The Mathematical Operators block includes character encodings for operators, relations, geometric symbols and a few other symbols with special usages confined largely to mathematical contexts.

In addition to the characters in this block, mathematical operators are also found in the Basic Latin and Latin-1 Supplement blocks with a few more esoteric ones in Miscellaneous Technical, General Punctuation, Greek and Coptic and Letterlike Symbols. See also Miscellaneous Mathematical Symbols A, Miscellaneous Mathematical Symbols B, Supplemental Mathematical Operators and Mathematical Alphanumeric Symbols.

Among the standards covered by this block are ANSI Y10.20, ISO 6862, ISO 8879, portions of the collection of the American Mathematical Society as well as the original repertoire of TeX.

Encoding in this block is shape based, thus U+2218    ring operator   might mean white small circle or composite function or APL jot. Graphical variants on the same symbol are likewise not encoded separately.

For the mathematical operator implies use U+21D2    rightwards double arrow. For the mathematical operator if and only if use U+2194    left right arrow.

Some Greek letters exist in both this block and the Greek code block. This redundancy is included to match the usage in existing standards.

U+2212    minus sign   is the mathematical operator, as opposed to U+002D  -  hyphen minus   which has many other uses.


Unicode's Mathematical Operators code block reserves the 256 code points from U+2200 to U+22FF, of which all 256 are currently assigned.

Arrows <-- Mathematical Operators --> Miscellaneous Technical

Number of characters added in each version of the Unicode standard :
Unicode 1.1 : 242
Unicode 3.2 : 14

All the characters in this code block are in general category Symbol, Math Sm

Number of characters in each Bidirectional Category :

European Number Separator    ES :  1
European Number Terminator   ET :  1
Other Neutral                ON :254

The columns below should be interpreted as :

  1. The Unicode code for the character
  2. The character in question
  3. The Unicode name for the character
  4. The Unicode Bidirectional Category for the character
  5. The Unicode version when this character was added

If the characters below show up poorly, or not at all, see Unicode Support for possible solutions.

 

Mathematical Operators

     Miscellaneous mathematical symbols

U+2200   ∀   for all ON 1.1
html &forall;
sgml &ForAll; &forall;
aka universal quantifier
U+2201   ∁   complement ON 1.1
sgml &comp; &complement;
ref U+0297   ʗ   Latin letter stretched c (IPA Extensions)
U+2202   ∂   partial differential ON 1.1
html &part;
sgml &PartialD; &part;
U+2203   ∃   there exists ON 1.1
html &exist;
sgml &Exists; &exist;
aka existential quantifier
U+2204   ∄   there does not exist ON 1.1
sgml &NotExists; &nexist; &nexists;
U+2205   ∅   empty set ON 1.1
html &empty;
sgml &empty; &emptyset; &emptyv; &varnothing;
aka null set
* used in linguistics to indicate a null morpheme or phonological "zero"
ref U+00D8   Ø   Latin capital letter O with stroke (Latin-1 Supplement)
ref U+2300   ⌀   diameter sign (Miscellaneous Technical)
U+2206   ∆   increment ON 1.1
aka laplace operator
aka forward difference
aka symmetric difference (in set theory)
* other symbols may also be used for symmetric difference
ref U+0394   Δ   Greek capital letter delta (Greek and Coptic)
ref U+25B3   △   white up pointing triangle (Geometric Shapes)
U+2207   ∇   nabla ON 1.1
html &nabla;
sgml &Del; &nabla;
aka backward difference
aka gradient, del
* used for Laplacian operator (written with superscript 2)
ref U+25BD   ▽   white down pointing triangle (Geometric Shapes)

     Set membership

U+2208   ∈   element of ON 1.1
html &isin;
sgml &Element; &isin; &isinv;
U+2209   ∉   not an element of ON 1.1
html &notin;
sgml &NotElement; &notin; &notinva;
U+220A   ∊   small element of ON 1.1
sgml &epsi; &epsis; &in; &isin; &straightepsilon;
* originates in math pi fonts; not the straight epsilon
ref U+03F5   ϵ   Greek lunate epsilon symbol (Greek and Coptic)
U+220B   ∋   contains as member ON 1.1
html &ni;
sgml &ReverseElement; &ni; &niv;
aka such that
U+220C   ∌   does not contain as member ON 1.1
sgml &NotReverseElement; &notni; &notniva;
U+220D   ∍   small contains as member ON 1.1
sgml &SuchThat; &bepsi; &ni;
ref U+03F6   ϶   Greek reversed lunate epsilon symbol (Greek and Coptic)

     Miscellaneous mathematical symbol

U+220E   ∎   end of proof ON 1.1
aka q.e.d.
ref U+2023   ‣   triangular bullet (General Punctuation)
ref U+25AE   ▮   black vertical rectangle (Geometric Shapes)

