (xī yuán, "Western Era"), which is still used in Taiwan in formal documents. In 1949, the People's Republic of China adopted 公元 (gōngyuán, "Common Era") for both internal and external affairs in mainland China. This notation was extended to Hong Kong in 1997 and Macau in 1999 (de facto extended in 1966) through Annex III of Hong Kong Basic Law and Macau Basic Law, thus eliminating the ROC calendar in these areas. BC is translated into Chinese as 公元前 (gōngyuánqián, "Before the Common Era").
 * In Czech, the "n. l." (našeho letopočtu which translates as of our year count) and "př. n. l." or "před n. l." (před naším letopočtem meaning before our year count) is used, always after the year number. The direct translation of AD (léta Páně, abbreviated as L. P.) or BC (před Kristem, abbreviated as př. Kr.) is seen as archaic.
 * In Croatian the common form used for BC and AD are pr. Kr. (prije Krista, "before Christ") and p. Kr. (poslije Krista, after Christ). The abbreviations pr. n. e. (prije nove ere, before new era) and n. e. (nove ere, (of the) new era) have also recently been introduced.
 * In Danish, "f.v.t." (før vor tidsregning, before our time reckoning) and "e.v.t." (efter vor tidsregning, after our time reckoning) are used as BCE/CE are in English. Also commonly used are "f.Kr." (før Kristus, before Christ) and "e.Kr." (efter Kristus, after Christ), which are both placed after the year number in contrast with BC/AD in English.
 * In Macedonian, the terms "п.н.е." (пред нашата ера "before our era") and "н.е." (наша ера "our era") are used in every aspect.
 * In Estonian, "e.m.a." (enne meie ajaarvamist, before our time reckoning) and "m.a.j." (meie ajaarvamise järgi, according to our time reckoning) are used as BCE and CE, respectively. Also in use are terms "eKr" (enne Kristust, before Christ) and "pKr" (pärast Kristust, after Christ). In all cases, the abbreviation is written after the year number.
 * In Finnish, "eaa." (ennen ajanlaskun alkua, before time reckoning) and "jaa." (jälkeen ajanlaskun alun, after the start of time reckoning) are used as BCE and CE, respectively. Also (decreasingly) in use are terms "eKr", (ennen Kristusta, before Christ) and "jKr". (jälkeen Kristuksen, after Christ). In all cases, the abbreviation is written after the year number.

title: Common Era


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Talk:Creationist

Not encyclopedic
It's not in the style of an encyclopedia to describe a topic under the heading of its followers. This page should be abolished and/or integrated and/or redirect to Creationism --Creaktop

Please explain, I do not understand why "abolished" and why it is not "encyclopedic style" (I ain't no expert on enyclopedias, mind you) -- Piotr Wozniak

Well, it's very simple. If you want to have an article about a school of thought (here Creationism) it would be stupid to have either two similar definitions and explanations or identical ones under the name of the school of thought and under the followers of this school of thought. In other words you would have two pages for marxism, and marxists; atheism, and atheists; etc. This is dumb because in both you would have a definition and explanation of the school of thought, but it would be duplicate effort with no enhancement of the encyclopedia as a whole. And it would also fragment the encyclopedia somewhat. --Creaktop

Clear. However, you need to take into account the fact that Wikipedia <> Encyclopedia. In my case, I assumed a very simple contribution strategy: write short rough outlines if I see anything missing. Meticulous effort is a bad investment as others ruin the structure of thought. According to this strategy, I create "creationist" as soon as I do not see it in WP. Perhaps others will merge/redirect/correct, etc. I simply do not belive in time-efficient extensive writing for WP (except when I paste my own texts written for other purposes). Last but not least, duplication does not seem a great detraction from value (esp. in the context of Wikipedia's mix of values, styles, quality and opinion). -- Piotr Wozniak

It certainly does not detract from the value of the encyclopedia. Your strategy is entirely correct, but the thing is that there was nothing really missing for Creationist. I assume that people can conclude that a Creationist believes in Creationism. And there already was an article for Creationism (was there?). Some of the info that you put on Creationist is definately missing on Creationism, but wouldnt you agree that it is better if you simply added that info to Creationism, rather than creating a new definition. BTW: i dont understand what you mean with: "Wikipedia <> Encyclopedia" --Creaktop

I agree with Creaktop; this content should be folded into Creationism. Also, as most fundamentalist Christians are evangelical Protestants (and a significant number of them believe the Catholic Church to be evil), the stance of the Vatican would hold no weight for them. -- Stephen Gilbert

 * 1) I agree with merging entries. My point was that my style is "too fast" to check out for other entries (call it lazy, I call it MyWikipedia-efficient). I just hope someone will pick useful pieces and put a redirect (which I do not know how to do, yet)
 * 2) Change to "Vatican position" may be justified. My knowledge is limited here (consider: In Poland-MyHome, Vatican's position stands as final judgement); hence: no contest -- Piotr Wozniak

The Vatican position is certainly relevant from an historical point of view (and I realize how very 'presentist' are many of Wikipedia's entries, but I'm an historian, so there you go). The Roman Catholic Church had a long debate about Darwinism and evolution (please note that I separate the 2). The most recent pronouncement is probably significant, American Baptists aside.
 * I don't deny the relevance of the Vatican position in general, but only in the context in which it was placed:

 * In 1999, despite the official stand of the Vatican, fundamentalist Christians on the Kansas board of education removed evolution from the state science curriculum.

 * The Vatican's stance has nothing to do with the stance of fundamentalist Protestant Christians. -- Stephen Gilbert

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

title: Talk:Creationist


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Charles Robert Malden

Charles Robert Malden (9 August 1797 – 23 May 1855), was a nineteenth-century British naval officer, surveyor and educator. He is the discoverer of Malden Island in the central Pacific, which is named in his honour. He also founded Windlesham House School at Brighton, England.

Biography
Malden was born in Putney, Surrey, son of Jonas Malden, a surgeon. He entered British naval service at the age of 11 on 22 June 1809. He served nine years as a volunteer 1st class, midshipman, and shipmate, including one year in the English Channel and Bay of Biscay (1809), four years at the Cape of Good Hope and in the East Indies (1809–14), two and a half years on the North American and West Indian stations (1814–16), and a year and a half in the Mediterranean (1817–18). He was present at the capture of Mauritius and Java, and at the battles of Baltimore and New Orleans.

