List of mathematical symbols

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This is a list of symbols found within all branches ofmathematics to express a formula or to represent aconstant.When reading the list, it is important to recognize thata mathematical concept is independent of the symbolchosen to represent it. For many of the symbols below,the symbol is usually synonymous with the correspondingconcept (ultimately an arbitrary choice made as a resultof the cumulative history of mathematics), but in somesituations a dierent convention may be used. For exam-ple, depending on context, the triple bar "" may repre-sent congruence or a denition. Further, in mathemati-cal logic, numerical equality is sometimes represented by"" instead of "=", with the latter representing equalityof well-formed formulas. In short, convention dictatesthe meaning.Each symbol is shown both in HTML, whose display de-pends on the browsers access to an appropriate font in-stalled on the particular device, and in TeX, as an image.

1 GuideThis list is organized by symbol type and is intended tofacilitate nding an unfamiliar symbol by its visual ap-pearance. For a related list organized by mathematicaltopic, see List of mathematical symbols by subject. Thatlist also includes LaTeX and HTMLmarkup and Unicodecode points for each symbol.

Basic symbols: Symbols widely used in mathemat-ics, roughly through rst-year calculus. More ad-vanced meanings are included with some symbolslisted here.

Symbols based on equality "=": Symbols derivedfrom or similar to the equal sign, including double-headed arrows. Not surprisingly these symbols areoften associated with an equivalence relation.

Symbols that point left or right: Symbols, such as< and >, that appear to point to one side or another.

Brackets: Symbols that are placed on either side ofa variable or expression, such as |x|.

Other non-letter symbols: Symbols that do not fallin any of the other categories.

Letter-based symbols: Many mathematical sym-bols are based on, or closely resemble, a letter insome alphabet. This section includes such symbols,including symbols that resemble upside-down let-ters. Many letters have conventional meanings invarious branches of mathematics and physics. Theseare not listed here. The See also section, below, hasseveral lists of such usages.

Letter modiers: Symbols that can be placedon or next to any letter to modify the lettersmeaning.

Symbols based on Latin letters, includingthose symbols that resemble or contain an X

Symbols based on Hebrew or Greek letterse.g. , , , , , , , , .Note: symbols re-sembling are grouped with V under Latinletters.

Variations: Usage in languages written right-to-left

2 Basic symbols

3 Symbols based on equality sign

4 Symbols that point left or right

5 Brackets

6 Other non-letter symbols

7 Letter-based symbols

Includes upside-down letters.

1

2 11 EXTERNAL LINKS

7.1 Letter modiers

7.2 Symbols based on Latin letters

7.3 Symbols based on Hebrew or Greekletters

8 VariationsIn mathematics written in Arabic, some symbols maybe reversed to make right-to-left writing and readingeasier.[13]

9 See also Greek letters used in mathematics, science, and en-gineering

ISO 31-11 (Mathematical signs and symbols for usein physical sciences and technology)

Latin letters used in mathematics List of mathematical abbreviations List of mathematical symbols by subject Mathematical alphanumeric symbols Mathematical constants and functions Mathematical notation Mathematical operators and symbols in Unicode Notation in probability and statistics Physical constants Table of logic symbols Table of mathematical symbols by introduction date Typographical conventions in mathematical formu-lae

10 References[1] http://www.mathsisfun.com/geometry/symbols.html.

Missing or empty |title= (help)

[2] Rnyai, Lajos (1998), Algoritmusok(Algorithms), TYPO-TEX, ISBN 963-9132-16-0

[3] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. (2002).A fast and elitist multiobjective genetic algorithm:NSGA-II. IEEE Transactions on Evolutionary Compu-tation 6 (2): 182. doi:10.1109/4235.996017.

[4] Copi, Irving M.; Cohen, Carl (1990) [1953], Chapter8.3: Conditional Statements and Material Implication,Introduction to Logic (8th ed.), New York: MacmillanPublishers (United States), pp. 268269, ISBN 0-02-325035-6, LCCN 89037742

[5] Goldrei, Derek (1996), Classic Set Theory, London:Chapman and Hall, p. 4, ISBN 0-412-60610-0

[6] Nielsen, Michael A; Chuang, Isaac L (2000), Quan-tum Computation and Quantum Information, New York:Cambridge University Press, p. 66, ISBN 0-521-63503-9, OCLC 43641333

[7] Goldrei, Derek (1996), Classic Set Theory, London:Chapman and Hall, p. 3, ISBN 0-412-60610-0

[8] Nielsen, Michael A; Chuang, Isaac L (2000), Quan-tum Computation and Quantum Information, New York:Cambridge University Press, p. 62, ISBN 0-521-63503-9, OCLC 43641333

[9] Berman, Kenneth A; Paul, Jerome L. (2005), Algorithms:Sequential, Parallel, and Distributed, Boston: CourseTechnology, p. 822, ISBN 0-534-42057-5

[10] Goldrei, Derek (1996), Classic Set Theory, London:Chapman and Hall, p. 5, ISBN 0-412-60610-0

[11] Nielsen, Michael A; Chuang, Isaac L (2000), Quan-tum Computation and Quantum Information, New York:Cambridge University Press, pp. 6970, ISBN 0-521-63503-9, OCLC 43641333

[12] Nielsen, Michael A; Chuang, Isaac L (2000), Quan-tum Computation and Quantum Information, New York:Cambridge University Press, pp. 7172, ISBN 0-521-63503-9, OCLC 43641333

[13] M. Benatia, A. Lazrik, and K. Sami, "Arabic mathemat-ical symbols in Unicode", 27th Internationalization andUnicode Conference, 2005.