     N-ary operators

U+220F   ∏   n ary product ON 1.1
html &prod;
sgml &prod;
aka product sign
ref U+03A0   Π   Greek capital letter pi (Greek and Coptic)
U+2210   ∐   n ary coproduct ON 1.1
sgml &Coproduct; &amalg; &coprod; &samalg;
aka coproduct sign
U+2211   ∑   n ary summation ON 1.1
html &sum;
sgml &Sum; &sum;
aka summation sign
ref U+03A3   Σ   Greek capital letter sigma (Greek and Coptic)
ref U+2140   ⅀   double struck n ary summation (Letterlike Symbols)

     Operators

U+2212   −   minus sign ES 1.1
html &minus;
sgml &minus;
ref U+002D   -   hyphen minus (Basic Latin)
U+2213   ∓   minus or plus sign ET 1.1
sgml &MinusPlus; &mnplus; &mp;
ref U+00B1   ±   plus minus sign (Latin-1 Supplement)
U+2214   ∔   dot plus ON 1.1
sgml &dotplus; &plusdo;
U+2215   ∕   division slash ON 1.1
* generic division operator
ref U+002F   /   solidus (Basic Latin)
ref U+2044   ⁄   fraction slash (General Punctuation)
U+2216   ∖   set minus ON 1.1
sgml &Backslash; &setminus; &setmn; &smallsetminus; &ssetmn;
ref U+005C   \   reverse solidus (Basic Latin)
U+2217   ∗   asterisk operator ON 1.1
html &lowast;
sgml &ast; &lowast; &midast;
ref U+002A   *   asterisk (Basic Latin)
U+2218   ∘   ring operator ON 1.1
sgml &SmallCircle; &cir; &circ; &compfn;
aka composite function
aka APL jot
ref U+00B0   °   degree sign (Latin-1 Supplement)
ref U+25E6   ◦   white bullet (Geometric Shapes)
U+2219   ∙   bullet operator ON 1.1
ref U+00B7   ·   middle dot (Latin-1 Supplement)
ref U+2022   •   bullet (General Punctuation)
ref U+2024   ․   one dot leader (General Punctuation)
U+221A   √   square root ON 1.1
html &radic;
sgml &Sqrt; &radic;
aka radical sign
ref U+2713   ✓   check mark (Dingbats)
U+221B   ∛   cube root ON 1.1
ref U+0606   ؆   Arabic indic cube root (Arabic)
U+221C   ∜   fourth root ON 1.1
ref U+0607   ؇   Arabic indic fourth root (Arabic)
U+221D   ∝   proportional to ON 1.1
html &prop;
sgml &Proportional; &prop; &propto; &varpropto; &vprop;
ref U+03B1   α   Greek small letter alpha (Greek and Coptic)

     Miscellaneous mathematical symbols

U+221E   ∞   infinity ON 1.1
html &infin;
sgml &infin;
U+221F   ∟   right angle ON 1.1
sgml &ang90; &angrt;
U+2220   ∠   angle ON 1.1
html &ang;
sgml &ang; &angle;
U+2221   ∡   measured angle ON 1.1
sgml &angmsd; &measuredangle;
U+2222   ∢   spherical angle ON 1.1
sgml &angsph;
aka angle arc

     Operators

U+2223   ∣   divides ON 1.1
sgml &VerticalBar; &mid; &shortmid; &smid;
aka such that
aka APL stile
ref U+007C   |   vertical line (Basic Latin)
ref U+01C0   ǀ   Latin letter dental click (Latin Extended B)
U+2224   ∤   does not divide ON 1.1
sgml &NotVerticalBar; &nmid; &nshortmid; &nsmid;
U+2225   ∥   parallel to ON 1.1
sgml &DoubleVerticalBar; &par; &parallel; &shortparallel; &spar;
ref U+01C1   ǁ   Latin letter lateral click (Latin Extended B)
ref U+2016   ‖   double vertical line (General Punctuation)
U+2226   ∦   not parallel to ON 1.1
sgml &NotDoubleVerticalBar; &npar; &nparallel; &nshortparallel; &nspar;

     Logical and set operators

U+2227   ∧   logical and ON 1.1
html &and;
sgml &And; &and; &wedge;
aka wedge, conjunction
ref U+22C0   ⋀   n ary logical and (Mathematical Operators)
ref U+2303   ⌃   up arrowhead (Miscellaneous Technical)
U+2228   ∨   logical or ON 1.1
html &or;
sgml &Or; &or; &vee;
aka vee, disjunction
ref U+22C1   ⋁   n ary logical or (Mathematical Operators)
ref U+2304   ⌄   down arrowhead (Miscellaneous Technical)
U+2229   ∩   intersection ON 1.1
html &cap;
sgml &cap;
aka cap, hat
ref U+22C2   ⋂   n ary intersection (Mathematical Operators)
U+222A   ∪   union ON 1.1
html &cup;
sgml &cup;
aka cup
ref U+22C3   ⋃   n ary union (Mathematical Operators)

