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Mathematical Operators

U+2200 – U+22FF   (8704–8959)

The plus sign (43) is in the Basic Latin range; the plus-minus sign (177), multiplication sign (215) and the division sign (247) are in the Latin-1 Supplement range. Characters 8706, 8710, 8719, 8721, 8722, 8725, 8729, 8730, 8734, 8735, 8745, 8747, 8776, 8800, 8801, 8804 and 8805 are present in Microsoft’s WGL4 character set. Characters 8706, 8710, 8719, 8721, 8730, 8734, 8747, 8776, 8800, 8804 and 8805 provide Unicode equivalents for some of the characters in Apple’s MacRoman character set.

This range provides Unicode equivalents for some of the characters in Monotype’s Symbol font. Other mathematical operators can be found in the Supplemental Mathematical Operators range.

The characters that appear in the first column of the following table depend on the browser that you are using, the fonts installed on your computer, and the browser options you have chosen that determine the fonts used to display particular character sets, encodings or languages. The entries in the “Entity” column are character entity references that can be used in HTML pages.

You can find some or all of the characters in this range in the Windows Unicode fonts Alexander, Alfios, Alkaios, ALPHABETUM Unicode, Anaktoria, Andale Mono (few), Andika Basic, AR PL ShanHeiSun Uni, AR PL ZenKai Uni, Arev Sans, Arial, Arial Unicode MS, Aroania, Atavyros, AttikaU, Avdira, BabelStone Han, Baekmuk Batang, Baekmuk Dotum, Baekmuk Gulim, Baekmuk Headline, Batang, BatangChe, Berling Antiqua, BosporosU, BPG Paata Khutsuri U, Calibri, Cambria Math, Candara, Cardo, Caslon, Century, Chandas, Charis SIL, Chrysanthi Unicode, CN-Arial, CN-Times, Code2000, Consolas, Constantia, Corbel, Courier MonoThai, Courier New, DejaVu Sans, DejaVu Sans Condensed, DejaVu Sans Mono, DejaVu Serif, DejaVu Serif Condensed, Dialekt Uni, Doulos SIL, e-PhonTranslit UNI, EversonMono, Fixedsys Excelsior, FMBF Bardi, Free Idg Serif, Free Monospaced, Free Sans, Free Serif, Frutiger Linotype, Gandhari Unicode (few), Garava, Georgia (few), GFS Bodoni, GFS Didot, GFS Neohellenic, Gulim Che, Gungsuh, GungsuhChe, HAN NOM A, HAN NOM B, Hindsight Unicode, HY Shin Myeongjo Std Acro, Impact, jGaramond, Jomolhari, Junicode, KadmosU, Khmer OS, Khmer OS Fasthand, Khmer OS Freehand, Khmer OS Metal Chrieng, Khmer OS Muol, Khmer OS System, Kidprint, Kliment Std, Kochi Gothic, Kochi Mincho, Kozuka Mincho Pro