View source for Number sign

{{Short description|Typographic symbol (#)}}The symbol {{char|'''#'''}} is known as the '''number sign''',<ref name="oedNumberSign">{{cite web|url=https://en.oxforddictionaries.com/definition/number_sign|archive-url=https://web.archive.org/web/20180403112505/https://en.oxforddictionaries.com/definition/number_sign|url-status=dead|archive-date=April 3, 2018|title=number sign|website=Oxford English Dictionary}}</ref> '''hash''',<ref name="oedHash">{{cite web|url=https://en.oxforddictionaries.com/definition/hash|archive-url=https://web.archive.org/web/20171231152808/https://en.oxforddictionaries.com/definition/hash|url-status=dead|archive-date=December 31, 2017|title=hash|website=Oxford English Dictionary}}</ref> or (in North America) the '''pound sign'''.<ref>{{cite web|url=https://en.oxforddictionaries.com/definition/pound_sign|archive-url=https://web.archive.org/web/20180403051651/https://en.oxforddictionaries.com/definition/pound_sign|url-status=dead|archive-date=April 3, 2018|title=pound sign|website=Oxford English Dictionary|access-date=5 May 2016}}</ref> The symbol has historically been used for a wide range of purposes including the designation of an [[ordinal number]] and as a [[Typographic ligature|ligatured]] abbreviation for [[Pound (mass)|pounds avoirdupois]] – having been derived from the now-rare {{char|℔}}.<ref name="Houston">{{cite book |last1=Houston|first1=Keith |title=Shady Characters: The Secret Life of Punctuation, Symbols, and Other Typographical Marks |publisher=W. W. Norton & Company |year=2013 |isbn=978-0-393-06442-1 |chapter-url=https://books.google.com/books?id=3fbWAAAAQBAJ&pg=PA41 |pages=41–57 |chapter=The Octothorpe }}</ref>

Since 2007, widespread usage of the symbol to introduce [[metadata tag]]s on [[social media]] platforms has led to such tags being known as "[[hashtag]]s",<ref>{{cite book|last=Piercy |first=Joseph |title=Symbols: A Universal Language|chapter-url=https://books.google.com/books?id=XRbdAgAAQBAJ&pg=PT84 |chapter=Part III: Symbnols of value, ownership and exchange |access-date=4 October 2014 |date=25 October 2013 |publisher=Michael OMara|isbn=978-1-78243-073-5 |pages=84–85}}</ref> and from that, the symbol itself is sometimes called a '''hashtag'''.<ref name=hashtag>{{cite web |url=https://www.britannica.com/dictionary/eb/qa/why-is-the-symbol-called-the-hashtag-in-twitter |title=Why is the symbol # called the hashtag in Twitter? |website=The Britannica Dictionary |access-date=2022-09-23 |archive-date=2022-09-23 |archive-url=https://web.archive.org/web/20220923225746/https://www.britannica.com/dictionary/eb/qa/why-is-the-symbol-called-the-hashtag-in-twitter |url-status=live }}</ref>

The symbol is distinguished from similar symbols by its combination of level horizontal strokes and right-tilting vertical strokes.

==History==
[[File:Pfund.svg|thumb|A stylized version of the abbreviation for ''[[Roman pound|libra pondo]]'' ("pound weight")|upright]]
[[File:Libra pondo abbreviation newton.jpg|thumb|The abbreviation written by [[Isaac Newton]], showing the evolution from "{{not a typo|℔}}" toward "#"]]
It is believed that the symbol traces its origins to the symbol {{angbr|[[wikt:℔|℔]]}},{{efn|{{unichar|2114|html=|nlink=}} }} an abbreviation of the Roman term ''[[Roman pound|libra pondo]]'', which translates as "pound weight".<ref>{{cite book | quote=The Italian ''libbra'' (from the old Latin word ''libra'', 'balance') represented a weight almost exactly equal to the [[avoirdupois]] pound of England. The Italian abbreviation of lb with a line drawn across the letters was used for both weights. | author =Keith Gordon Irwin | title= The romance of writing, from Egyptian hieroglyphics to modern letters, numbers, and signs | page= 125 | location= New York |publisher= Viking Press | year = 1967 | orig-year = 1956}}</ref><ref name="NewYorker" /> The abbreviation "lb" was printed as a dedicated [[Ligature (writing)|ligature]] including a horizontal line across (which indicated abbreviation).<ref>{{cite web | url= http://www.royalmintmuseum.org.uk/Default.aspx?PageID=14314417 | title=The Origins of £sd | publisher=The Royal Mint Museum |archive-url = https://web.archive.org/web/20200308111135/http://www.royalmintmuseum.org.uk/Default.aspx?PageID=14314417 |archive-date= 8 March 2020 |quote=It is not known for certain when the horizontal line or lines, which indicate an abbreviation, first came to be drawn through the L.}}</ref><ref name="NewYorker" /> Ultimately, the symbol was reduced for clarity as an overlay of two horizontal strokes "=" across two slash-like strokes "//".<ref name="NewYorker">{{cite news|last=Houston|first=Keith|title=The Ancient Roots of Punctuation|url=http://www.newyorker.com/online/blogs/books/2013/09/origins-of-hashtag-manicule-diple-pilcrow-ampersand-explained.html|access-date=16 October 2013|newspaper=The New Yorker|date=2013-09-06|archive-date=2014-06-25|archive-url=https://web.archive.org/web/20140625175614/http://www.newyorker.com/online/blogs/books/2013/09/origins-of-hashtag-manicule-diple-pilcrow-ampersand-explained.html|url-status=live}}</ref> 