11 External links The complete set of mathematics Unicode charac-ters

Je Miller: Earliest Uses of Various MathematicalSymbols

Numericana: Scientic Symbols and Icons GIF and PNG Images for Math Symbols Mathematical Symbols in Unicode Using Greek and special characters from Symbolfont in HTML

UnicodeMath Symbols - a quick form for using uni-code math symbols.

DeTeXify handwritten symbol recognition doo-dle a symbol in the box, and the program will tellyou what its name is

3Some Unicode charts of mathematical operators:

Index of Unicode symbols Range 2100214F: Unicode Letterlike Symbols Range 219021FF: Unicode Arrows Range 220022FF: Unicode Mathematical Opera-tors

Range 27C027EF: Unicode Miscellaneous Math-ematical SymbolsA

Range 298029FF: Unicode Miscellaneous Mathe-matical SymbolsB

Range 2A002AFF: Unicode SupplementaryMath-ematical Operators

Some Unicode cross-references:

Short list of commonly used LaTeX symbols andComprehensive LaTeX Symbol List

MathML Characters - sorts out Unicode, HTMLand MathML/TeX names on one page

Unicode values and MathML names Unicode values and Postscript names from thesource code for Ghostscript

4 12 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

12 Text and image sources, contributors, and licenses12.1 Text

List of mathematical symbols Source: http://en.wikipedia.org/wiki/List%20of%20mathematical%20symbols?oldid=651640327 Con-tributors: AxelBoldt, Bryan Derksen, Zundark, Eclecticology, Toby Bartels, Rade Kutil, David spector, Camembert, Stevertigo, Ubiquity,Patrick, Boud, Michael Hardy, Tim Starling, JakeVortex, Dominus, Elano, Darkwind, LittleDan, AugPi, BenKovitz, BAxelrod, NikolaSmolenski, Ideyal, Charles Matthews, Berteun, Dysprosia, WhisperToMe, Markhurd, Furrykef, David Shay, Zero0000, Secretlondon, PhilBoswell, Robbot, YahoKa, Fredrik, Benwing, MathMartin, Sverdrup, Bkell, Hoot, Robinh, Alpharigel, Wile E. Heresiarch, Alan Liefting,Snobot, Ancheta Wis, Giftlite, Mikez, BenFrantzDale, Tom harrison, Monedula, Moyogo, Markus Kuhn, Jason Quinn, Daniel Brockman,Estel, Karol Langner, MFNickster, Corti, Skal, Noisy, Vincom2, Discospinster, Rich Farmbrough, TedPavlic, Kevinb, Pak21, Mecanismo,ArnoldReinhold, Sam Derbyshire, Paul August, ESkog, Sunborn, Zaslav, CanisRufus, Spoon!, BrokenSegue, PWilkinson, Pschemp, SamKorn, LutzL, Lexw, JohnyDog, Jezmck, Sl, ABCD, Hoary, Sligocki, Thezulu, Mysdaao, Bart133, Tauwasser, Dirac1933, H2g2bob, OlegAlexandrov, Linas, Mindmatrix, Bkkbrad, Bonus Onus, Orz, Smmurphy, Michiel Helvensteijn, Joshdick, Waldir, Calrfa Wn, Qwertyus,Grammarbot, Jshadias, Josh Parris, DrHow, Rjwilmsi, Tizio, Salix alba, MZMcBride, R.e.b., Sango123, FlaBot, Mathbot, Tumble, Gurch,Srleer, Kri, Lguero, Chobot, YurikBot, Wavelength, Agent Foxtrot, Wigie, Kauner, Mathaxiom, Anomalocaris, Trovatore, Nutiketaiel,Thallinger, Renata3, Alex43223, DavidHouse, Psy guy, Pooryorick, Avraham, Letdinosaursdie, Arthur Rubin, KGasso, Jaranda, Allens,LakeHMM, Tyomitch, Efnar, Capitalist, Btipling, Erik Postma, Teo64x, Itub, Jbalint, SmackBot, RDBury, Tom Lougheed, InverseHy-percube, Melchoir, Kaimbridge, Nerd42, BiT, Commander Keane bot, Gilliam, IMacWin95, Psiphiorg, Bluebot, SMP, Jprg1966, Prime-Hunter, MovGP0, Colonies Chris, Tekhnoend, Timothy Clemans, Nima Baghaei, Voyajer, Decltype, DRLB, G716, Jbergquist, Vina-iwbot, Joc, RNLion, Lambiam, OliverTwist, DA3N, Kuru, FrozenMan, Michael