Acro, LeedsUni, Legendum, Linux Biolinum O, Linux Libertine O, Lucida Bright, Lucida Grande, Lucida Sans, Lucida Sans Typewriter, Lucida Console (few), Lucida Sans Unicode, Malgun Gothic, Marin, MD King KhammuRabi, MgOpen Canonica, Microsoft Sans Serif, Ming(for ISO10646), MingLiU, MingLiU_HKSCS, Minion Pro, Monospace, MPH 2B Damase, MS Gothic, MS Mincho, MS PGothic, MS PMincho, MS Reference Sans Serif, MS Reference Serif, MS UI Gothic, MSung Std Acro, MyMyanmar, Myriad Pro, New Athena Unicode, New Gulim, NSimSun, NSimSun-18030, OpenSymbol, PakType Naqsh, Palatino Linotype, ParabaikSans, PMingLiU, Quivira, Reader Sans, RomanCyrillic Std, Roman Unicode, Rupakara (few), Sazanami Gothic, Sazanami Mincho, Segoe Print, Segoe Script, Segoe UI, SimHei, SImPL, SimSun, SimSun-18030, sixpack, Sophia Nubian (few), StarSymbol, STIXGeneral, STSong Std Acro, Sun-ExtA, Symbola, Tahoma (few), Tibetan Machine Uni, Times New Roman, TITUS Cyberbit Basic, Trebuchet MS (few), TSC FMing S TT, TSC JSong S TT, UnBatang, UniBurma, Uttara (few), Verajja, Verdana, WenQuanYi Zen Hei, WenQuanYi Zen Hei Mono, XTashi, YOzFontN and Zawgyi-One (few); in the Macintosh OS 9 Unicode fonts Apple Chancery, AppleGothic, Apple LiGothic, Apple LiSung, AppleMyungjo, Beijing, BiauKai, Capitals, Charcoal, Charcoal CE, Chicago, Chicago CE, ChuGothic, Courier, Courier CE, Fang Song, Gadget, Geneva, Geneva CE, Gungseouche, Hei, HeiseiKakuGothic, HeiseiMincho, Helvetica, Helvetica CE, Hoefler Text, Kai, Monaco, Monaco CE, New York, Osaka, Osaka-Mono, Palatino, Palatino CE, Pilgiche, Sand, SaiMincho, Seoul, Skia, Song, Tahoma, Taipei, Techno, Texile, Times and Times CE; in the Macintosh OS X Unicode fonts Alkaios, AppleGothic, Apple LiGothic, Apple LiSung, AppleMyungjo, Apple Symbols, Arial, Ayuthya, Batang, Beijing, BiauKai, Century, Chalkboard, Charcoal, Chicago, Courier, Didot, Fang Song, Futura, Geneva, #GothicMedium, Gulim, #GungSeo, Hangang, Hei, Helvetica, Hiragino Kaku Gothic Pro, Hiragino Kaku Gothic Std, Hiragino Maru Gothic Pro, Hiragino Mincho Pro, Junicode, Kai, Krungthep, Lucida Grande, Monaco, MS Gothic, MS Mincho, MS PGothic, MS PMincho, #MyungjoNeue, New Athena Unicode, New York, Osaka, Osaka-Mono, #PCMyungjo, #PilGi, PMingLiU, Sand, Sathu, Seoul, Silom, SimSun, Skia, Song, STFangsong, STHeiti, STKaiti, STSong, Symbol, #TaeGraphic, Taipei, TektonPro, Thonburi, Times, Times New Roman, Trebuchet MS, Verdana, Zapfino and Zuzumbo; and in the Unix Unicode font Caslon.