The symbol is described as the "number" character in an 1853 treatise on [[bookkeeping]],<ref>{{cite book|last1=Crittendon|first1=S. W.|title=An Elementary Treatise on Book-keeping by Single and Double Entry |date=1853 |publisher=E., C., & J. Biddle |location=Philadelphia |page=10 |url=https://archive.org/details/anelementarytre00critgoog/page/n16/mode/1up |access-date=7 February 2023}}</ref> and its double meaning is described in a bookkeeping text from 1880.<ref>{{cite book|last1=Duff|first1=C. P.|last2=Duff|first2=W. H.|last3=Duff|first3=R. P.|title=Book-Keeping By Single and Double Entry|date=1880|publisher=Harper and Brothers|page=[https://archive.org/details/bookkeepingbysi00duffgoog/page/n27 21]|url=https://archive.org/details/bookkeepingbysi00duffgoog|access-date= 24 November 2015}}</ref> The instruction manual of the [[Blickensderfer typewriter#Model 5|Blickensderfer model 5]] typewriter ({{Circa|1896}}) appears to refer to the symbol as the "number mark".<ref>{{cite book |author= |url=http://site.xavier.edu/polt/typewriters/Blick5manual.pdf |title=Method of Operating and Instructions for Practice on the Blickensderfer Typewriter |publisher=K. M. Turner |year=1896 |location=Atlanta, GA |page=14 |quote=It is best to use the 'number mark' for plus; the hyphen for minus, and two hyphens for the sign = |archive-url=https://web.archive.org/web/20211014223637/https://site.xavier.edu/polt/typewriters/Blick5manual.pdf |archive-date=Oct 14, 2021}}</ref> Some early-20th-century U.S. sources refer to it as the "number sign",<ref>e.g. J. W. Marley, "The Detection and Illustration of Forgery By Comparison of Handwriting", in {{cite book |url=https://books.google.com/books?id=Z_NEAQAAMAAJ&pg=PA180 |title=Proceedings of the Sixteenth Annual Convention of the Kansas Bankers' Association |publisher=Rusell |year=1903 |location=Kansas City |page=180}}</ref> although this could also refer to the [[numero sign]]  ({{not a typo|№}}).<ref>e.g. [https://books.google.com/books?id=CPodAQAAIAAJ&pg=RA2-PA395 ''The British Printer'' vol. viii] (1895), p. 395</ref> A 1917 manual distinguishes between two uses of the sign: "number (written before a figure)" and "pounds (written after a figure)".<ref>{{cite book |title=Business Arithmetic for Secondary Schools |first=Ernest L. |last=Thurston |location=New York |publisher=Macmillan |year=1917 |page=[https://archive.org/details/businessarithme02thurgoog/page/n439 419] |url=https://archive.org/details/businessarithme02thurgoog|quote=business symbols pound. }}</ref> The use of the phrase "pound sign" to refer to this symbol is found from 1932 in U.S. usage.<ref>{{cite book |first=Nancy M. |last=Lawrence |author2=F. Ethel McAfee |author3=Mildred M. Butler |title=Correlated studies in stenography |publisher=Gregg |year=1932 |page=141 |url=https://books.google.com/books?id=oCsOAQAAIAAJ}}</ref> The term ''hash sign'' is found in South African writings from the late 1960s.<ref>''Research Review. Navorsingsoorsig'' vols. 18–21, pp. 117, 259 (1968)</ref>

For mechanical devices, the symbol appeared on the keyboard of the [[E. Remington and Sons|Remington]] Standard typewriter ({{Circa|1886}}).<ref>{{cite web|url=http://pds.lib.harvard.edu/pds/view/2574435?n=52&s=4&printThumbnails=no|title=Remington Standard typewriter |location=New York |publisher=Wyckoff, Seamans & Benedict |date=1886 |page=50}}</ref> It appeared in many of the early teleprinter codes and from there was copied to [[ASCII]], which made it available on computers and thus caused many more uses to be found for the character. The symbol was introduced on the bottom right button of [[Push-button telephone|touch-tone]] keypads in 1968, but that button was not extensively used until the advent of large-scale [[voicemail]] (PBX systems, etc.) in the early 1980s.<ref name="Houston" />

One of the uses in computers was to label the following text as having a different interpretation (such as a command or a comment) from the rest of the text. It was adopted for use within internet relay chat ([[Internet Relay Chat|IRC]]) networks circa 1988 to label groups and topics.<ref>"Channel Scope". Section 2.2. {{IETF RFC|2811}}</ref> This usage inspired [[Chris Messina (open source advocate)|Chris Messina]] to propose a similar system to be used on [[Twitter]] to tag topics of interest on the microblogging network;<ref>{{cite web|url=http://www.cmu.edu/homepage/computing/2014/summer/originstory.shtml|title=#OriginStory|publisher=Carnegie Mellon University|date=August 29, 2014|access-date=August 23, 2019|archive-date=June 1, 2019|archive-url=https://web.archive.org/web/20190601233044/https://www.cmu.edu/homepage/computing/2014/summer/originstory.shtml|url-status=live}}</ref><ref>{{cite news |author=Parker, Ashley |date=June 10, 2011 |title=Twitter's Secret Handshake |work=The New York Times |url=https://www.nytimes.com/2011/06/12/fashion/hashtags-a-new-way-for-tweets-cultural-studies.html?_r=1&pagewanted=all |url-status=live |url-access=limited |access-date=July 26, 2011 |archive-url=https://web.archive.org/web/20110617001914/https://www.nytimes.com/2011/06/12/fashion/hashtags-a-new-way-for-tweets-cultural-studies.html?_r=1&pagewanted=all |archive-date=Jun 17, 2011}}</ref> this became known as a [[hashtag]]. Although used initially and most popularly on Twitter, hashtag use has extended to other social media sites.<ref>{{cite news |last=Warren |first=Christina |title=Facebook finally gets #hashtags |website=CNN |url=http://www.cnn.com/2013/06/12/tech/social-media/facebook-hashtags/index.html |url-status=live |access-date=July 16, 2006 |archive-url=https://web.archive.org/web/20130613102217/https://www.cnn.com/2013/06/12/tech/social-media/facebook-hashtags/index.html |archive-date=Jun 13, 2013}}</ref>
{{anchor|Other_names_in_English}}

