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Mathematical Operators

U+2200 – U+22FF   (8704–8959)

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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 ALPHABETUM Unicode, Arial, Arial Unicode MS, Baekmuk Batang, Baekmuk Dotum, Baekmuk Gulim, Baekmuk Headline, Batang, Berling Antiqua, Bitstream CyberBase, Bitstream CyberBit, Bitstream CyberCJK, Cardo, Caslon, CN-Arial, CN-Times, Code2000, Courier MonoThai, Courier New, Free Monospaced, Free Serif, Frutiger Linotype, Gulim Che, HY Shin Myeongjo Std Acro, Junicode, Kidprint, Kozuka Mincho Pro Acro, Lucida Sans, Lucida Sans Typewriter, Lucida Sans Unicode, MD King KhammuRabi, Ming(for ISO10646), Monospace, MS Mincho, MS Reference Sans Serif, MS Reference Serif, MSung Std Acro, Naqsh, New Gulim, OpenSymbol, Palatino Linotype, SILDoulosUnicodeIPA, SimHei, SImPL, SimSun, SimSun-18030, StarSymbol, STSong Std Acro, Times New Roman, TITUS Cyberbit Basic, TSC FMing S TT, TSC JSong S TT, UVN Gia Dinh and UVN Giay Trang; 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 AppleGothic, Apple LiGothic, Apple LiSung, AppleMyungjo, Beijing, BiauKai, Courier, Didot, Everson Mono Unicode, Fang Song, Futura, Geneva, #GothicMedium, #GungSeo, Hangang, Hei, Helvetica, Hiragino Kaku Gothic Pro, Hiragino Kaku Gothic Std, Hiragino Maru Gothic Pro, Hiragino Mincho Pro, Kai, Lucida Grande, Monaco, #MyungjoNeue, Osaka, Osaka-Mono, #PCMyungjo, #PilGi, Skia, Seoul, Song, STFangsong, STHeiti, STKaiti, STSong, Symbol, #TaeGraphic, Taipei, TektonPro, Times, Trebuchet MS and Zapfino; 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, Bjondi’s Character Agent, 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.

CharacterDecimalHexEntityName
∀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
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Copyright © 1999–2003 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 18th June 2003

Send comments or questions to Alan Wood

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