To see exactly which characters are included in a particular font, you can use a utility such as Andrew West’s BabelMap, Apple’s TrueEdit, or WunderMoosen’s FontChecker.

If you are not familiar with the characters, you can check the characters displayed here with the graphical display at http://www.unicode.org/charts/PDF/U2200.pdf.

Character
(decimal)
DecimalCharacter
(hex)
HexEntityName
87042200∀FOR ALL   (present in Symbol font)
87052201 COMPLEMENT
87062202∂PARTIAL DIFFERENTIAL   (present in WGL4, in MacRoman, and in Symbol font)
87072203∃THERE EXISTS   (present in Symbol font)
87082204 THERE DOES NOT EXIST
87092205∅EMPTY SET   (present in Symbol font)
87102206 INCREMENT   (present in WGL4 and in MacRoman)
87112207∇NABLA   (present in Symbol font)
87122208∈ELEMENT OF   (present in Symbol font)
87132209∉NOT AN ELEMENT OF   (present in Symbol font)
8714220A SMALL ELEMENT OF
8715220B∋CONTAINS AS MEMBER
8716220C DOES NOT CONTAIN AS MEMBER
8717220D SMALL CONTAINS AS MEMBER   (present in Symbol font)
8718220E END OF PROOF
8719220F∏N-ARY PRODUCT   (present in WGL4, in MacRoman, and in Symbol font)
87202210 N-ARY COPRODUCT
87212211∑N-ARY SUMMATION   (present in WGL4, in MacRoman, and in Symbol font)
87222212−MINUS SIGN   (present in WGL4 and in Symbol font)
87232213 MINUS-OR-PLUS SIGN
87242214 DOT PLUS
87252215 DIVISION SLASH   (present in WGL4)
87262216 SET MINUS
87272217∗ASTERISK OPERATOR   (present in Symbol font)
87282218 RING OPERATOR
87292219 BULLET OPERATOR   (present in WGL4 and in Symbol font)
8730221A√SQUARE ROOT   (present in WGL4, in MacRoman, and in Symbol font)
8731221B CUBE ROOT
8732221C FOURTH ROOT
8733221D∝PROPORTIONAL TO   (present in Symbol font)
8734221E∞INFINITY   (present in WGL4, in MacRoman, and in Symbol font)
8735221F RIGHT ANGLE   (present in WGL4)
87362220∠ANGLE   (present in Symbol font)
87372221 MEASURED ANGLE
87382222 SPHERICAL ANGLE
87392223 DIVIDES
87402224 DOES NOT DIVIDE
87412225 PARALLEL TO
87422226 NOT PARALLEL TO
87432227∧LOGICAL AND   (present in Symbol font)
87442228∨LOGICAL OR   (present in Symbol font)
87452229∩INTERSECTION   (present in WGL4 and in Symbol font)
8746222A∪UNION   (present in Symbol font)
8747222B∫INTEGRAL   (present in WGL4, in MacRoman, and in Symbol font)
8748222C DOUBLE INTEGRAL
8749222D TRIPLE INTEGRAL
8750222E CONTOUR INTEGRAL
8751222F SURFACE INTEGRAL
87522230 VOLUME INTEGRAL
87532231 CLOCKWISE INTEGRAL
87542232 CLOCKWISE CONTOUR INTEGRAL
87552233 ANTICLOCKWISE CONTOUR INTEGRAL
87562234∴THEREFORE   (present in Symbol font)
87572235 BECAUSE
87582236 RATIO
87592237 PROPORTION
87602238 DOT MINUS
87612239 EXCESS
8762223A GEOMETRIC PROPORTION
8763223B HOMOTHETIC
8764223C∼TILDE OPERATOR   (present in Symbol font)
8765223D REVERSED TILDE
8766223E INVERTED LAZY S
8767223F SINE WAVE
87682240 WREATH PRODUCT
87692241 NOT TILDE
87702242 MINUS TILDE
87712243 ASYMPTOTICALLY EQUAL TO
87722244 NOT ASYMPTOTICALLY EQUAL TO
87732245≅APPROXIMATELY EQUAL TO   (present in Symbol font)
87742246 APPROXIMATELY BUT NOT ACTUALLY EQUAL TO
87752247 NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
87762248≈ALMOST EQUAL TO   (present in WGL4, in MacRoman, and in Symbol font)
87772249 NOT ALMOST EQUAL TO
8778224A ALMOST EQUAL OR EQUAL TO
8779224B TRIPLE TILDE
