Unicode block mathematical operators

The Unicode block Mathematical Operators (Mathematical operator, U + 2200 to U + 22ff) contains various texts used in mathematical characters , especially symbols of mathematical operators , including in the field of set theory and formal logic .

The block also contains variants of originally non-mathematical symbols that are often used in mathematics and are adapted in the set of formulas to the glyphs of other mathematical symbols, for example the asterisk (U + 002A), which is used here as the mathematical operator (U + 2217) is used.

As with the other Unicode characters for mathematical symbols , the operators have been coded according to their appearance so that a character can be used with different meanings.

There is also the Unicode block Additional mathematical operators .

table

All characters have the general category "Mathematical Symbol". The character U + 2212 has the bidirectional class “European separator”, the character U + 2213 has the class “European final character” and all other characters have the class “other neutral character”.

Unicode number	Characters (400%)	Official name	description
U + 2200 (8704)	∀	FOR ALL	Universal quantifier
U + 2201 (8705)	∁	COMPLEMENT	complement
U + 2202 (8706)	∂	PARTIAL DIFFERENTIAL	Partial differential
U + 2203 (8707)	∃	THERE EXISTS	Existential quantifier
U + 2204 (8708)	∄	THERE DOES NOT EXIST	There is no / there is no
U + 2205 (8709)	∅	EMPTY SET	Empty set
U + 2206 (8710)	∆	INCREMENT	Difference sign ( increment or Laplace operator )
U + 2207 (8711)	∇	NABLA	Nabla
U + 2208 (8712)	∈	ELEMENT OF	Element character
U + 2209 (8713)	∉	NOT AN ELEMENT OF	Non-element characters
U + 220A (8714)	∊	SMALL ELEMENT OF	small element sign
U + 220B (8715)	∋	CONTAINS AS MEMBER	inverted element sign
U + 220C (8716)	∌	DOES NOT CONTAIN AS MEMBER	inverted non-element sign
U + 220D (8717)	∍	SMALL CONTAINS AS MEMBER	small inverted element sign
U + 220E (8718)	∎	END OF PROOF	End of proof
U + 220F (8719)	∏	N-ARY PRODUCT	Product mark
U + 2210 (8720)	∐	N-ARY COPRODUCT	Co-product mark
U + 2211 (8721)	∑	N-ARY SUMMATION	Sum symbol
U + 2212 (8722)	-	MINUS SIGN	Minus sign
U + 2213 (8723)	∓	MINUS-OR-PLUS SIGN	Minus / plus sign
U + 2214 (8724)	∔	DOT PLUS	Plus sign with dot
U + 2215 (8725)	∕	DIVISION SLASH	Division slash
U + 2216 (8726)	∖	SET MINUS	Difference set sign
U + 2217 (8727)	∗	ASTERISK OPERATOR	Star operator (general linkage of a group , Hodge star operator , ...)
U + 2218 (8728)	∘	RING OPERATOR	Ring operator (general linkage of a group, concatenation characters , ...)
U + 2219 (8729)	∙	BULLET OPERATOR	Circle operator
U + 221A (8730)	√	SQUARE ROOT	Square root sign
U + 221B (8731)	∛	CUBE ROOT	Cube root sign
U + 221C (8732)	∜	FOURTH ROOT	fourth root
U + 221D (8733)	∝	PROPORTIONAL TO	Proportionality symbol