==Names==
'''Number sign'''
:"Number sign" is the name chosen by the [[Unicode Consortium]]. Most common in Canada<ref>{{cite book |editor-last=Barber |editor-first=Katherine |title=The Canadian Oxford dictionary |date=2004 |publisher=Oxford University Press |location=Toronto |isbn=0195418166 |edition=2nd}}</ref> and the northeastern United States.{{citation needed|date=October 2020}}<!-- I am from Massachusetts and it certainly was called "number sign" there-->  American telephone equipment companies which serve Canadian callers often have an option in their programming to denote [[Canadian English]], which in turn instructs the system to say ''number sign'' to callers instead of ''pound''.<ref>{{cite web |title=Norstar Voice Mail 4.1 {{!}} Software Add-on Guide |publisher=[[Nortel]] |page=12 |url=https://downloads.avaya.com/css/P8/documents/100141949 |access-date=2015-12-11 |archive-date=2015-12-22 |archive-url=https://web.archive.org/web/20151222090552/https://downloads.avaya.com/css/P8/documents/100141949 |url-status=live }}</ref> This name is rarely used elsewhere in the world, where numbers are normally represented by the letters "[[Numero sign|No.]]".
'''Pound sign or pound'''
:In the United States and Canada, the "#" key on a phone is commonly referred to as the pound sign, ''pound key'', or simply ''pound''. Dialing instructions to an extension such as #77, for example, can be read as "pound seven seven".<ref name="nyt">{{cite news | url=https://www.nytimes.com/1991/03/24/magazine/on-language-hit-the-pound-sign.html | title=On Language; Hit the Pound Sign | author=William Safire | newspaper=[[The New York Times]] | access-date=May 21, 2011 | date=March 24, 1991 | author-link=William Safire | archive-date=July 21, 2010 | archive-url=https://web.archive.org/web/20100721065416/http://www.nytimes.com/1991/03/24/magazine/on-language-hit-the-pound-sign.html | url-status=live }}</ref> This name is rarely used elsewhere, as the term ''pound sign'' is understood to mean [[pound sign|the currency symbol £]].
'''Hash, [[wikt:hash mark|hash mark]], [[wikt:hashmark|hashmark]]'''
:In the United Kingdom,<ref>{{cite news |url=https://www.theguardian.com/artanddesign/2010/dec/08/hash-symbol-twitter-typography |title=How the # became the sign of our times |newspaper=[[The Guardian]] |access-date=30 December 2014 |archive-date=31 December 2014 |archive-url=https://web.archive.org/web/20141231061916/http://www.theguardian.com/artanddesign/2010/dec/08/hash-symbol-twitter-typography |url-status=live }}</ref> Australia,<ref>{{cite web |url=https://getproofed.com.au/writing-tips/writing-tips-how-to-use-the-hash-sign/ |title=Writing Tips: How to Use the Hash Sign (#) |website=GetProofed |date=6 February 2020 |quote=In Australia, however, it was better known as the 'hash' sign and only used to mean 'number'. |access-date=9 January 2023 |archive-date=9 January 2023 |archive-url=https://web.archive.org/web/20230109105954/https://getproofed.com.au/writing-tips/writing-tips-how-to-use-the-hash-sign/ |url-status=live }}</ref> and some other countries,{{citation needed|date=November 2021}} it is frequently called a "hash" (probably from "hatch", referring to cross-[[hatching]]<ref>{{cite dictionary |url=http://www.oed.com/view/Entry/84445 |title=Hash sign |dictionary=Oxford English Dictionary |access-date=14 October 2013 |archive-date=16 November 2018 |archive-url=https://web.archive.org/web/20181116124751/http://www.oed.com/view/Entry/84445 |url-status=live }}</ref>).
:Programmers also use this term; for instance {{code|#!}} is "hash, bang" or [[Shebang (Unix)|"shebang"]].
'''[[Hashtag]]'''
:Derived from the previous, the word "hashtag" is often used when reading social media messages aloud, indicating the start of a hashtag. For instance, the text "#foo" is often read out loud as "hashtag foo" (as opposed to "hash foo"). This leads to the common belief that the symbol itself is called ''hashtag''.<ref name=hashtag /> Twitter documentation refers to it as "the hashtag symbol".<ref>{{cite web|url=https://support.twitter.com/articles/49309|title=Using hashtags on Twitter|website=Twitter|access-date=5 May 2016|archive-date=4 May 2016|archive-url=https://web.archive.org/web/20160504192917/https://support.twitter.com/articles/49309|url-status=live}}</ref>
'''Hex'''
:"Hex" is commonly used in Singapore and Malaysia, as spoken by many recorded telephone directory-assistance menus: "Please enter your phone number followed by the 'hex' key". The term "hex" is discouraged in Singapore in favour of "hash". In Singapore, a hash is also called "hex" in apartment addresses, where it precedes the floor number.<ref>{{cite web|title=A Dictionary of Singlish and Singapore English|author=Jack Tsen-Ta Lee|url=http://mysmu.edu/faculty/jacklee/singlish_H.htm#hex|access-date=14 January 2016|archive-date=19 January 2016|archive-url=https://web.archive.org/web/20160119143130/http://www.mysmu.edu/faculty/jacklee/singlish_H.htm#hex|url-status=live}}</ref><ref>{{cite web|title=Address Formats|url=http://www.informatica.com/products/data-quality/data-as-a-service/address-verification/address-formats.html?code=SGP|access-date=14 January 2016|archive-date=8 March 2016|archive-url=https://web.archive.org/web/20160308064622/https://www.informatica.com/products/data-quality/data-as-a-service/address-verification/address-formats.html?code=SGP|url-status=live}}</ref>
'''{{vanchor|[[wikt:octothorp|Octothorp]]}}, [[wikt:octothorpe|octothorpe]], octathorp, octatherp'''