He passed the examination in the elements of mathematics and the theory of navigation at the Royal Naval Academy on 2–4 September 1816, and became a 1st Lieutenant on 1 September 1818. In eight years of active service as an officer, he served two and a half years in a surveying ship in the Mediterranean (1818–21), one and a half years in a surveying sloop in the English Channel and off the coast of Ireland (1823–24), and one and a half years as Surveyor of the frigate HMS Blonde (1819) during a voyage (1824–26) to and from the Hawaiian Islands (then known as the "Sandwich islands"). In Hawaii he surveyed harbours which, he noted, were "said not to exist by Captains Cook and Vancouver." On the return voyage he discovered and explored uninhabited Malden Island in the central Pacific on 30 July 1825. After his return he left active service but remained at half pay. He served for several years as hydrographer to King William IV.

He married Frances Cole, daughter of Rev. William Hodgson Cole, rector of West Clandon and Vicar of Wonersh, near Guildford, Surrey, on 8 April 1828. Malden became the father of seven sons and a daughter.

From 1830 to 1836 he took pupils for the Royal Navy at Ryde, Isle of Wight. He purchased the school of Henry Worsley at Newport, Isle of Wight, in December 1836, reopened it as a preparatory school on 20 February 1837, and moved it to Montpelier Road in Brighton in December 1837. He built the Windlesham House School at Brighton in 1844, and conducted the school until his death there in 1855. He was succeeded as headmaster by his son Henry Charles Malden.

title: Charles Robert Malden


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Talk:Color code

Untitled
Since the entry was here, I decided it needed an example. I also changed the color links to standard form (Color/Red, not color/red) and replaced "purple" and "grey" with "violet" and "gray", since those have been the names I've always seen used in electronics references. --loh

can anyone point me to a capacitor which users color codes? all the ones i've seen either out and out state the capacitance, or use the funny little 3 digit system which is even more confusing than resistor color codes. --User:jkominek

Can someone add a page for TIE/EIA-598—Optical Fiber Cable Color Coding - one reference at http://www.cisco.com/univercd/cc/td/doc/product/cable/cab_rout/cr72hig/ub72wire.htm

Color Coded Bumpers
Are advertised in used car advertisements

Johnny English
Requests color coded ropes from his assistent.

Expand
A lot more could be written on the subject. origins, methods, variations, limitations, etc. ability of humans to perceive shades of gray vs different colors, etc. — Omegatron 01:35, 25 July 2007 (UTC)

Removed section about friendly-fire system
These sections were plopped down in the article in incorrect spots, and seemed to be nothing but a promotion for a certain person's patent. If the invention in question is notable, then it needs its own article, and a link from this article, not just two big, largely unformatted paragraphs here. Adam850 (talk) 10:50, 15 December 2013 (UTC)

Requested move 16 August 2021

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: not moved

Neither the proposer nor the sole supporting editor gives any policy reason for the proposed move. The two opposing editors give cogent reasons against the primary proposal.

No such user supports the secondary but not the primary move. I find no consensus on that point. In any case, I consider it would be irregular to make the secondary move where the consensus is to reject the primary move. A freestanding move of Color-coding should be proposed on that page.

David Eppstein makes a counter-proposal to change the redirect at Color coding (without the hyphen). Whatever the merits of that suggestion, it is out of scope of this RM. (non-admin closure) Havelock Jones (talk) 10:09, 14 September 2021 (UTC)

– A color code is merely the consequence of using color-coding as a method. I think the method is more prominent. I propose to move this article to "Color-coding" (or "color coding" if that is the more proper title) and merge Color coding technology for visualization into it. BD2412 T 23:31, 16 August 2021 (UTC)
 * Color code → Color-coding
 * Color-coding → Color-coding (graph theory)

 * New to wikipedia, but this is a good suggestion. It should be accepted. My background is in Computer Science with graduate studies in Color Science and the moves are logical and make the topics more clear. TDcolor (talk) 02:53, 17 August 2021 (UTC)
 * Oppose. The normal name for an article should be its base noun (the code), not a derivative from it (the technique of using colors as codes to convey information). So the current name, "color code", is a better choice. Additionally, this article is primarily about the codes themselves, not about the general technique of choosing codes to convey information (which has a separate article, Color coding technology for visualization). That frees up "color coding" to continue to keep its current meaning, the algorithmic technique which is not really about colors and does not have as clear a choice of base noun. Additionally, the current name is less ambiguous. "Color coding" has at least six meanings in its top Google Scholar hits: (1) the algorithmic technique (far and away the most heavily cited), (2) the use of colors to convey information in visualizations, (3) the ways that biological vision systems encode color in neural transmissions, (4) the encoding of color information in artificial systems, (5) the use of colored markers on surgical instruments to distinguish them from tissue in medical imaging, and (6) the use of stereotyped colors to demark gender norms. It is far from clear to me that the present article should be the WP:PRIMARYTOPIC, so proposing to usurp that title from a different article is premature. —David Eppstein (talk) 04:00, 17 August 2021 (UTC)
 * The use of colors to encode surgical instruments or signal gender are merely special cases of the broader topic of color coding (i.e. uses of colors to convey distinguishing information). The fact that the algorithmic technique "is not really about colors" seems at least curious for it to have that title. Perhaps color-coding is ambiguous? BD2412  T 05:08, 17 August 2021 (UTC)
 * They are not the same thing. This article is about standardized assignments of colors to enumerated meanings, to convey those meanings to humans quickly and intelligably, in a broad class of contexts. Color coding technology for visualization is about how to choose new assignments of colors, in a more specific context of information visualization. The use of colors on surgical instruments is more like green screening or camouflage; it's a technical trick to make the instrument stand out in automated analysis of the images. The use of colors to enforce gender norms in society could to some extent be conveying information to others (this child is a boy) but is to a large extent a marketing strategy (girls raised under these norms like pink so let's make this object pink so that girls will like it) rather than about information, and is not standardized in the way that the colors listed here are. The fact that you find it curious that the algorithmic technique is not really about colors suggests to me that you have not even investigated what it is about or how heavily this term is used in that part of the academic literature before making this proposal, something I find curious. But to answer your curiosity: in graph theory, more generally, the idea of a "color" is just used as a convenient and intuitive way of thinking about labeling objects with distinct values. Those values usually aren't RGB values or frequencies or spectra or whatever you think of actual colors as being. Color-coding is an instance of that idea, applied in a particular way to make certain algorithms run fast. As a computer science term, it is not at all ambiguous. What is ambiguous is that other people also use the same phrase "color coding" to mean many other different things. As for ambiguity, a disambiguation page already exists: Color code (disambiguation). Anyway, maybe a more salient question is: why does the CS color-coding article use a hyphen, and why is this move proposing to take over the hyphenated name? The unhyphenated color coding would make more sense in the context of this article (and currently redirects here), but I still think color code is a better choice of title. —David Eppstein (talk) 06:20, 17 August 2021 (UTC)
 * Counter-proposal: keep the list of standardized color meanings in this article and the information visualization methods in its own separate article, as too different from each other to merge. Semaphores, traffic lights, and resistors are not really about information visualization, and for those sorts of topics the existence of a standardized code is more central than the coding process used to come up with it. Leave color-coding alone, as the infoviz meaning does not need a hyphen and the other hyphenated meanings listed at the dab page are not primary. But, change the redirect for color coding to point to Color code (disambiguation) rather than here, so that the Filipinos can more directly find their traffic reduction system and the information visualizers can more directly find the infoviz without being distracted by semaphores, traffic lights, and resistors. —David Eppstein (talk) 06:58, 17 August 2021 (UTC)