U + 221E (8734)	∞	INFINITY	Infinity sign
U + 221F (8735)	∟	RIGHT ANGLE	Right angle
U + 2220 (8736)	∠	ANGLE	Flat angle (math) or position tolerance
U + 2221 (8737)	∡	MEASURED ANGLE	Directional angle (literally 'measured angle')
U + 2222 (8738)	∢	SPHERICAL ANGLE	Solid angle
U + 2223 (8739)	∣	DIVIDES	Splits
U + 2224 (8740)	∤	DOES NOT DIVIDE	does not share
U + 2225 (8741)	∥	PARALLEL TO	parallel to
U + 2226 (8742)	∦	NOT PARALLEL TO	not parallel to
U + 2227 (8743)	∧	LOGICAL AND	logical and
U + 2228 (8744)	∨	LOGICAL OR	logical or
U + 2229 (8745)	∩	INTERSECTION	Intersection sign
U + 222A (8746)	∪	UNION	Union set symbol
U + 222B (8747)	∫	INTEGRAL	Integral sign
U + 222C (8748)	∬	DOUBLE INTEGRAL	double integral sign
U + 222D (8749)	∭	TRIPLE INTEGRAL	triple integral sign
U + 222E (8750)	∮	CONTOUR INTEGRAL	Edge integral sign
U + 222F (8751)	∯	SURFACE INTEGRAL	Surface integral characters
U + 2230 (8752)	∰	VOLUME INTEGRAL	Volume integral sign
U + 2231 (8753)	∱	CLOCKWISE INTEGRAL	Integral clockwise
U + 2232 (8754)	∲	CLOCKWISE CONTOUR INTEGRAL	Curve integral clockwise
U + 2233 (8755)	∳	ANTICLOCKWISE CONTOUR INTEGRAL	Curve integral counterclockwise
U + 2234 (8756)	∴	THEREFORE	consequently
U + 2235 (8757)	∵	BECAUSE	because
U + 2236 (8758)	∶	RATIO	Ratio sign
U + 2237 (8759)	∷	PROPORTION	Proportion sign
U + 2238 (8760)	∸	DOT MINUS	Minus sign with period
U + 2239 (8761)	∹	EXCESS	excess
U + 223A (8762)	∺	GEOMETRIC PROPORTION	geometric proportion
U + 223B (8763)	∻	HOMOTHETIC	Homothetie sign
U + 223C (8764)	∼	TILDE OPERATOR	Tile operator
U + 223D (8765)	∽	REVERSED TILDE	reverse tilde
U + 223E (8766)	∾	INVERTED LAZY S	inverted mute S
U + 223F (8767)	∿	SINE WAVE	Sine wave
U + 2240 (8768)	≀	WREATH PRODUCT	Wreath product
U + 2241 (8769)	≁	NOT TILDE	crossed out tilde
U + 2242 (8770)	≂	MINUS TILDE	Minuses about tilde
U + 2243 (8771)	≃	ASYMPTOTICALLY EQUAL TO	asymptotically equal
U + 2244 (8772)	≄	NOT ASYMPTOTICALLY EQUAL TO	not asymptotically equal
U + 2245 (8773)	≅	APPROXIMATELY EQUAL TO	about the same
U + 2246 (8774)	≆	APPROXIMATELY BUT NOT ACTUALLY EQUAL TO	roughly, but not exactly the same
U + 2247 (8775)	≇	NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO	neither roughly nor exactly the same
U + 2248 (8776)	≈	ALMOST EQUAL TO	almost equal
U + 2249 (8777)	≉	NOT ALMOST EQUAL TO	not almost the same
U + 224A (8778)	≊	ALMOST EQUAL OR EQUAL TO	almost the same or the same
U + 224B (8779)	≋	TRIPLE TILDE	triple tilde
U + 224C (8780)	≌	ALL EQUAL TO	all the same
U + 224D (8781)	≍	EQUIVALENT TO	equivalent to
U + 224E (8782)	≎	GEOMETRICALLY EQUIVALENT TO	geometrically equivalent
U + 224F (8783)	≏	DIFFERENCE BETWEEN	Difference between
U + 2250 (8784)	≐	APPROACHES THE LIMIT	Limit value approximation
U + 2251 (8785)	≑	GEOMETRICALLY EQUAL TO	geometrically the same
U + 2252 (8786)	≒	APPROXIMATELY EQUAL TO OR THE IMAGE OF	about the same or picture of