:Most scholars believe the word was invented by workers at the [[Bell Labs|Bell Telephone Laboratories]] by 1968,<ref>{{cite magazine |url=http://www.svpal.org/~dickel/octothorp/Encore_magazine.pdf |magazine=Encore |title=Pressing Matters: Touch-tone phones spark debate |author=Hochhester, Sheldon |date=2006-09-29 |access-date=2006-12-17 |archive-date=2007-09-26 |archive-url=https://web.archive.org/web/20070926100216/http://www.svpal.org/~dickel/octothorp/Encore_magazine.pdf |url-status=live }}</ref> who needed a word for the symbol on the [[Dual-tone multi-frequency signaling|telephone keypad]]. Don MacPherson is said to have created the word by combining ''octo'' and the last name of [[Jim Thorpe]], an Olympic medalist.<ref>Ralph Carlsen, "What the ####?" ''Telecoms Heritage Journal'' 28 (1996): 52–53.</ref> Howard Eby and Lauren Asplund claim to have invented the word as a joke in 1964, combining ''octo'' with the syllable ''therp'' which, because of the "th" [[digraph (orthography)|digraph]], was hard to pronounce in different languages.<ref name="Kerr">{{cite web |url=http://dougkerr.net/pumpkin/articles/Octatherp.pdf |author=Douglas A. Kerr |title=The ASCII Character "Octatherp" |date=2006-05-07 |access-date=2010-08-23 |archive-date=2010-12-15 |archive-url=https://web.archive.org/web/20101215025150/http://dougkerr.net/pumpkin/articles/Octatherp.pdf |url-status=live }}</ref> ''The Merriam-Webster New Book of Word Histories'', 1991, has a long article that is consistent with Doug Kerr's essay,<ref name="Kerr"/> which says "octotherp" was the original spelling, and that the word arose in the 1960s among telephone engineers as a joke. Other hypotheses for the origin of the word include the last name of [[James Oglethorpe]]<ref>John Baugh, Robert Hass, Maxine H. Kingston, et al., "Octothorpe", ''The American Heritage Dictionary of the English Language'' (Boston: Houghton Mifflin, 2000)</ref> or using the Old English word for village, ''[[thorp]]'', because the symbol looks like a village surrounded by eight fields.<ref>{{cite web|url=http://www.worldwidewords.org/weirdwords/ww-oct1.htm|title=Octothorpe|last=Quinion|first=Michael|date=19 May 2010|website=World Wide Words|access-date=10 May 2016|archive-date=18 May 2016|archive-url=https://web.archive.org/web/20160518172649/http://www.worldwidewords.org/weirdwords/ww-oct1.htm|url-status=live}}</ref><ref>Bringhurst, "Octothorpe". ''Elements of Typographic Style''</ref> The word was popularized within and outside Bell Labs.<ref>"You Asked Us: About the * and # on the New Phones", ''The Calgary Herald'', September 9, 1972, 90.</ref> The first appearance of "octothorp" in a US patent is in a 1973 filing. This patent also refers to the six-pointed asterisk (✻) used on telephone buttons as a "[[Astrological aspect#Sextile|sextile]]".<ref>{{cite web|url=http://www.google.com/patents?vid=USPAT3920926|title=U.S. Patent No. 3,920,926|access-date=16 September 2014|archive-date=2 March 2013|archive-url=https://web.archive.org/web/20130302144808/http://www.google.com/patents?vid=USPAT3920926|url-status=dead}}</ref>
'''[[Sharp (music)|Sharp]]'''
: Use of the name "sharp" is due to the symbol's resemblance to {{unichar|266F|nlink=}}. The same derivation is seen in the name of the [[Microsoft]] programming languages [[C Sharp (programming language)|C#]], [[J Sharp|J#]] and [[F Sharp (programming language)|F#]]. Microsoft says that the name ''C#'' is pronounced 'see sharp'."<ref>{{cite web |url=https://learn.microsoft.com/en-us/dotnet/csharp/tour-of-csharp/ |title=A tour of the C# language |date=5 April 2023 |access-date=4 April 2024 |website=learn.microsoft.com |archive-date=8 March 2024 |archive-url=https://web.archive.org/web/20240308153937/https://learn.microsoft.com/en-us/dotnet/csharp/tour-of-csharp/ |url-status=live }}</ref> According to the ECMA-334 C# Language Specification, the name of the language is written "C#" ("{{resize|LATIN CAPITAL LETTER C}} (U+0043) followed by the {{resize|NUMBER SIGN}} # (U+0023)") and pronounced "C Sharp".<ref>{{cite book |url=https://ecma-international.org/wp-content/uploads/ECMA-334_7th_edition_december_2023.pdf |title=ECMA-334 C# language specification |edition=7th |publisher=[[Ecma International]] |page=xxiii |chapter=Introduction |date=December 2023 |access-date=4 April 2024 |archive-date=16 December 2023 |archive-url=https://web.archive.org/web/20231216004437/https://ecma-international.org/wp-content/uploads/ECMA-334_7th_edition_december_2023.pdf |url-status=live }}</ref>
'''Square'''
[[File:Detail-Tastatur-FeTAp-751-1982.JPG|thumb|right|Detail of a telephone keypad displaying the [[Viewdata]] square]]
:On telephones, the [[International Telecommunication Union]] specification [[E.161|ITU-T E.161]] 3.2.2 states: "The symbol may be referred to as the square or the most commonly used equivalent term in other languages."<ref>{{cite web | url = http://www.itu.int/rec/T-REC-E.161-200102-I/en | title = E.161 : Arrangement of digits, letters and symbols on telephones and other devices that can be used for gaining access to a telephone network | publisher = [[International Telecommunication Union]] | date = 2 February 2001 | access-date = 23 December 2019 | archive-date = 2 November 2019 | archive-url = https://web.archive.org/web/20191102055736/https://www.itu.int/rec/T-REC-E.161-200102-I/en | url-status = live }}</ref> Formally, this is not a number sign but rather another character, {{unichar|2317|nlink=}}. The real or virtual keypads on almost all modern telephones use the simple {{code|#}} instead, as does most documentation.{{cn|date=January 2023}}