 * Support second, neutral on first. I do not see any evidence that the term "color-coding", with a hyphen, dominantly refers to this very specialist topic. Color coding, Color-coding and Color code (as well as their "colour" variants) are near-synonymous terms that all refer to the same WP:BROADCONCEPT topic (this one) and should redirect to the same place. No such user (talk) 13:38, 19 August 2021 (UTC)
 * In the second, "graph theory" is not even the right disambiguator. It's not a topic in graph theory. It's a method in algorithms (or more precisely parameterized complexity) that happens to be used for graphs (and hypergraphs, and related structures). That's a different area than graph theory. And try doing a Google Scholar search for these phrases and look at the citation counts to get a very different idea of which topics are specialist. —David Eppstein (talk) 15:35, 19 August 2021 (UTC)
 * If we went by Google Scholar for topics of general cultural applicability, the primary topic of Monty Hall would be Monty Hall problem. BD2412  T 20:16, 19 August 2021 (UTC)
 * The use of color codes for real-world meanings like traffic lights (the current meaning of this article) may be of general cultural applicability, but your proposed takeover of that topic by an article about infovis research is not. It is not any less specialized than the algorithmic meaning. —David Eppstein (talk) 00:57, 20 August 2021 (UTC)
 * I wouldn't consider it a takeover of "Color code" at all. The bulk of the content in the data visualization article is about very common problems of color coding generally - picking the right colors so the coding efficiently serves its purpose. That would be the content below the fold. There is always room to expand the cultural context, if for example material could be introduced on the history of color coding, the earliest instances of human use of the method, etc. BD2412  T 01:52, 20 August 2021 (UTC)
 * "picking the right colors so the coding efficiently serves its purpose" is exactly the technical infovis topic. The article you are trying to take over is on a very different topic, the standardized sets of color-encoded information (NOT information visualization, just information, and NOT the process of picking those colors) that everyone knows about already. You are trying to have it both ways, by arguing that the common knowledge of these codes justifies the use of taking over their name for an article about a different and technical topic that is far from the primary meaning of the phrase. Look, I've published at least one technical paper on methods for choosing distinctive colors for visualizations . I think it's an interesting topic. But it's a different topic from the topic of this article, a niche topic, and one that should not take over as the primary topic for this phrase. —David Eppstein (talk) 02:03, 20 August 2021 (UTC)
 * Do you think that the use of colors to code information is a different topic from the methods for picking those colors? I think it is the common practice to cover both aspects in a single article. Textile, for example, discusses both what textiles are and are used for, and how they are made. BD2412  T 02:13, 20 August 2021 (UTC)
 * I don't think that the methods used to pick colors for information visualizations are in any way related to the methods used to standardize colors for color code standards for safety and engineering information. I think that it would be misleading and wrong to talk about color code standards for safety and engineering information (the widely-used and widely-known application of color codes) as if they are a subtopic of information visualization (a niche topic). —David Eppstein (talk) 02:18, 20 August 2021 (UTC)
 * Perhaps a broader restructuring is needed then—one in which we talk about color coding in information visualization as one of several subtopics of color code standards for areas including (as the most significant major component) safety and engineering information. BD2412  T 03:38, 20 August 2021 (UTC)
 * Note: WikiProject Computer science has been notified of this discussion. — Shibboleth ink  (♔ ♕) 22:55, 29 August 2021 (UTC)
 * Note: WikiProject Graphic design has been notified of this discussion. — Shibboleth ink  (♔ ♕) 22:56, 29 August 2021 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose - Noun preferred for an article that enumerates color codes. The article could be about something else but it's currently not so renaming it is putting the cart before the horse. ~Kvng (talk) 14:56, 3 September 2021 (UTC)

title: Talk:Color code


text:
Talk:Countable set

Archives:
 * Talk:Countable set/Archive 1

Countable rationals
There are lesser-known sequences for counting the rationals other than Cantor's mapping. For example, the following sequence assigns each natural to a unique positive rational:
 * S(0) = 0 S(1) = 1 S(2n) = S(n) + 1 for all n > 0 S(2n+1) = 1/S(2n) for all n > 0

This sequence is based on Farey sequences and Stern-Brocot trees. It can be extended to cover the negative rationals as well. — Loadmaster (talk) 17:40, 3 February 2008 (UTC)

Cantor: A Mathematical Charlatan
Consider the set of natural numbers listed in the usual order. That is, starting with 1,2,3... and written from left to right. By Cantorian definition, this set is both "countable" and infinite. Therefore we should be able to place the elements of this set in 1 to 1 correspondence with the set of natural numbers listed in any other order. Let us choose to use 'reverse order' for this second set. Now suppose we place the first set above the second and try to match elements. Then we should find one and only one entry under the number "1" in the first set. What is this number? Clearly, there is no such number! The concept of "countably infinite sets" is inherently flawed. This concept is the basis of the pseudo-mathematics of Cantor and his followers.