U + 2253 (8787)	≓	IMAGE OF OR APPROXIMATELY EQUAL TO	Picture or about the same
U + 2254 (8788)	≔	COLON EQUALS	Equal sign preceded by a colon (definition sign)
U + 2255 (8789)	≕	EQUALS COLON	Equal sign followed by a colon
U + 2256 (8790)	≖	RING IN EQUAL TO	Circle in the equal sign
U + 2257 (8791)	≗	RING EQUAL TO	Circle over equal sign (roughly equal)
U + 2258 (8792)	≘	CORRESPONDS TO	Equivalent sign (uncommon)
U + 2259 (8793)	≙	ESTIMATES	corresponds
U + 225A (8794)	≚	EQUIANGULAR TO	equiangular
U + 225B (8795)	≛	STAR EQUALS	Equal sign with a star
U + 225C (8796)	≜	DELTA EQUAL TO	Equal sign with delta
U + 225D (8797)	≝	EQUAL TO BY DEFINITION	right by definition
U + 225E (8798)	≞	MEASURED BY	measured according to
U + 225F (8799)	≟	QUESTIONED EQUAL TO	maybe right away
U + 2260 (8800)	≠	NOT EQUAL TO	Un equal sign
U + 2261 (8801)	≡	IDENTICAL TO	is congruent to
U + 2262 (8802)	≢	NOT IDENTICAL TO	is not congruent to
U + 2263 (8803)	≣	STRICTLY EQUIVALENT TO	exactly equivalent
U + 2264 (8804)	≤	LESS-THAN OR EQUAL TO	less than / equal
U + 2265 (8805)	≥	GREATER-THAN OR EQUAL TO	greater or equal
U + 2266 (8806)	≦	LESS-THAN OVER EQUAL TO	less than about equal
U + 2267 (8807)	≧	GREATER-THAN OVER EQUAL TO	greater than about equal
U + 2268 (8808)	≨	LESS-THAN BUT NOT EQUAL TO	less than, but not equal to
U + 2269 (8809)	≩	GREATER-THAN BUT NOT EQUAL TO	greater than, but not equal to
U + 226A (8810)	≪	MUCH LESS-THAN	much smaller than
U + 226B (8811)	≫	MUCH GREATER-THAN	much bigger than
U + 226C (8812)	≬	BETWEEN	between
U + 226D (8813)	≭	NOT EQUIVALENT TO	not equivalent
U + 226E (8814)	≮	NOT LESS-THAN	is not less than
U + 226F (8815)	≯	NOT GREATER-THAN	is not greater than
U + 2270 (8816)	≰	NEITHER LESS-THAN NOR EQUAL TO	neither less than nor equal
U + 2271 (8817)	≱	NEITHER GREATER-THAN NOR EQUAL TO	neither greater than nor equal
U + 2272 (8818)	≲	LESS-THAN OR EQUIVALENT TO	less than or equivalent
U + 2273 (8819)	≳	GREATER-THAN OR EQUIVALENT TO	greater than or equivalent
U + 2274 (8820)	≴	NEITHER LESS-THAN NOR EQUIVALENT TO	neither less than nor equivalent
U + 2275 (8821)	≵	NEITHER GREATER-THAN NOR EQUIVALENT TO	neither greater than nor equivalent
U + 2276 (8822)	≶	LESS-THAN OR GREATER-THAN	smaller / larger than
U + 2277 (8823)	≷	GREATER-THAN OR LESS-THAN	greater / less than
U + 2278 (8824)	≸	NEITHER LESS-THAN NOR GREATER-THAN	neither smaller nor larger than
U + 2279 (8825)	≹	NEITHER GREATER-THAN NOR LESS-THAN	neither greater nor less than
U + 227A (8826)	≺	PRECEDES	previous
U + 227B (8827)	≻	SUCCEEDS	below
U + 227C (8828)	≼	PRECEDES OR EQUAL TO	previous or equal
U + 227D (8829)	≽	SUCCEEDS OR EQUAL TO	subsequent or equal
U + 227E (8830)	≾	PRECEDES OR EQUIVALENT TO	preceding or equivalent
U + 227F (8831)	≿	SUCCEEDS OR EQUIVALENT TO	subsequent or equivalent
U + 2280 (8832)	⊀	DOES NOT PRECEDE	not preceding