== Usage ==
When {{angbr|#}} prefixes a number, it is read as "number". "A #2 pencil", for example, indicates "a number-two pencil". This usage is rare in print,<ref>{{cite web|url=
https://books.google.com/ngrams/graph?content=%22+%23+1+%22%2C%22+No.+1+%22&year_start=1800&year_end=2008&corpus=15&smoothing=3|title=
Google Ngram Viewer|access-date=
2021-02-05|archive-date=
2024-04-05|archive-url=
https://web.archive.org/web/20240405004325/https://books.google.com/ngrams/graph?content=%22+%23+1+%22%2C%22+No.+1+%22&year_start=1800&year_end=2008&corpus=15&smoothing=3|url-status=
live}}</ref> or outside North America. Instead the abbreviation {{notatypo|'No.'}} or the symbol {{notatypo|'№'}} or just "number" is used.{{cn|date=November 2023}}

When {{angbr|#}} is ''after'' a number, it is read as "pound" or "pounds", meaning the unit of weight.<ref>{{Cite web |title=Number Sign/Hashtag - Punctuation {{!}} Ultius |url=https://www.ultius.com/glossary/grammar/punctuation/number-signhashtag |access-date=2025-06-05 |website=www.ultius.com}}</ref><ref>{{Cite web |title=Language Log » The "pound sign" mystery |url=https://languagelog.ldc.upenn.edu/nll/?p=2461 |access-date=2025-06-05}}</ref> The text "5# bag of flour" would mean "five-pound bag of flour". This is rare outside North America.

=== Mathematics ===
* In [[set theory]], #''S'' is one possible notation for the [[cardinality]] or size of the [[set (mathematics)|set]] ''S'', instead of <math>|S|</math>. That is, for a set <math>S = \{s_1,s_2,s_3, \dots , s_n\}</math>, in which all <math>s_i</math> are mutually distinct, <math>\#S = n = |S|.</math> This notation is only sometimes used for [[finite set]]s, usually in [[number theory]], to avoid confusion with the [[divisibility]] symbol, e.g. <math>a \mid b</math>.
* In [[topology]], ''A''#''B'' is the [[connected sum]] of [[manifold]]s ''A'' and ''B'', or of knots ''A'' and ''B'' in [[knot theory]].
* In [[number theory]], ''n''# is the [[primorial]] of ''n''.
* In [[constructive mathematics]], # denotes an [[apartness relation]].
* In [[computational complexity theory]], [[♯P|#P]] denotes a [[complexity class]] of [[counting problem (complexity)|counting problems]]. The standard notation for this class uses the number sign symbol, not the [[sharp sign]] from music, but it is pronounced "sharp P". More generally, the number sign may be used to denote the class of counting problems associated with any class of search problems.