What can be counted can not possibly be infinite, and what is infinite can not be counted. Carl Friedrich Gauss pointed this out when he wrote "I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics". The flaw in the 'diagonal argument' has precisely this defect. —Preceding unsigned comment added by 66.67.96.142 (talk) 22:16, 23 May 2008 (UTC)
 * Sets do not distinguish order. The set of the natural numbers in any other order is the exact same thing as the set of the natural numbers in their usual order. Therefore the bijection is trivial. 195.197.240.134 (talk) 11:08, 28 May 2008 (UTC)
 * It doesn't matter whether there is any way of arranging the elements so that they do not form a correspondence. All that matters is that there exists even one way or more to arrange them so that there is a one-to-one correspondence between the sets. And for the infinite sets there are infinitely many different ways of arranging the elements so that they correspond.

 * "What is infinite cannot be counted" -- not so either. Countably infinite is defined as having a bijection to the set of natural numbers. —Preceding unsigned comment added by 41.241.23.249 (talk) 15:19, 2 September 2008 (UTC)

 * This sounds like Weyl's position which I was just reading about. I personally am very curious whether Weyl changed his mind and why he said he changed it.  Either here or in his bio would be a good place 4.249.3.202 (talk) 20:15, 2 July 2009 (UTC)

 * What sounds like Weyl's opinion, exactly? — Carl (CBM · talk) 20:33, 2 July 2009 (UTC)

Why drag topology into this article?
The new section Countable set seem to be out of place in this article. It is about topology, not really about countable sets. Also, from my limited knowledge of topology, the proof appears to be incorrect. Specifically, in the indiscrete topology one-point sets are not open. JRSpriggs (talk) 17:16, 13 June 2008 (UTC)

 * Not disagreeing, but the indiscrete topology doesn't satisfy the hypotheses because it is non-Hausdorff. (It is in fact mentioned as a counterexample in the indicated section.)  siℓℓy rabbit  (  talk  ) 17:21, 13 June 2008 (UTC)

It can make sense to include a short proof that any topological space satisfying certain simple conditions must be uncountable and perhaps that the reals do satisfy those conditions. That the reals are uncountable can be proved more simply from the fact that they are linearly ordered such that between any two points there is another and they satisfy the least-upper-bound property (you certainly DON'T need to talk about decimals, even though that's one way to do it). Michael Hardy (talk) 17:29, 13 June 2008 (UTC)

Some details missing about bijection from Q to N
How does the proof of the assertion 'Q (the set of all rational numbers) is countable' contradict the intuition that 'the cardinality of Q is larger than that of N'? Either some details are left out or it doesn't.

(0,1,0), (1,1,0), (1,1,1) and so on are not members of N. They are rather triples composed of members of N.  Is there assumed another bijection from these tuples to N?  If this bijection exists and is assumed, it may be useful to explicitly state it. Johanatan (talk) 23:55, 20 October 2008 (UTC)
 * Since the article begins by defining a countable set to be one with an injection from it to N, why are people bending over backwards to created bijections when it is much simpler to create injections? For example the nonnegative rationals m/n are obviously a subset of N2, namely those pairs (m,n) for which n is nonzero and m and n are relatively prime (gcd is 1).  And there are lots of very simple injections of N2 into N, for example f(m,n) = 2m3n, that don't require a diagram to explain.  --Vaughan Pratt (talk) 15:55, 17 August 2009 (UTC)

Wikipedia is not a math textbook
I am concerned about some recent edits that make use of the "proposition - proof" style of math textbooks. I feel these style elements reduce the accessibility of the article to the layman as they destroy the flow of the text and make heavy use of (standard) math notation. (They also are partially redundant to the section More formal introduction.) I would suggest to at least move the text after the section Gentle introduction and, preferably, to reword it into more accessible prose. —Tobias Bergemann (talk) 11:29, 11 February 2009 (UTC)

I am responsible for the recent additions, but not for the definition (which is in my opinion the correct one). Also the terms injective, surjective, bijective have been around for some time, as has the $$f: A \to B$$ notation for a function. I have only edited the section called Definition and Basic Properties. The label THEOREM is used many places in the article. I believe the intent (and certainly my intent) was to indicate a precise mathematically correct statement. Mathematics is proofs. It may be valuable in a wikipedia article to give heuristic arguments or give examples. But when a proof is given it I think it is useful for the reader to know "This is a proof, not an example and not a heuristic argument." That is the function of the labels Proof. The proofs given are all extremely short, though, in principle I see no reason not to include longer proofs. Increasingly Wikipedia is becoming a useful place for students to learn serious mathematics, as opposed to popularized versions (which are also very valuable). Indeed many mathematics articles discuss topics at a level not usually encountered until graduate school. This is a 'good thing.'

Achieving a balance between something for the layman (to use your phrase) and something useful for, say, a university level student, is very difficult and has not been achieved in this article. For example the section on the minimal model for set theory is inaccessible even to most professional mathematicians.

While Wikipedia is not a textbook I think it is very useful to have textbook like sections on particular topics like this one. I believe it enhances other entries. If you look, for example, at measure theory which is more highly rated than this article you might imagine that someone reading that would want to refer to an article on countable which had a quick summary of basic properties. I am open to moving the section later if others think that is appropriate. Johnfranks (talk) 16:00, 11 February 2009 (UTC)

I moved the main content of the section "Definition and basic properties" later in the article. I combined the short section "Other results about uncountable sets" with it. I added references at the beginning. Johnfranks (talk) 20:01, 11 February 2009 (UTC)

 * Thanks, I think these changes really helped to improve the flow of the article. I guess I basically agree with everything you write above, though I would argue that PlanetMath or MathWorld are better places for students to learn serious mathematics.
 * I don't object to the content so much as to the presentation. My gripe with what I was calling above the "proposition - proof" style is that if used badly the presentation of the subject decays into a sequence of theorems/propositions/corollaries/lemmata without motivation of the proposed statements.
 * If you haven't already done so, may I suggest you have a look at Manual of Style (mathematics)? —Tobias Bergemann (talk) 08:40, 12 February 2009 (UTC)
 * I'm glad to hear you like the new changes. I absolutely agree with your (Tobias's) remarks, but when I looked over the article to fix it, I found myself spending more time doing WP:MOS and WP:MSM fixes in the other sections.  Especially with the new content in its current place, the article flows very nicely.  I do wish there was more prose and less uninterrupted prop-proof chains, but I don't see how to achieve that without degrading the article.  I do worry that future editors may continue the prop-proof chains until the article is the type of mess Tobias and I imagine/have seen, but for now it seems quite good. JackSchmidt (talk) 14:37, 12 February 2009 (UTC)