U + 2281 (8833)	⊁	DOES NOT SUCCEED	not following
U + 2282 (8834)	⊂	SUBSET OF	is (real) subset of
U + 2283 (8835)	⊃	SUPERSET OF	is (real) superset of
U + 2284 (8836)	⊄	NOT A SUBSET OF	is not a (real) subset of
U + 2285 (8837)	⊅	NOT A SUPERSET OF	is not a (true) superset of
U + 2286 (8838)	⊆	SUBSET OF OR EQUAL TO	Subset or equal
U + 2287 (8839)	⊇	SUPERSET OF OR EQUAL TO	Superset or equal
U + 2288 (8840)	⊈	NEITHER A SUBSET OF NOR EQUAL TO	neither subset nor equal
U + 2289 (8841)	⊉	NEITHER A SUPERSET OF NOR EQUAL TO	neither superset nor equal
U + 228A (8842)	⊊	SUBSET OF WITH NOT EQUAL TO	Subset with unequal
U + 228B (8843)	⊋	SUPERSET OF WITH NOT EQUAL TO	Superset with unequal
U + 228C (8844)	⊌	MULTISET	Multiset
U + 228D (8845)	⊍	MULTISET MULTIPLICATION	Multi-set multiplication
U + 228E (8846)	⊎	MULTISET UNION	Multi-set union
U + 228F (8847)	⊏	SQUARE IMAGE OF	square picture
U + 2290 (8848)	⊐	SQUARE ORIGINAL OF	square original
U + 2291 (8849)	⊑	SQUARE IMAGE OF OR EQUAL TO	square picture or the same
U + 2292 (8850)	⊒	SQUARE ORIGINAL OF OR EQUAL TO	square original or the same
U + 2293 (8851)	⊓	SQUARE CAP	rectangle open downwards
U + 2294 (8852)	⊔	SQUARE CUP	rectangle open at the top
U + 2295 (8853)	⊕	CIRCLED PLUS	circled plus sign
U + 2296 (8854)	⊖	CIRCLED MINUS	circled minus sign
U + 2297 (8855)	⊗	CIRCLED TIMES	circled multiplication sign
U + 2298 (8856)	⊘	CIRCLED DIVISION SLASH	circled division line
U + 2299 (8857)	⊙	CIRCLED DOT OPERATOR	circled point operator
U + 229A (8858)	⊚	CIRCLED RING OPERATOR	circled ring operator
U + 229B (8859)	⊛	CIRCLED ASTERISK OPERATOR	circled star operator
U + 229C (8860)	⊜	CIRCLED EQUALS	circled equal sign
U + 229D (8861)	⊝	CIRCLED DASH	circled dash
U + 229E (8862)	⊞	SQUARED PLUS	framed plus sign
U + 229F (8863)	⊟	SQUARED MINUS	framed minus sign
U + 22A0 (8864)	⊠	SQUARED TIMES	framed multiplication sign
U + 22A1 (8865)	⊡	SQUARED DOT OPERATOR	framed point operator
U + 22A2 (8866)	⊢	RIGHT TACK	results
U + 22A3 (8867)	⊣	LEFT TACK	does not result
U + 22A4 (8868)	⊤	DOWN TACK	perpendicular from
U + 22A5 (8869)	⊥	UP TACK	perpendicular to
U + 22A6 (8870)	⊦	ASSERTION	Assertion
U + 22A7 (8871)	⊧	MODELS	Models
U + 22A8 (8872)	⊨	TRUE	true
U + 22A9 (8873)	⊩	FORCES	force
U + 22AA (8874)	⊪	TRIPLE VERTICAL BAR RIGHT GYM	triple vertical bar with right turnstile
U + 22AB (8875)	⊫	DOUBLE VERTICAL BAR DOUBLE RIGHT GYM	double vertical bar with double right turnstile
U + 22AC (8876)	⊬	DOES NOT PROVE	does not prove
U + 22AD (8877)	⊭	NOT TRUE	Is not it
U + 22AE (8878)	⊮	DOES NOT FORCE	do not force
U + 22AF (8879)	⊯	NEGATED DOUBLE VERTICAL BAR DOUBLE RIGHT GYM	negated double vertical bar with double right turnstile
U + 22B0 (8880)	⊰	PRECEDES UNDER RELATION	previous in relation
U + 22B1 (8881)	⊱	SUCCEEDS UNDER RELATION	below in relation
U + 22B2 (8882)	⊲	NORMAL SUBGROUP OF	normal subgroup