=== Computing ===
* In [[Unicode]] and [[ASCII]], the symbol has a [[code point]] as {{unichar|0023}} and [[entity code]] {{code|&num;}} in [[HTML5]].<ref>HTML5 is the only version of HTML that has a named entity for the number sign, see https://www.w3.org/TR/html4/sgml/entities.html {{Webarchive|url=https://web.archive.org/web/20180401051616/http://www.w3.org/TR/html4/sgml/entities.html |date=2018-04-01 }} ("The following sections present the complete lists of character entity references.") and https://www.w3.org/TR/2014/CR-html5-20140731/syntax.html#named-character-references {{Webarchive|url=https://web.archive.org/web/20170805013240/http://www.w3.org/TR/2014/CR-html5-20140731/syntax.html#named-character-references |date=2017-08-05 }} ("num;").</ref>
* In many scripting languages and data file formats, especially ones that originated on Unix, {{code|#}} introduces a comment that goes to the end of the line.<ref name="hash character">{{cite web |title=CSS Syntax and Selectors |url=https://www.w3schools.com/css/css_syntax.asp |website=W3Schools |access-date=2019-07-15 |archive-date=2019-07-12 |archive-url=https://web.archive.org/web/20190712051145/https://www.w3schools.com/css/css_syntax.asp |url-status=live }}</ref> The combination {{code|#!}} at the start of an executable file is a "[[Shebang (Unix)|shebang]]", "hash-bang" or "pound-bang", used to tell the operating system which program to use to run the script (see [[Magic number (programming)|magic number]]). This combination was chosen so it would be a comment in the scripting languages.
* In the [[C preprocessor]] (used by [[C (programming language)|C]] and many other languages), {{code|#}} at the start of a line starts a preprocessor [[Directive (programming)|directive]]. Inside macros (after {{code|#define}}) it is used for various purposes; for example {{code|##}} is used for token [[concatenation]].
* In [[Unix shell]]s, {{code|#}} is placed by convention at the end of a [[command prompt]] to denote that the user is working as [[Superuser|root]].
* {{code|#}} is used in a [[URL]] of a [[web page]] or other resource to introduce a "[[fragment identifier]]" – an id which defines a position within that resource. In HTML, this is known as an [[HTML element#Anchor|anchor link]]. For example, in the URL {{code|https://en.wikipedia.org/wiki/Number_sign#Computing}} the portion after the {{code|#}} ({{code|Computing}}) is the fragment identifier, in this case denoting that the display should be moved to show the tag marked by {{code|1=<span id="Computing">...</span>|2=html}} in the HTML.<ref>{{cite web|url=http://www.w3.org/TR/html4/intro/intro.html#fragment-uri|title=Introduction to HTML|access-date=16 September 2014|archive-date=16 August 2008|archive-url=https://web.archive.org/web/20080816014507/http://www.w3.org/TR/html4/intro/intro.html#fragment-uri|url-status=live}}</ref>
* [[Internet Relay Chat]]: on (IRC) servers, {{code|#}} precedes the name of every [[IRC channels|channel]] that is available across an entire IRC network.
* In [[blog]]s, {{code|#}} is sometimes used to denote a [[permalink]] for that particular weblog entry.
* In [[lightweight markup language]]s, such as [[wiki]]text, {{code|#}} is often used to introduce numbered list items.
* In the [[Perl]] programming language, {{code|#}} is used as a modifier to array syntax to return the index number of the last element in the [[Array data type|array]], e.g., an array's last element is at {{code|$array[$#array]}}. The number of elements in the array is {{code|$#array + 1}}, since Perl arrays default to using zero-based indices. If the array has not been defined, the return is also undefined. If the array is defined but has not had any elements assigned to it, e.g., {{code|1=@array = ()}}, then {{code|$#array}} returns {{code|−1}}. See the section on [[Perl language structure#Array functions|Array functions]] in the Perl language structure article.
* {{code|#}} is used in the [[Modula-2]] and [[Oberon (programming language)|Oberon]] programming languages designed by [[Niklaus Wirth]] and in the [[Component Pascal]] language derived from Oberon to denote the ''not equal'' symbol, as a stand-in for the mathematical unequal sign {{char|≠}}, being more intuitive than {{code|<>}} or {{code|1=!=}}. For example: {{nowrap|{{code|IF i # 0 THEN ...|cp}}}}
* In [[Rust (programming language)|Rust]], {{code|#}} is used for attributes such as in {{code|#[test]}}.
* In [[OCaml]], {{code|#}} is the operator used to call a method.
* In [[Common Lisp]],<ref>{{cite web|url=http://www.lispworks.com/documentation/HyperSpec/Body/02_dh.htm|title=Lispworks.com|access-date=16 September 2014|archive-date=10 October 2014|archive-url=https://web.archive.org/web/20141010014731/http://www.lispworks.com/documentation/HyperSpec/Body/02_dh.htm|url-status=live}}</ref> {{code|#}} is a dispatching [[Lisp reader|read macro]] character used to extend the [[S-expression]] syntax with short cuts and support for various data types ([[complex number]]s, vectors and more).
* In [[Scheme (programming language)|Scheme]], {{code|#}} is the prefix for certain syntax with special meaning.
* In [[Standard ML]], {{code|#}}, when prefixed to a field name, becomes a projection function (function to access the field of a record or tuple); also, {{code|#}} prefixes a [[string literal]] to turn it into a character literal.
* In [[Wolfram Mathematica|Mathematica]] syntax, {{code|#}}, when used as a variable, becomes a pure function (a placeholder that is mapped to any variable meeting the conditions).
* In [[LaTeX]], {{code|#}}, when prefixing a number, references an arguments for a user defined command. For instance <syntaxhighlight lang="tex" inline>\newcommand{\code}[1]{\texttt{#1}}</syntaxhighlight>.
* In [[Javadoc]],<ref>{{cite web|url=http://download.oracle.com/javase/1.5.0/docs/tooldocs/windows/javadoc.html#@see|title=Oracle.com|access-date=16 September 2014|archive-date=28 October 2011|archive-url=https://web.archive.org/web/20111028092204/http://download.oracle.com/javase/1.5.0/docs/tooldocs/windows/javadoc.html#@see|url-status=live}}</ref> {{code|#}} is used with the {{code|@see}} tag to introduce or separate a field, constructor, or method member from its containing class.
* In [[Core War|Redcode]] and some other dialects of [[assembly language]], {{code|#}} is used to denote immediate mode addressing, e.g., {{code|LDA #10}}, which means "load accumulator A with the value 10" in [[MOS 6502]] assembly language.
* in [[HTML]], [[Cascading Style Sheets|CSS]], [[Scalable Vector Graphics|SVG]], and other computing applications {{code|#}} is used to identify a color specified in [[hexadecimal]] format, e.g., {{code|#FFAA00}}. This usage comes from [[X11]] color specifications, which inherited it from early assembler dialects that used {{code|#}} to prefix hexadecimal constants, e.g.: ZX Spectrum [[Zilog Z80|Z80]] assembly.<ref>{{cite web|url=http://www.worldofspectrum.org/pub/sinclair/games-info/h/HiSoftDevpacV3.pdf|title=HISOFT DEVPAC ZX Spectrum Programmer's Manual|website=worldofspectrum.org|access-date=2017-10-03|archive-date=2018-11-12|archive-url=https://web.archive.org/web/20181112231113/http://www.worldofspectrum.org/pub/sinclair/games-info/h/HiSoftDevpacV3.pdf|url-status=live}}</ref>
* In [[Be-Music Script]], every command line starts with {{code|#}}. Lines starting with characters other than "#" are treated as comments.
* The use of the hash symbol in a [[hashtag]] is a phenomenon conceived by [[Chris Messina (open-source advocate)|Chris Messina]], and popularized by social media network [[Twitter]], as a way to direct conversations and topics amongst users. This has led to an increasingly common tendency to refer to the symbol itself as "hashtag".<ref name="Time">{{Cite magazine|url=https://time.com/2870942/hashtag-oed-oxford-english-dictionary/|title=You'll Never Guess the Real Name for a Hashtag|last=Nicks|first=Denver|date=June 13, 2014|magazine=TIME|access-date=May 5, 2016|archive-date=May 11, 2016|archive-url=https://web.archive.org/web/20160511235410/http://time.com/2870942/hashtag-oed-oxford-english-dictionary/|url-status=live}}</ref>
* In programming languages like PL/1 and Assembler used on IBM mainframe systems, as well as JCL (Job Control Language), the {{code|#}} (along with {{code|$}} and {{code|@}}) are used as additional letters in identifiers, labels and data set names.
* In [[J (programming language)|J]], {{code|#}} is the ''Tally'' or ''Count'' function,<ref>{{cite web|url=https://code.jsoftware.com/wiki/Vocabulary/number|title=Vocabulary/number|access-date=November 20, 2019|website=J NuVoc|archive-date=February 14, 2020|archive-url=https://web.archive.org/web/20200214105150/https://code.jsoftware.com/wiki/Vocabulary/number|url-status=live}}</ref> and similarly in [[Lua (programming language)|Lua]], {{code|#}} can be used as a shortcut to get the length of a table, or get the length of a string. Due to the ease of writing "#" over longer function names, this practice has become standard in the Lua community.
* In Dyalog [[APL (programming language)|APL]], {{code|#}} is a reference to the root [[namespace]] while {{code|##}} is a reference to the current space's parent namespace.
* In [[Ada (programming language)|Ada]], the {{code|#}} character is used in based integer literals, which take the form {{code|base#digits#}}, where {{code|base}} is an integer from 2 to 16 specifying the radix, and {{code|digits}} are the digits valid in that base (0-9, optionally A-F for bases above 10).