8780224C ALL EQUAL TO
8781224D EQUIVALENT TO
8782224E GEOMETRICALLY EQUIVALENT TO
8783224F DIFFERENCE BETWEEN
87842250 APPROACHES THE LIMIT
87852251 GEOMETRICALLY EQUAL TO
87862252 APPROXIMATELY EQUAL TO OR THE IMAGE OF
87872253 IMAGE OF OR APPROXIMATELY EQUAL TO
87882254 COLON EQUALS
87892255 EQUALS COLON
87902256 RING IN EQUAL TO
87912257 RING EQUAL TO
87922258 CORRESPONDS TO
87932259 ESTIMATES
8794225A EQUIANGULAR TO
8795225B STAR EQUALS
8796225C DELTA EQUAL TO
8797225D EQUAL TO BY DEFINITION
8798225E MEASURED BY
8799225F QUESTIONED EQUAL TO
88002260≠NOT EQUAL TO   (present in WGL4, in MacRoman, and in Symbol font)
88012261≡IDENTICAL TO   (present in WGL4 and in Symbol font)
88022262 NOT IDENTICAL TO
88032263 STRICTLY EQUIVALENT TO
88042264≤LESS-THAN OR EQUAL TO   (present in WGL4, in MacRoman, and in Symbol font)
88052265≥GREATER-THAN OR EQUAL TO   (present in WGL4, in MacRoman, and in Symbol font)
88062266 LESS-THAN OVER EQUAL TO
88072267 GREATER-THAN OVER EQUAL TO
88082268 LESS-THAN BUT NOT EQUAL TO
88092269 GREATER-THAN BUT NOT EQUAL TO
8810226A MUCH LESS-THAN
8811226B MUCH GREATER-THAN
8812226C BETWEEN
8813226D NOT EQUIVALENT TO
8814226E NOT LESS-THAN
8815226F NOT GREATER-THAN
88162270 NEITHER LESS-THAN NOR EQUAL TO
88172271 NEITHER GREATER-THAN NOR EQUAL TO
88182272 LESS-THAN OR EQUIVALENT TO
88192273 GREATER-THAN OR EQUIVALENT TO
88202274 NEITHER LESS-THAN NOR EQUIVALENT TO
88212275 NEITHER GREATER-THAN NOR EQUIVALENT TO
88222276 LESS-THAN OR GREATER-THAN
88232277 GREATER-THAN OR LESS-THAN
88242278 NEITHER LESS-THAN NOR GREATER-THAN
88252279 NEITHER GREATER-THAN NOR LESS-THAN
8826227A PRECEDES
8827227B SUCCEEDS
8828227C PRECEDES OR EQUAL TO
8829227D SUCCEEDS OR EQUAL TO
8830227E PRECEDES OR EQUIVALENT TO
8831227F SUCCEEDS OR EQUIVALENT TO
88322280 DOES NOT PRECEDE
88332281 DOES NOT SUCCEED
88342282⊂SUBSET OF   (present in Symbol font)
88352283⊃SUPERSET OF   (present in Symbol font)
88362284⊄NOT A SUBSET OF   (present in Symbol font)
88372285 NOT A SUPERSET OF
88382286⊆SUBSET OF OR EQUAL TO   (present in Symbol font)
88392287⊇SUPERSET OF OR EQUAL TO   (present in Symbol font)
88402288 NEITHER A SUBSET OF NOR EQUAL TO
88412289 NEITHER A SUPERSET OF NOR EQUAL TO
8842228A SUBSET OF WITH NOT EQUAL TO
8843228B SUPERSET OF WITH NOT EQUAL TO
8844228C MULTISET
8845228D MULTISET MULTIPLICATION
8846228E MULTISET UNION
8847228F SQUARE IMAGE OF
88482290 SQUARE ORIGINAL OF
88492291 SQUARE IMAGE OF OR EQUAL TO
88502292 SQUARE ORIGINAL OF OR EQUAL TO
88512293 SQUARE CAP
88522294 SQUARE CUP
88532295⊕CIRCLED PLUS   (present in Symbol font)
88542296 CIRCLED MINUS
88552297⊗CIRCLED TIMES   (present in Symbol font)
88562298 CIRCLED DIVISION SLASH
88572299 CIRCLED DOT OPERATOR
8858229A CIRCLED RING OPERATOR
8859229B CIRCLED ASTERISK OPERATOR
8860229C CIRCLED EQUALS
8861229D CIRCLED DASH
8862229E SQUARED PLUS
8863229F SQUARED MINUS
886422A0 SQUARED TIMES
886522A1 SQUARED DOT OPERATOR
886622A2 RIGHT TACK
886722A3 LEFT TACK
886822A4 DOWN TACK
886922A5⊥UP TACK   (present in Symbol font)
887022A6 ASSERTION
887122A7 MODELS
887222A8 TRUE
887322A9 FORCES
887422AA TRIPLE VERTICAL BAR RIGHT TURNSTILE
887522AB DOUBLE VERTICAL BAR DOUBLE RIGHT TURNSTILE
887622AC DOES NOT PROVE
887722AD NOT TRUE