U + 22B3 (8883)	⊳	CONTAINS AS NORMAL SUBGROUP	included as a normal subgroup
U + 22B4 (8884)	⊴	NORMAL SUBGROUP OF OR EQUAL TO	normal subgroup or equal
U + 22B5 (8885)	⊵	CONTAINS AS NORMAL SUBGROUP OR EQUAL TO	contained as a normal subgroup or equal
U + 22B6 (8886)	⊶	ORIGINAL OF	original
U + 22B7 (8887)	⊷	IMAGE OF	image
U + 22B8 (8888)	⊸	MULTIMAP	Multiple assignment
U + 22B9 (8889)	⊹	HERMITIAN CONJUGATE MATRIX	Hermitian conjugated matrix
U + 22BA (8890)	⊺	INTERCALATE	turn on
U + 22BB (8891)	⊻	XOR	Exclusive or
U + 22BC (8892)	⊼	NAND	Nand-linked with
U + 22BD (8893)	⊽	NOR	Nor
U + 22BE (8894)	⊾	RIGHT ANGLE WITH ARC	right angle with arch
U + 22BF (8895)	⊿	RIGHT TRIANGLE	right triangle
U + 22C0 (8896)	⋀	N-ARY LOGICAL AND	N-level logical and
U + 22C1 (8897)	⋁	N-ARY LOGICAL OR	N-ary logical or
U + 22C2 (8898)	⋂	N-ARY INTERSECTION	N-grade average
U + 22C3 (8899)	⋃	N-ARY UNION	N-ary union
U + 22C4 (8900)	⋄	DIAMOND OPERATOR	Diamond operator
U + 22C5 (8901)	⋅	DOT OPERATOR	Multiplication point
U + 22C6 (8902)	⋆	STAR OPERATOR	Star operator
U + 22C7 (8903)	⋇	DIVISION TIMES	Number of divisions
U + 22C8 (8904)	⋈	BOWTIE	loop
U + 22C9 (8905)	⋉	LEFT NORMAL FACTOR SEMIDIRECT PRODUCT	left semi-direct product (normal factor)
U + 22CA (8906)	⋊	RIGHT NORMAL FACTOR SEMIDIRECT PRODUCT	right semi-direct product (normal factor)
U + 22CB (8907)	⋋	LEFT SEMIDIRECT PRODUCT	left semi-direct product
U + 22CC (8908)	⋌	RIGHT SEMIDIRECT PRODUCT	right semi-direct product
U + 22CD (8909)	⋍	REVERSED TILDE EQUALS	reverse tilde equal
U + 22CE (8910)	⋎	CURLY LOGICAL OR	curly logical or
U + 22CF (8911)	⋏	CURLY LOGICAL AND	curly logical and
U + 22D0 (8912)	⋐	DOUBLE SUBSET	double subset
U + 22D1 (8913)	⋑	DOUBLE SUPERSET	double superset
U + 22D2 (8914)	⋒	DOUBLE INTERSECTION	double average
U + 22D3 (8915)	⋓	DOUBLE UNION	double union
U + 22D4 (8916)	⋔	PITCHFORK	real average
U + 22D5 (8917)	⋕	EQUAL AND PARALLEL TO	equal and parallel (similar to the double cross )
U + 22D6 (8918)	⋖	LESS-THAN WITH DOT	smaller than with point
U + 22D7 (8919)	⋗	GREATER-THAN WITH DOT	bigger than with point
U + 22D8 (8920)	⋘	VERY MUCH LESS-THAN	Much smaller than
U + 22D9 (8921)	⋙	VERY MUCH GREATER-THAN	much larger than
U + 22DA (8922)	⋚	LESS-THAN EQUAL TO OR GREATER-THAN	less than, equal to or greater than
U + 22DB (8923)	⋛	GREATER-THAN EQUAL TO OR LESS-THAN	greater than, equal to or less than
U + 22DC (8924)	⋜	EQUAL TO OR LESS-THAN	equal to or less than
U + 22DD (8925)	⋝	EQUAL TO OR GREATER-THAN	equal to or greater than
U + 22DE (8926)	⋞	EQUAL TO OR PRECEDES	same or previous
U + 22DF (8927)	⋟	EQUAL TO OR SUCCEEDS	same or subsequent
U + 22E0 (8928)	⋠	DOES NOT PRECEDE OR EQUAL	neither previous nor equal
U + 22E1 (8929)	⋡	DOES NOT SUCCEED OR EQUAL	neither below nor the same
U + 22E2 (8930)	⋢	NOT SQUARE IMAGE OF OR EQUAL TO	no square picture or the same