     Integrals

U+222B   ∫   integral ON 1.1
html &int;
sgml &Integral; &int;
ref U+0283   ʃ   Latin small letter esh (IPA Extensions)
U+222C   ∬   double integral ON 1.1
sgml &Int;
U+222D   ∭   triple integral ON 1.1
sgml &iiint; &tint;
ref U+2A0C   ⨌   quadruple integral operator (Supplemental Mathematical Operators)
U+222E   ∮   contour integral ON 1.1
sgml &ContourIntegral; &conint; &oint;
ref U+2A15   ⨕   integral around a point operator (Supplemental Mathematical Operators)
U+222F   ∯   surface integral ON 1.1
sgml &Conint; &DoubleContourIntegral;
U+2230   ∰   volume integral ON 1.1
sgml &Cconint;
U+2231   ∱   clockwise integral ON 1.1
sgml &cwint;
U+2232   ∲   clockwise contour integral ON 1.1
sgml &ClockwiseContourIntegral; &cwconint;
U+2233   ∳   anticlockwise contour integral ON 1.1
sgml &CounterClockwiseContourIntegral; &awconint;
* clockwise or anticlockwise arrows do not reverse during layout mirroring

     Miscellaneous mathematical symbols

U+2234   ∴   therefore ON 1.1
html &there4;
sgml &Therefore; &there4; &therefore;
U+2235   ∵   because ON 1.1
sgml &Because; &becaus; &because;

     Relations

U+2236   ∶   ratio ON 1.1
sgml &Colon; &ratio;
ref U+003A   :   colon (Basic Latin)
U+2237   ∷   proportion ON 1.1
sgml &Colon; &Proportion;

     Operator

U+2238   ∸   dot minus ON 1.1
sgml &dotminus; &minusd;
aka saturating subtraction
* sometimes claimed as notation for symmetric set difference, but 2206 is preferred

     Relation

U+2239   ∹   excess ON 1.1

     Operator

U+223A   ∺   geometric proportion ON 1.1
sgml &mDDot;

     Relations

U+223B   ∻   homothetic ON 1.1
sgml &homtht;
ref U+2A6B   ⩫   tilde operator with rising dots (Supplemental Mathematical Operators)
U+223C   ∼   tilde operator ON 1.1
html &sim;
sgml &Tilde; &sim; &thicksim; &thksim;
aka varies with (proportional to)
aka difference between
aka similar to
aka not
aka cycle
aka APL tilde
ref U+007E   ~   tilde (Basic Latin)
ref U+00AC   ¬   not sign (Latin-1 Supplement)
ref U+02DC   ˜   small tilde (Spacing Modifier Letters)
U+223D   ∽   reversed tilde ON 1.1
sgml &backsim; &bsim;
aka lazy s
* reversed tilde and lazy S are glyph variants
U+223E   ∾   inverted lazy s ON 1.1
sgml &mstpos;
aka most positive

     Miscellaneous mathematical symbol

U+223F   ∿   sine wave ON 1.1
sgml &acd;
aka alternating current

     Operator

U+2240   ≀   wreath product ON 1.1
sgml &VerticalTilde; &wr; &wreath;