887822AE DOES NOT FORCE
887922AF NEGATED DOUBLE VERTICAL BAR DOUBLE RIGHT TURNSTILE
888022B0 PRECEDES UNDER RELATION
888122B1 SUCCEEDS UNDER RELATION
888222B2 NORMAL SUBGROUP OF
888322B3 CONTAINS AS NORMAL SUBGROUP
888422B4 NORMAL SUBGROUP OF OR EQUAL TO
888522B5 CONTAINS AS NORMAL SUBGROUP OR EQUAL TO
888622B6 ORIGINAL OF
888722B7 IMAGE OF
888822B8 MULTIMAP
888922B9 HERMITIAN CONJUGATE MATRIX
889022BA INTERCALATE
889122BB XOR
889222BC NAND
889322BD NOR
889422BE RIGHT ANGLE WITH ARC
889522BF RIGHT TRIANGLE
889622C0 N-ARY LOGICAL AND
889722C1 N-ARY LOGICAL OR
889822C2 N-ARY INTERSECTION
889922C3 N-ARY UNION
890022C4 DIAMOND OPERATOR
890122C5⋅DOT OPERATOR   (present in Symbol font)
890222C6 STAR OPERATOR
890322C7 DIVISION TIMES
890422C8 BOWTIE
890522C9 LEFT NORMAL FACTOR SEMIDIRECT PRODUCT
890622CA RIGHT NORMAL FACTOR SEMIDIRECT PRODUCT
890722CB LEFT SEMIDIRECT PRODUCT
890822CC RIGHT SEMIDIRECT PRODUCT
890922CD REVERSED TILDE EQUALS
891022CE CURLY LOGICAL OR
891122CF CURLY LOGICAL AND
891222D0 DOUBLE SUBSET
891322D1 DOUBLE SUPERSET
891422D2 DOUBLE INTERSECTION
891522D3 DOUBLE UNION
891622D4 PITCHFORK
891722D5 EQUAL AND PARALLEL TO
891822D6 LESS-THAN WITH DOT
891922D7 GREATER-THAN WITH DOT
892022D8 VERY MUCH LESS-THAN
892122D9 VERY MUCH GREATER-THAN
892222DA LESS-THAN EQUAL TO OR GREATER-THAN
892322DB GREATER-THAN EQUAL TO OR LESS-THAN
892422DC EQUAL TO OR LESS-THAN
892522DD EQUAL TO OR GREATER-THAN
892622DE EQUAL TO OR PRECEDES
892722DF EQUAL TO OR SUCCEEDS
892822E0 DOES NOT PRECEDE OR EQUAL
892922E1 DOES NOT SUCCEED OR EQUAL
893022E2 NOT SQUARE IMAGE OF OR EQUAL TO
893122E3 NOT SQUARE ORIGINAL OF OR EQUAL TO
893222E4 SQUARE IMAGE OF OR NOT EQUAL TO
893322E5 SQUARE ORIGINAL OF OR NOT EQUAL TO
893422E6 LESS-THAN BUT NOT EQUIVALENT TO
893522E7 GREATER-THAN BUT NOT EQUIVALENT TO
893622E8 PRECEDES BUT NOT EQUIVALENT TO
893722E9 SUCCEEDS BUT NOT EQUIVALENT TO
893822EA NOT NORMAL SUBGROUP OF
893922EB DOES NOT CONTAIN AS NORMAL SUBGROUP
894022EC NOT NORMAL SUBGROUP OF OR EQUAL TO
894122ED DOES NOT CONTAIN AS NORMAL SUBGROUP OR EQUAL
894222EE VERTICAL ELLIPSIS
894322EF MIDLINE HORIZONTAL ELLIPSIS
894422F0 UP RIGHT DIAGONAL ELLIPSIS
894522F1 DOWN RIGHT DIAGONAL ELLIPSIS
894622F2 ELEMENT OF WITH LONG HORIZONTAL STROKE
894722F3 ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
894822F4 SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
894922F5 ELEMENT OF WITH DOT ABOVE
895022F6 ELEMENT OF WITH OVERBAR
895122F7 SMALL ELEMENT OF WITH OVERBAR
895222F8 ELEMENT OF WITH UNDERBAR
895322F9 ELEMENT OF WITH TWO HORIZONTAL STROKES
895422FA CONTAINS WITH LONG HORIZONTAL STROKE
895522FB CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
895622FC SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
895722FD CONTAINS WITH OVERBAR
895822FE SMALL CONTAINS WITH OVERBAR
895922FF Z NOTATION BAG MEMBERSHIP

Copyright © 1999–2010 Alan Wood

The hexadecimal numbers and the character names in the above table are taken from the Unicode 3.2 Character Database, Copyright © 1991–2002 Unicode, Inc., as contained in UnicodeData.txt on the Unicode Web site (http://www.unicode.org/Public/UNIDATA/) in April 2002.

Created 3rd February 1999   Last updated 7th November 2010

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