=== Other uses ===
* [[Algebraic notation (chess)|Algebraic notation for chess]]: A hash after a move denotes [[checkmate]].
* [[American Sign Language]] transcription: The hash prefixing an all-caps word identifies a lexicalized fingerspelled sign, having some sort of blends or letter drops. All-caps words without the prefix are used for standard English words that are fingerspelled in their entirety.<ref>{{cite web |last1=Vicars |first1=Bill |title=Lexicalization |url=http://www.lifeprint.com/asl101/topics/lexicalized_fingerspelling.htm |publisher=ASL University |access-date=6 September 2015 |archive-date=10 September 2015 |archive-url=https://web.archive.org/web/20150910183425/http://www.lifeprint.com/asl101/topics/lexicalized_fingerspelling.htm |url-status=live }}</ref>
* [[copy writer|Copy writing]] and [[copy editing]]: Technical writers in [[press release]]s often use three number signs, {{char|###}} directly above the boilerplate or underneath the body copy, indicating to media that there is no further copy to come.<ref>{{cite web |title=###: What does ### mean at the end of a press release? |publisher=The Halo Group |url=https://www.thehalogroup.com/what-does-mean-at-the-end-of-a-press-release/ |first=Lara |last=Cohn |access-date=18 November 2021 |archive-date=17 November 2021 |archive-url=https://web.archive.org/web/20211117221859/https://www.thehalogroup.com/what-does-mean-at-the-end-of-a-press-release/ |url-status=live }}</ref>
* [[Note (typography)|Footnote]] symbols (or endnote symbols): Due to ready availability in many fonts and directly on computer keyboards, "#" and other symbols (such as the [[caret]]) have in recent years begun to be occasionally used in catalogues and reports in place of more traditional symbols (esp. [[Dagger (mark)|dagger, double-dagger]], [[pilcrow]]).
* Linguistic [[phonology]]: {{char|#}} denotes a word boundary. For instance, {{code|/d/ → [t] / _#}} means that {{char|/d/}} becomes {{char|[t]}} when it is the last segment in a word (i.e. when it appears before a word boundary).
* Linguistic [[syntax]]: A hash before an example sentence denotes that the sentence is semantically ill-formed, though grammatically well-formed. For instance, "#The toothbrush is pregnant" is a grammatically correct sentence, but the meaning is odd.<ref>{{cite book|last=Carnie|first=Andrew|year=2006|title=Syntax: A Generative Introduction|location=Oxford|publisher=Wiley-Blackwell|isbn=1-4051-3384-8|edition=2nd|url-access=registration|url=https://archive.org/details/syntaxgenerative0000carn}}</ref><ref>{{Cite book | first=R. L. | last=Trask | author-link=Larry Trask | title=A Dictionary of Grammatical Terms in Linguistics | location=London | publisher=Routledge | year=1993 | isbn=0-415-08627-2 | page=125}}</ref>
* [[Medical prescription]] drug delimiter: In some countries, such as [[Norway]] or [[Poland]], {{char|#}} is used as a [[delimiter]] between different drugs on medical prescriptions.
* Medical shorthand: The hash is often used to indicate a [[bone fracture]].<ref>{{Cite web |url=http://radiographics.rsnajnls.org/cgi/reprint/23/1/195.pdf |title=Glossary of Medical Devices and Procedures: Abbreviations, Acronyms, and Definitions |access-date=2008-05-16 |archive-date=2008-06-25 |archive-url=https://web.archive.org/web/20080625213552/http://radiographics.rsnajnls.org/cgi/reprint/23/1/195.pdf |url-status=live }}</ref> For example, "#NOF" is often used for "fractured [[Femur neck|neck of femur]]". In radiotherapy, a full dose of radiation is divided into smaller doses or 'fractions'. These are given the shorthand {{char|#}} to denote either the number of treatments in a prescription (e.g. 60Gy in 30#), or the fraction number (#9 of 25).
* As a [[List of proofreader's marks|proofreading mark]], to indicate that a space should be inserted.<ref>{{cite web |url=http://www.merriam-webster.com/mw/table/proofrea.htm |title=Proofreaders' Marks |access-date=2020-09-03 |archive-date=2010-08-16 |archive-url=https://web.archive.org/web/20100816210104/http://www.merriam-webster.com/mw/table/proofrea.htm |url-status=dead }} from [[Merriam Webster]]</ref>
* Publishing: When submitting a science fiction manuscript for publication, a number sign on a line by itself (indented or centered)  indicates a [[Section (typography)|section break]] in the text.<ref>{{cite web|url=http://www.sfwa.org/wp-content/uploads/2009/06/Mssprep.pdf|title=Manuscript Preparation|last=McIntyre|first=Vonda|date=October 2008|website=sfwa.org|publisher=Science Fiction & Fantasy Writers of America|access-date=28 May 2020|archive-date=3 October 2020|archive-url=https://web.archive.org/web/20201003095936/http://www.sfwa.org/wp-content/uploads/2009/06/Mssprep.pdf|url-status=live}}</ref>
* [[Scrabble]]: Putting a number sign after a word indicates that the word is found in the British word lists, but not the [[Official Tournament and Club Word List|North American lists.]]<ref>{{cite web|url=http://www.tucsonscrabble.com/articles/glossary.html|title=Scrabble Glossary|publisher=Tucson Scrabble Club|access-date=2012-02-06|archive-url=https://web.archive.org/web/20110830073348/http://www.tucsonscrabble.com/articles/glossary.html|archive-date=2011-08-30|url-status=dead}}</ref>
* [[Teletext]] and [[Digital Video Broadcasting|DVB]] [[subtitle]]s (in the UK and Ireland): The hash symbol, resembling music notation's sharp sign, is used to mark text that is either sung by a character or heard in background music, e.g. {{mono|''#&nbsp;For he's a jolly good fellow&nbsp;#''}}