Is zero a natural number?
Is there a consensus that zero is a natural number? If so I am happy to go along. I have never seen this usage. Can someone give a reference? The recent edit declaring 0 a natural number broke one statement which assumed one could divide by a natural number. I think I have fixed it. I believe there is another place in this article (in a section I have not edited) that asserts that 0 is not in the natural numbers. Johnfranks (talk) 22:35, 11 February 2009 (UTC)

 * This is a standard convention that differs in various fields of mathematics. See natural number.  Presumably this article is set theoretic, so set theory conventions apply.  See ordinal number and von Neumann ordinals for the reason for the convention. JackSchmidt (talk) 22:51, 11 February 2009 (UTC)

 * OK. I edited the other section which declared natural numbers to start with 1.Johnfranks (talk) 23:50, 11 February 2009 (UTC)

 * Excellent, thanks for keeping/making-for-the-first-time the article consistent. I usually see 0 as not in the set of natural numbers myself, but while looking for an algebra reference I noticed that Jacobson's Basic Algebra I, section 0.4 (The natural numbers), p15, ISBN 0716704536, defines 0 as a natural number without comment.  It looks just like standard Peano arithmetic (successor function), but instead of "1 is not a successor" it has "0 is not a successor".  Actually on wikipedia, apparently 0 is the first guy in Peano arithmetic too.  At any rate, you asked for a reliable source type of reference as much as whether there was consensus, so I figured it would be nice to provide both. JackSchmidt (talk) 05:03, 12 February 2009 (UTC)

 * Interesting. I have Jacobson's Lectures in Abstract Algebra I: Basic Concepts which asserts in section 0.4 that the natural numbers are 1,2,...  He also says in that section that "As usual, we denote the unique non-successor as 1."  Of course he also writes all his functions on the right indicating a strong willingness to buck convention.Johnfranks (talk) 14:56, 12 February 2009 (UTC)

 * Since it is clear that the smallest cardinal number is zero and the smallest ordinal number is zero, there is a definite advantage in defining the natural numbers to include zero. That way, the natural numbers are just the finite cardinals and also the finite ordinals. JRSpriggs (talk) 05:54, 13 February 2009 (UTC)

 * There are many issues (including this one) that I would argue should not be done as they currently are if we were starting over in creating mathematical language. Your argument addresses the way things should be done, not the way they are, i.e. not what current conventional usage is.  This topic is discussed fairly extensively in two parts of Talk:Natural_number.  While I believe the overwhelmingly dominant usage in mathematics written in English is to start the natural numbers with 1, I was surprised to learn this is apparently not true in French.  There is even the suggestion that positif can mean non-negative.  I certainly defer to others for usage in set theory and computer science.
 * Johnfranks (talk) 21:46, 14 February 2009 (UTC)
 * There is a discussion of some of these problems and more in the introduction to Cohen, Henri. "Number theory. Vol. I. Tools and Diophantine equations." Graduate Texts in Mathematics, 239. Springer, New York, 2007. ISBN 978-0-387-49922-2.  As a French number theorist, the problem that "N is the set of positive integers" defines unequivocally two different sets depending on whether the person he is talking to was trained in the French schools, has bugged him to the point of spending a few pages on it. JackSchmidt (talk) 23:46, 14 February 2009 (UTC)
 * Can you give me a section or page number, please? Or do you mean the short paragraph under "Warning"? Hans Adler 17:23, 17 August 2009 (UTC)

Combinatorics
I am removing this from the lede: "But countability has little to do with combinatorics (the mathematical study of counting). Rather, it is a property of certain sets in the mathematical area of set theory."

Of course infinite countable sets have little to do with finite combinatorics, but that is because they are infinite, not because of countability. On the other hand countability is an important concern in infinitary combinatorics, and so it seems wrong to me to say that countability has little to do with combinatorics overall. For example, Martin's axiom uses countability in an central way. — Carl (CBM · talk) 11:04, 28 October 2009 (UTC)

Under 'More Formal Introduction'
This sections discusses how the set N and 2N have the same cardinality. Not bad so far. However, in the paragraph just below the line "1 ↔ 2, 2 ↔ 4, 3 ↔ 6, 4 ↔ 8, ...." it suggests that "(t)his gives an example of a set which is of the same size as one of its proper subsets". Not quite. If 2N were strictly a subset of N, it would be skipping every other number/element in the set, so would DEFINITELY NOT be the exact same size -- it would be exactly half the size! Infinity math or not, if it doesn't include all of the same elements it cannot be both a subset and equal in size. It's only when considering 2N as a strictly independent set that it would have the same cardinality. KhyranLeander (talk) 21:24, 19 August 2010 (UTC)
 * The cardinality of a set doesn't change, whether you are considering it as the subset of some other set, or not. So the set N = {1, 2, 3, ...} and the set 2N = {2, 4, 6, ...} have the same cardinality, by definition, since the function f(x) = 2x, is a one-to-one correspondence between the two sets. And this is so despite the fact that one set is a prober subset of the other. That's one of the properties of the cardinality of infinite sets that set them apart from finite sets, where the cardinality of a proper subset is always strictly smaller. Since the "size" of N is infinite, in order for your statement that 2N is "exactly half the size" of N, to have any meaning, the notion of "half of infinity" needs to be defined. It turns out this can be done, in a reasonable way, and under the usual definitions, half of infinity equals infinity. In which case both the statements "2N and N have the same size", and  "2N is half the size of N" are true. Paul August ☎ 22:32, 19 August 2010 (UTC)

An analogy in the introduction?
How about adding a short analogy to the introduction. Such as a countable set being a set of temperature readings, that may go on for ever but every individual reading is clearly spaced. Where as an uncountable set you can mine more and more numbers simply by increasing the resolution, like the level of detail if you're zooming in on fractal, or dividing 1 by x with x>1. You will allways end up with a number, regardless of what you put in unless the number is infenite in size, so there is really no end to how small 1/x can get. (Axioms that suppose a largest uncountable non infenite number aside) —Preceding unsigned comment added by 194.132.104.253 (talk) 09:33, 29 October 2010 (UTC)

 * We usually try to avoid analogies in mathematics since they can easily be misunderstood. If you have a precise example, that could be added at the appropriate place in the article, i.e. further down rather than in the lead. JRSpriggs (talk) 10:59, 29 October 2010 (UTC)