U + 22E3 (8931)	⋣	NOT SQUARE ORIGINAL OF OR EQUAL TO	no square original or the same
U + 22E4 (8932)	⋤	SQUARE IMAGE OF OR NOT EQUAL TO	square picture or unequal
U + 22E5 (8933)	⋥	SQUARE ORIGINAL OF OR NOT EQUAL TO	square original or unequal
U + 22E6 (8934)	⋦	LESS-THAN BUT NOT EQUIVALENT TO	less than but not equivalent
U + 22E7 (8935)	⋧	GREATER-THAN BUT NOT EQUIVALENT TO	greater than, but not equivalent
U + 22E8 (8936)	⋨	PRECEDES BUT NOT EQUIVALENT TO	previous but not equivalent
U + 22E9 (8937)	⋩	SUCCEEDS BUT NOT EQUIVALENT TO	below, but not equivalent
U + 22EA (8938)	⋪	NOT NORMAL SUBGROUP OF	not a normal subgroup
U + 22EB (8939)	⋫	DOES NOT CONTAIN AS NORMAL SUBGROUP	not included as a normal subgroup
U + 22EC (8940)	⋬	NOT NORMAL SUBGROUP OF OR EQUAL TO	no normal subgroup or equal
U + 22ED (8941)	⋭	DOES NOT CONTAIN AS NORMAL SUBGROUP OR EQUAL	not included as a normal subgroup or equal
U + 22EE (8942)	⋮	VERTICAL ELLIPSIS	Vertical ellipse
U + 22EF (8943)	⋯	MIDLINE HORIZONTAL ELLIPSIS	Centered horizontal ellipse
U + 22F0 (8944)	⋰	UP RIGHT DIAGONAL ELLIPSIS	Diagonal ellipse, bottom left to top right
U + 22F1 (8945)	⋱	DOWN RIGHT DIAGONAL ELLIPSIS	Diagonal ellipse, top left to bottom right
U + 22F2 (8946)	⋲	ELEMENT OF WITH LONG HORIZONTAL STROKE	Element with long horizontal bar
U + 22F3 (8947)	⋳	ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE	Element with a vertical line at the end of the horizontal line
U + 22F4 (8948)	⋴	SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE	small element with a vertical line at the end of the horizontal line
U + 22F5 (8949)	⋵	ELEMENT OF WITH DOT ABOVE	Element with point (top)
U + 22F6 (8950)	⋶	ELEMENT OF WITH OVERBAR	Element with overline
U + 22F7 (8951)	⋷	SMALL ELEMENT OF WITH OVERBAR	small element with overline
U + 22F8 (8952)	⋸	ELEMENT OF WITH UNDERBAR	Element with underscore
U + 22F9 (8953)	⋹	ELEMENT OF WITH TWO HORIZONTAL STROKES	Element with 2 horizontal lines
U + 22FA (8954)	⋺	CONTAINS WITH LONG HORIZONTAL STROKE	inverted element sign with long horizontal bar
U + 22FB (8955)	⋻	CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE	inverted element character with a vertical bar at the end of the horizontal bar
U + 22FC (8956)	⋼	SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE	small inverted element character with a vertical bar at the end of the horizontal bar
U + 22FD (8957)	⋽	CONTAINS WITH OVERBAR	inverted element character with overline
U + 22FE (8958)	⋾	SMALL CONTAINS WITH OVERBAR	small inverted element sign with overline
U + 22FF (8959)	⋿	Z NOTATION BAG MEMBERSHIP

annotation

1. ↑ (in this form also common in Europe for the flat angle )

Graphic board

Representation of the characters as graphics

Web links

Commons : Mathematical symbols  - collection of images, videos, and audio files

• PDF of the Unicode Consortium (English; 155 kB)