==Unicode==

The number sign was assigned code 35 (hex 0x23) in ASCII where it was inherited by many character sets. In [[EBCDIC]] it is often at 0x7B or 0xEC.

Unicode characters with "number sign" in their names:
* {{unichar|0023}} (Other [[Unicode character property|attested names in Unicode]] are: {{sc|pound sign (weight), hashtag, hash, crosshatch, octothorpe}}.<ref>{{cite web |author=Unicode Consortium |title=C0 Controls and Basic Latin| url=https://www.unicode.org/charts/PDF/U0000.pdf}}</ref>)
* {{unichar|0600|html=|nlink=}}
* {{unichar|0BFA|html=|nlink=}}
* {{unichar|1AC6|nlink=}}
* {{unichar|FE5F}}
* {{unichar|FF03}}
* {{unichar|110BD|nlink=}}
* {{unichar|110CD|nlink=}}
* {{unichar|11FE9|nlink=}}
* {{unichar|E0023|nlink=}}

Additionally, a Unicode named sequence {{resize|KEYCAP NUMBER SIGN}} is defined for the [[grapheme cluster]] {{code|U+0023+FE0F+20E3}} (#️⃣).<ref>{{cite web |url=https://www.unicode.org/Public/UCD/latest/ucd/NamedSequences.txt |title=Unicode Named Character Sequences |work=Unicode Character Database |author=Unicode Consortium |author-link=Unicode Consortium |access-date=2020-07-16 |archive-date=2020-07-11 |archive-url=https://web.archive.org/web/20200711232858/http://www.unicode.org/Public/UCD/latest/ucd/NamedSequences.txt |url-status=live}}</ref>{{efn|{{unichar|0023}}, {{unichar|FE0F|nlink=}}, {{unichar|20E3|nlink=}} }}

==On keyboards==
On the standard [[QWERTY|US keyboard layout]], the {{char|#}} symbol is {{keypress|Shift|3}}. On standard UK and some other European keyboards, the same keystrokes produce the [[Pound sign|pound (sterling) sign, {{char|£}} symbol]], and {{keypress|#}} may be moved to a separate key above the right shift key.

==See also==
{{Wiktionary|number sign}}
* {{unichar|266F|nlink=}}
* {{unichar|2317|nlink=}}
* {{unichar|22D5|nlink=}}
* {{unichar2|⌘|nlink=}} ("looped square")
* {{unichar|4E95|nlink=}}, the [[Chinese character]] for "well" ({{Zh-cjp|c=[[wiktionary:井|井]]|p=jǐng|j=zeng2}})
* the game [[tic-tac-toe]], which uses a similar grid pattern 

{{For|uses of # within Wikipedia|Wikipedia:Number sign}}

== Explanatory notes ==
{{Notelist}}

==References==
{{Reflist|2}}

{{navbox punctuation}}

[[Category:Typographical symbols]]