Question
In many textbooks, it is said that a set is countable if we can list the elements as $$a_1, a_2, \dots$$. My question is: is it true that a set is countable if and only if there exists a Turing machine to enumerate (without termination) all the elements in the set? — Preceding unsigned comment added by Tmbu (talk • contribs) 01:56, 9 March 2011 (UTC)

 * No, you're confused. The elements of a countable set may themselves be extremely large infinite sets. There's no way that a Turing machine can enumerate such things. — Carl (CBM · talk) 02:02, 9 March 2011 (UTC)

 * A set which can be enumerated by a Turing machine is a recursively enumerable set. All such set are countable. However, there are many countable sets which are not recursively enumerable, even among subset of the natural numbers. For example, the set of Gödel numbers of true sentences of arithmetic is countable, but not recursively enumerable.
 * You should not take those textbooks too literally. They are just trying to give you an intuitive feel for what a countable set is. The listing of the elements need not be something that real humans or real machines can do. It is sufficient that there be (in principle) a formula of set theory with parameters (arbitrary sets, possibly undefinable) which associates a distinct natural number with each element of the set in question. JRSpriggs (talk) 05:01, 9 March 2011 (UTC)

Definition wrong?
Under definition it states : "If f is also surjective and therefore bijective, then S is called countably infinite." A function being surjective does NOT imply it is bijective, however the reverse is true. For instance if a function is bijective it is also therefore surjective. But a surjective function is not always bijective, in the case when more than one element of the first set maps to the same element of the second set. — Preceding unsigned comment added by 24.63.136.210 (talk) 14:22, 2 February 2012 (UTC)

 * The function f is defined to be injective. So it is surjective if and only if it is bijective. --Zundark (talk) 14:52, 2 February 2012 (UTC)

 * Thanks for the clarification. I am going to go ahead and specify the reason why it is bijective in paranthesis next to it to avoid confusion. 24.63.136.210 (talk) 02:13, 3 February 2012 (UTC)

Nevertheless, the given definition is wrong (If THIS f is also surjective...). You don't suppose the function f which showed you that S is countable to be surjective in case S is countably infinite. Example: f(n):=n+1 as function from N to N is injective. So this shows us N is countable. But f is not surjective. So N is not countably infinite? To correct the definition you have to find a new function which is bijective (in case f is only injective but not surjective). --Jobu0101 (talk) 20:37, 9 December 2014 (UTC)

1) What's with the Jainist thing in history? It would be cool if that were accurate, but I'm doubtful given some of the dates and the complete lack on non-Jainist material. 2) What's with all the "citation needed"'s on the Jainist material. It is plenty well cited, much more thoroughly cited than the rest of the article to say the least. If you wish to *dispute* the citations, which seems reasonable, do that clearly, don't just paste 'citation needed' on all of the clearly cited material. Also, text citations that aren't available online are valid citations, if that's what's drawing your ire. 73.170.107.159 (talk) 06:45, 15 April 2015 (UTC)

 * I guess most the the 'citation needed' originate from me. I gave a detailled reason for each of it. If it doesn't appear when you move the mouse pointer over it, you can see it in the source code. - Jochen Burghardt (talk) 07:50, 15 April 2015 (UTC)

Definition of mapping is not precise
Q can be defined as the set of all fractions a/b where a and b are integers and b > 0. This can be mapped onto the subset of ordered triples of natural numbers (a, b, c) such that a ≥ 0, b > 0, a and b are coprime, and c ∈ {0, 1} such that c = 0 if a/b ≥ 0 and c = 1 otherwise.

If a ≥ 0 and b > 0 then by definition a/b ≥ 0. — Preceding unsigned comment added by 24.84.237.14 (talk) 03:48, 9 September 2015 (UTC)
 * Perhaps more varied examples would be needed. For instance, the rational number -4/2 would be mapped to the triple (2, 1, 1) as would all rational numbers that are equivalent to -2. The fraction formed by the first two coordinates will always be positive as you say, but the sign of the number is determined by the third coordinate. I hope this helps. Bill Cherowitzo (talk) 04:31, 9 September 2015 (UTC)
 * I understand the intention from the examples, but the text cited by 24.84.237.14 says something different, and does not make sense.
 * Moreover, it is not too clear why such a mapping will lead to a proof of countability of Q. Apparently the two preceeding theorems, and the sole corollary given later in the article are tacitly used, aren't they? In this case I'd suggest that their use should be made explicit, and the injectivity of the mapping (needed for the corollary) should be stated, if not established. - Jochen Burghardt (talk) 08:24, 9 September 2015 (UTC)
 * I thought that the question was about the mechanics of this map ... maybe I was wrong in that. The existence of this map does not, as far as I can tell, lead to a proof of the countability of Q. All that is done is to map Q onto a countable set (this countablity is established by the earlier two theorems) and you can map any infinite set onto a countable one. The standard proof here is to establish that (an isomorphic copy of) Q is a subset of N × N which has been previously established to be countable (say, by using the two previous theorems). You could use the inverse of this map in that setting, but you would have to use a proper definition of Q as a set of equivalence classes to do so. It does not appear to me that this would be in keeping with the level of the current article. The set-up for the standard proof has already been made in establishing the countability of N × N, so I think a simple rewrite of this section would set things right. Bill Cherowitzo (talk) 17:50, 9 September 2015 (UTC)

 * On second thought, this can be fixed by simply removing the requirement that a and b be coprime. This map is then a bijection between the sets (fractions and these triples). We just have to point out that the fractions are not reduced and equivalent fractions are not treated as equal.Bill Cherowitzo (talk) 22:36, 9 September 2015 (UTC)

 * When I realized the mistake I made above (and have struck out) I also gained some insight into what is happening on this page. The correction is that Q is shown to be a subset of Z × Z, not N × N. The argument (standard in most elementary treatments) depends on first showing that Z is countable, which in turn usually uses the result that the union of two countable sets is countable. In the treatment we are looking at, this last result is being avoided and therefore there is no mention of Z in the early going. This then causes this convoluted representation of Q as integer triples of natural numbers (rather than integers, since these have not yet been shown to be countable). The fix I proposed above is still valid, but I am finding the article to be a strange mix of a rather sophisticated approach (which I am sure makes the logicians happy) with a very naive treatment of Q (making some mathematicians unhappy). The statements in the article that we are concerned with are exactly where these two approaches conflict and I am not surprised that this was incorrectly presented. Bill Cherowitzo (talk) 18:23, 10 September 2015 (UTC)