miceli, Jim.belk, Syrcatbot, Rev-san, Dicklyon, Mets501,NJA, Ryulong, Blokkendoos, Hu12, Rory O'Kane, KlaudiuMihaila, Mikay, Courcelles, Myncknm, DonkeyKong64, CRGreathouse, Ma-keemlighter, CBM, Jokes Free4Me, ShelfSkewed, Imaginationac, WeggeBot, Makuabob, Gregbard, AndrewHowse, Gremagor, Future Per-fect at Sunrise, WillowW, Alvesgaspar, HumbleGod, Julian Mendez, Alaibot, Davidhof, Thijs!bot, Epbr123, RobHar, NocNokNeo, Navi-gatr85, Mmortal03, Edokter, Random user 8384993, Jrw@pobox.com, JAnDbot, Mckee, .anacondabot, Acroterion, Puellanivis, VoABotII, Vanish2, Strange but untrue, JanGB, Hekerui, EagleFan, Mfhall, Hbent, Momojeng, MartinBot, Ulf Karlsson, Church of emacs, Xan-tolus, R'n'B, Thr4wn, Maurice Carbonaro, 12jbooher, Aqwis, IdLoveOne, Mikael Hggstrm, Belovedfreak, Kraftlos, Fylwind, Squidsand Chips, VolkovBot, Pasixxxx, Bwholm, JohnBlackburne, LokiClock, DoorsAjar, TXiKiBoT, Red Act, Anonymous Dissident, Simon-leyton, PaulTanenbaum, Greswik, Redacteur, Pfoifry, Sue Rangell, Nosferattr, Saom, Tresiden, Yonideworst, Triwbe, Jadony, Flyer22,Paolo.dL, MiNombreDeGuerra, Thehotelambush, Quief, MagicalPhats, Capitalismojo, Mygerardromance, Denisarona, Francvs, Iceera88,Loren.wilton, ClueBot, Rumping, Justin W Smith, Alksentrs, Jan1nad, Hult041956, P0mbal, ColinHelvensteijn, Niceguyedc, Psource,Lohray, Ybenharim, NuclearWarfare, Computer97, SoHome, Tanthanyes, Super-c-sharp, XLinkBot, Pierzz, SEoF, WikHead, Silvonen-Bot, N3rd4i, Wyatt915, Addbot, Some jerk on the Internet, Ronhjones, CanadianLinuxUser, Leszek Jaczuk, LaaknorBot, LinkFA-Bot,Bob K31416, Qmark42, OlEnglish, , Legobot, Yobot, Gowdasathish, Victoriaearle, Mmxx, Writer on wiki, AnomieBOT,Jkmaloo, Jim1138, Abshirdheere, Materialscientist, 90 Auto, Citation bot, Obersachsebot, Xqbot, Maxcyber10, Quintus314, Alumnum,Quartl, Thehelpfulbot, FrescoBot, LucienBOT, Lagelspeil, Knowandgive, QoppaGamma, Citation bot 1, Intelligentsium, Tkuvho, I dreamof horses, Jonesey95, RedBot, Flinx, Pokepal101, Cnwilliams, ItsZippy, Yunesj, Innotata, Israel.cma, DARTH SIDIOUS 2, Jowa fan,Deagle AP, Alison22, DASHBot, EmausBot, Ashleycocks, Wikipelli, ZroBot, Josve05a, NicatronTg, , Fixblor,Bamyers99, Quondum, Toshio Yamaguchi, Chewings72, Scientic29, Liuthar, Petrb, ClueBot NG, BOMBINI, Wcherowi, MelbourneS-tar, Raghith, Satellizer, Nilkanthvns, half-moon bubba, Special+Utilizator+$, Widr, Emmse12345, FMax, Scott776, Nobletripe, Vibhi-jain, Helpful Pixie Bot, Dave R Barton, Ignacitum, Lowercase sigmabot, BG19bot, ISTB351, MusikAnimal, J991, BenGliterate, Mattle-gend6, Heisler.thomas, N01b33tr, , Lukozade guy, Letsbeends, Ssbbplayer, Eptied, Lugia2453, Guest 9, Therealkalio, TheMol Man, Bobyjoyride, Epicgenius, JMCF125, Tentinator, Babitaarora, RazWiki, Erikag55, Impsswoon, Sbyru, Esquivalience, Jonnysg,Gmalaven1008, Pototanon 2015, Bilbo44tothe9 and Anonymous: 459

12.2 Images

12.3 Content license Creative Commons Attribution-Share Alike 3.0

GuideBasic symbolsSymbols based on equality signSymbols that point left or rightBracketsOther non-letter symbolsLetter-based symbolsLetter modifiersSymbols based on Latin lettersSymbols based on Hebrew or Greek letters

VariationsSee alsoReferencesExternal linksText and image sources, contributors, and licensesTextImagesContent license