 * An additional issue for cleanup is that right after the Corollary, the section starts all over again ("Proposition: Any subset of a countable set is countable. ..."). So several theorems are given twice; both versions of each should be merged into one. The second proof of countability of Q is based on that of Z × N, along the lines you sketched above, and is easier than the first one. - Jochen Burghardt (talk) 11:24, 11 September 2015 (UTC)
 * And the definition is given two times: in section Countable set and in Countable set. The latter section, as well as Countable set, is written in epic style, which is better suited for wikiversity than for wikipedia. However, much of its contents is useful here as it explains the background of the "countability" notion (notion of "size" for infinite sets; "proper subset" not implying "smaller size"; nevertheless existence of infinite sets of different sizes, "countably infinite" being their smallest one). - Jochen Burghardt (talk) 14:56, 11 September 2015 (UTC)
 * Looking at the page history I see what happened. Back in 2010 two sections were merged into one without much thought being given to the merger. The formal definition overview section was a gentle introduction that used no formulae to describe functions (hence the rather long lists of function assignments). The next section was called Basic properties and covered the same ground only this time using explicitly described functions. Some of the natural duplication in these sections (the Basic Theorem for instance) was removed. Besides this difference there was also a difference in approach; the first section putting off the theorem on the union of countable sets, while the other does it earlier and gets the countability of Z to work with. If we go through this and properly merge this material, one or the other of these approaches will be sacrificed, and I find value in each. I think I favor separating the sections again and explaining the difference in the approaches. Bill Cherowitzo (talk) 20:20, 11 September 2015 (UTC)

Problem with lede
The lede makes the misleading statement:"Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every element of the set is associated with a natural number." This statement has gone too far attempting to use simple concepts to explain what a countable set is. First, both element and set should be linked to the appropriate article, but that is a minor point. There are two major problems, imho, with the statement: #1. Time should NOT be brought in to the discussion ("one at a time", "may never finish"). This is so blatantly blindingly obvious that it should not need to be said. #2. "associated with a natural number" is wrong. So, if I have a set of, say 10^10^100 elements and associate EACH and EVERY one of them with the natural number 1, then the set is countable???? WRONG! Each element of the set must be able to be set into a one-to-one correspondence with a UNIQUE natural number. There are usually many ways to set up such a correspondence. That is, which natural number is assigned to label a particular element will depend on how the "numbering" or "counting" is chosen. (Take the set consisting of the three elements {A,B,C}. They may be put into correspondence with 1,2,3 or 2,1,3 or 6,4,2, or even 2,3,5 or 100,10,1000.) A countable set is one in which each element can be assigned a unique natural number. It turns out that some infinite sets have this property, countable sets may be finite or infinite. (some, actually most, infinite sets are not countable.)72.172.10.197 (talk) 13:48, 10 October 2015 (UTC)

Booleans
Wikipedia at the moment doesn't include Booleans as a countable set or indeed as a number system. Should Booleans be added, as a subset of the natural numbers with their own arithmetic just like any of the other sets listed in Template:Number_systems? 80.42.172.137 (talk) 11:43, 29 November 2016 (UTC)

 * What do you mean by "Booleans"? JRSpriggs (talk) 18:09, 30 November 2016 (UTC)

Set of polynomials countable ?
The section Countable_set outlines a proof of the proposition 'The algebraic numbers A are countable'. The outline of the proof relies on the set of n-degree polynomials to be countable, since their coefficient space can be one-to-one mapped to the set of rational numbers. As far as I can see, this only holds if each polynomial coefficient is integer (or rational, but that makes no difference). So it should either be stated that the polynomial coefficients are integer (or explained how the proof holds for non-integer (actually irrational) coefficients, in which case I missed something). Thanks. Lklundin (talk) 08:29, 12 September 2018 (UTC)

 * Thanks for the remark. The coefficients must be rational; by multiplying with the least common denominator, they can always be made integer. Admitting arbitrary real numbers as coefficients would make e.g. $$\pi$$ algebraic; admitting algebraic numbers as coefficients would use them in their own definition; both wouldn't make sense. - Jochen Burghardt (talk) 10:49, 12 September 2018 (UTC)
 * Thanks (also because I no longer doubt that I understand the underlying math). Although the text now mentions 'integer coefficients' twice which is possibly one more than necessary, it is very clear now. Thanks again. Lklundin (talk) 15:00, 12 September 2018 (UTC)

Encyclopedic tone
I've removed the "encyclopedic tone" cleanup tag. The specific objection (from the edit summary when the tag was added) was to the use of "you" and "we". There were only five occurrences of "you" in the article, and I've removed all five by rephrasing. The use of "we" is much more pervasive, but it is not clear that it is really a problem. The Manual of Style exhorts us to avoid "we" but admits that this can create problems with the readability of mathematics articles. I doubt seriously that removing "we" would improve this article. If anyone thinks it would, please demonstrate your point by actually making the desired changes; retagging the article is unlikely to accomplish anything useful.

—Syrenka V (talk) 11:17, 16 April 2019 (UTC)

"Denumerable" deserves a special note
Readers arriving at this page to learn what denumerable means would benefit from a special note to confirm whether or not it is synonymous with countable and/or enumerable. Because of its de prefix, the word gives the strong sense that it might mean the opposite of numerable, or somehow refers to being capable of having its numerability removed. It is especially unevocative when used in the term non-denumerable, adding to the value that could be provided to readers by having its meaning deliberately spelled out unambiguously. Gwideman (talk) 13:31, 22 February 2021 (UTC)

 * Originally, I would have guessed that "denumerable" requires the mapping f:S→N to be computable, while "countable" does not. However, that is apparently wrong — a quick web search showed that 5 of 5 URLs use "denumerable" to mean the same as "countable":    . I hesitate to  add a corresponding note before a native English speaker has commented on this issue. - Jochen Burghardt (talk) 15:22, 22 February 2021 (UTC)
 * actually all five of your links seem to use "denumerable" to mean "countably infinite" rather than "countable". I also had a vague recollection that "denumerable" typically meant "countably infinite".  However I'm not completely sure that it's not also sometimes used to mean just "countable" (that is, including finite sets).  In any case I think it's a fairly uncommon word to use in research mathematics today, irrespective of meaning. --Trovatore (talk) 21:13, 20 August 2021 (UTC)
 * ✅ It's discussed in the note on terminology. AFAICT it's ambiguous just like countable. Mathnerd314159 (talk) 18:16, 11 September 2022 (UTC)

Terminology - 20% is "common"?
Since the phrasing was changed from the original quote by User:Trovatore I thought I'd pull some numbers in from Google n-grams. "Countably infinite" is at 5.6 units and rising in popularity, while "at most countable" is at 1.3 units and mostly flat. (81% vs 19%) So clearly the countably infinite terminology is the most common terminology and the right one to use for the article. But as far as the other convention, can I say that the convention appears in 20% of publications? Or is that original research? Regardless 20% doesn't seem "common" so maybe it should be described as "alternative". --Mathnerd314159 (talk) 17:21, 17 September 2021 (UTC)
 * So it's not totally clear from the above which convention you are ascribing the 20% to. If an author uses the phrase "countably infinite", it's a good indication that he/she intends "countable" to include finite sets (the convention described as "common"), whereas using "at most countable" would seem to suggest he/she is using the convention that excludes finite sets (since otherwise he/she would just say "countable").  So taking this to be a quick-and-dirty estimate of the frequency of each convention, your results would give that 80% use the inclusive definition (finite sets are countable), the one used in the article currently, and 20% use the exlusive definition (finite sets are not countable).  Is that what you meant?
 * I don't think this is a very reliable guide, because many authors may not have occasion to use either phrase, and those that do may use it more than once, but to the extent that it is reliable, it seems to point in the direction of confirming the existing text. --Trovatore (talk) 18:18, 17 September 2021 (UTC)
 * Yes, that's what I meant. So I guess citing N-grams is out as the reasoning is somewhat tenuous, but changing "common" to "alternative" for the exclusive definition should be fine? --Mathnerd314159 (talk) 19:01, 17 September 2021 (UTC)
 * Oh, I see -- I stopped at the first hit for the word "common". Yes, "alternative" sounds good to me. --Trovatore (talk) 19:03, 17 September 2021 (UTC)

Examples of countable sets
Example of countable set 117.98.98.174 (talk) 06:47, 4 May 2022 (UTC)

intro is bad
sadly, the intro, as is the case for so many wiki articles on math, is not written at a level appropriate for a general encylopedia it is written at much high level, and uses way to much jargon (injective function !!) please delte and re write thanks — Preceding unsigned comment added by 72.43.78.113 (talk) 15:10, 11 September 2022 (UTC)

 * I have edited the lead. D.Lazard (talk) 17:06, 11 September 2022 (UTC)

Rationale of "citation needed"
Regarding the "citation needed" in the section "A note on terminology": A citation for what is asked for? The fact that the total number of letters in "at most countable" plus "countably infinite" exceeds bot the total number of letters in "at most countable" plus "countable" and the total number of letters in "countable" plus "countably infinite"? Hagman (talk) 20:22, 14 November 2023 (UTC)

 * I agree the "citation needed" is nonsensical there. If nobody objects, I'd remove the complete part, although with respect to concision this is the worst of both worlds.[citation needed]. I'd also like to remark that checking the definition is generally a good idea in mathematics. - Jochen Burghardt (talk) 21:19, 14 November 2023 (UTC)
 * The CN is from a deleted citation that was there before: https://en.wikipedia.org/w/index.php?title=Countable_set&diff=prev&oldid=1044657089. In the source there was a sentence "To avoid this ambiguity [countable vs. countably infinite], the term at most countable may be used when finite sets are included and countably infinite, enumerable, or denumerable otherwise". From what I can tell, deleting that citation was correct, it is the same as a sentence added to the article in 2014 and therefore WP:CIRCULAR. But when I was writing that paragraph, it was there in the article, and I thought that source was good, so I preserved it as best I could.
 * The citation needed is for the whole sentence, to establish that there is indeed this convention of using the combo "at most countable" + "countably infinite" to avoid ambiguity. Looking at Google Books, besides the deleted citation, the only books that show up in a search for both phrases are Marat Marvin's books, such as, with the sentence "To avoid ambiguity, the term 'at most countable' may be used when finite sets are included in the consideration". It also is suspiciously similar to the Wikipedia sentence but I think De Gruyter is at least not a scam publisher. I'm not sure the reference actually shows this convention exists though, he follows the countable/countably infinite convention in the rest of the book and never again mentions "at most countable".
 * So I would say to either delete the sentence entirely or to revise it to explain that although the combo "at most countable" + "countably infinite" is unambiguous nobody uses it in practice. Mathnerd314159 (talk) 02:52, 16 November 2023 (UTC)

title: Talk:Countable set


text:
CPD

CPD may refer to:

Organizations

 * Centre for Policy Development, an Australian think tank
 * Centre for Policy Dialogue, Bangladesh
 * Centres of Plant Diversity, an international classification initiative
 * Commission on Presidential Debates, an American nonprofit
 * Committee on the Present Danger, an American foreign policy interest group

Police

 * Cambridge Police Department (Massachusetts)
 * Camden Police Department (New Jersey), a defunct police department dissolved in 2012
 * Carmel Police Department (Indiana)
 * Charleston Police Department (West Virginia)
 * Chattanooga Police Department, Tennessee
 * Chicago Police Department, Illinois
 * Cincinnati Police Department, Ohio
 * Cleveland Police Department, Ohio
 * Columbus Police Department, Ohio
 * Town of Carmel Police Department (New York)

Science and technology

 * CPD (gene), a human gene encoding the protein Carboxypeptidase D
 * Canonical polyadic decomposition, in mathematics
 * Cephalopelvic disproportion, when the capacity of the pelvis is inadequate to allow the fetus to negotiate the birth canal
 * Chemical compound, a substance formed by chemical union
 * Chronic pulmonary disease, a pathological condition
 * Conditional probability distribution, a kind of distribution in statistics
 * Copy/Paste Detector, software to find duplicate computer code
 * Cyclobutane pyrimidine dimer, a common UV product
 * Cyclopentadiene, an organic compound
 * Cyproterone acetate, a progestin and antiandrogen

Other uses

 * Camperdown railway station, Australia
 * Carnet de Passages en Douane, a customs document
 * Collaborative product development, in business
 * The Constitutional Practice and Discipline of the Methodist Church of Great Britain
 * Construction Products Directive, a repealed EU Directive
 * Continuing professional development
 * Danio margaritatus (also known as the Celestial Pearl Danio), a fish native to Southeast Asia
 * Coober Pedy Airport, IATA airport code "CPD"

title: CPD