     Relations

U+2241   ≁   not tilde ON 1.1
sgml &NotTilde; &nsim;
U+2242   ≂   minus tilde ON 1.1
sgml &EqualTilde; &eqsim; &esim;
U+2243   ≃   asymptotically equal to ON 1.1
sgml &TildeEqual; &sime; &simeq;
U+2244   ≄   not asymptotically equal to ON 1.1
sgml &NotTildeEqual; &nsime; &nsimeq;
U+2245   ≅   approximately equal to ON 1.1
html &cong;
sgml &TildeFullEqual; &cong;
U+2246   ≆   approximately but not actually equal to ON 1.1
sgml &simne;
U+2247   ≇   neither approximately nor actually equal to ON 1.1
sgml &NotTildeFullEqual; &ncong;
U+2248   ≈   almost equal to ON 1.1
html &asymp;
sgml &TildeTilde; &ap; &approx; &asymp; &thickapprox; &thkap;
aka asymptotic to
U+2249   ≉   not almost equal to ON 1.1
sgml &NotTildeTilde; &nap; &napprox;
U+224A   ≊   almost equal or equal to ON 1.1
sgml &apE; &ape; &approxeq;
U+224B   ≋   triple tilde ON 1.1
sgml &apid;
U+224C   ≌   all equal to ON 1.1
sgml &backcong; &bcong;
* reversed tilde and lazy S are glyph variants
U+224D   ≍   equivalent to ON 1.1
sgml &CupCap; &asymp;
U+224E   ≎   geometrically equivalent to ON 1.1
sgml &Bumpeq; &HumpDownHump; &bump;
U+224F   ≏   difference between ON 1.1
sgml &HumpEqual; &bumpe; &bumpeq;
U+2250   ≐   approaches the limit ON 1.1
sgml &DotEqual; &doteq; &esdot;
U+2251   ≑   geometrically equal to ON 1.1
sgml &doteqdot; &eDot;
U+2252   ≒   approximately equal to or the image of ON 1.1
sgml &efDot; &fallingdotseq;
aka nearly equals
U+2253   ≓   image of or approximately equal to ON 1.1
sgml &erDot; &risingdotseq;
U+2254   ≔   colon equals ON 1.1
sgml &colone; &coloneq; &frac23;
U+2255   ≕   equals colon ON 1.1
sgml &ecolon; &eqcolon;
U+2256   ≖   ring in equal to ON 1.1
sgml &ecir; &eqcirc;
U+2257   ≗   ring equal to ON 1.1
sgml &circeq; &cire;
aka approximately equal to
U+2258   ≘   corresponds to ON 1.1
U+2259   ≙   estimates ON 1.1
sgml &wedgeq;
aka corresponds to
U+225A   ≚   equiangular to ON 1.1
sgml &veeeq;
U+225B   ≛   star equals ON 1.1
sgml &easter;
U+225C   ≜   delta equal to ON 1.1
sgml &triangleq; &trie;
aka equiangular
aka equal to by definition
U+225D   ≝   equal to by definition ON 1.1
U+225E   ≞   measured by ON 1.1
U+225F   ≟   questioned equal to ON 1.1
sgml &equest; &questeq;
U+2260   ≠   not equal to ON 1.1
html &ne;
sgml &NotEqual; &ne;
ref U+003D   =   equals sign (Basic Latin)
ref U+01C2   ǂ   Latin letter alveolar click (Latin Extended B)
U+2261   ≡   identical to ON 1.1
html &equiv;
sgml &Congruent; &equiv;
U+2262   ≢   not identical to ON 1.1
sgml &NotCongruent; &nequiv;
U+2263   ≣   strictly equivalent to ON 1.1
U+2264   ≤   less than or equal to ON 1.1
html &le;
sgml &le; &leq; &les;
U+2265   ≥   greater than or equal to ON 1.1
html &ge;
sgml &GreaterEqual; &ge; &geq; &ges;
U+2266   ≦   less than over equal to ON 1.1
sgml &LessFullEqual; &lE; &leqq;
U+2267   ≧   greater than over equal to ON 1.1
sgml &GreaterFullEqual; &gE; &geqq;
U+2268   ≨   less than but not equal to ON 1.1
sgml &lnE; &lne; &lneq; &lneqq; &lvnE;
U+2269   ≩   greater than but not equal to ON 1.1
sgml &gnE; &gne; &gneq; &gneqq; &gvnE;
U+226A   ≪   much less than ON 1.1
sgml &Lt; &NestedLessLess; &ll;
ref U+00AB   «   left pointing double angle quotation mark (Latin-1 Supplement)
U+226B   ≫   much greater than ON 1.1
sgml &Gt; &NestedGreaterGreater; &gg;
ref U+00BB   »   right pointing double angle quotation mark (Latin-1 Supplement)
U+226C   ≬   between ON 1.1
sgml &between; &twixt;
aka plaintiff, quantic
U+226D   ≭   not equivalent to ON 1.1
sgml &NotCupCap;
U+226E   ≮   not less than ON 1.1
sgml &NotLess; &nless; &nlt; &nvlt;
U+226F   ≯   not greater than ON 1.1
sgml &NotGreater; &ngt; &ngtr; &nvgt;
U+2270   ≰   neither less than nor equal to ON 1.1
sgml &NotGreaterFullEqual; &NotLessEqual; &NotLessSlantEqual; &nlE; &nle; &nleq; &nleqq; &nleqslant; &nles; &nvle;
U+2271   ≱   neither greater than nor equal to ON 1.1
sgml &NotGreaterEqual; &NotGreaterSlantEqual; &ngE; &nge; &ngeq; &ngeqq; &ngeqslant; &nges; &nvge;
U+2272   ≲   less than or equivalent to ON 1.1
sgml &LessTilde; &lap; &lessapprox; &lesssim; &lsim;
U+2273   ≳   greater than or equivalent to ON 1.1
sgml &GreaterTilde; &gap; &gsim; &gtrapprox; &gtrsim;
U+2274   ≴   neither less than nor equivalent to ON 1.1
sgml &NotLessTilde; &nlsim;
U+2275   ≵   neither greater than nor equivalent to ON 1.1
sgml &NotGreaterTilde; &ngsim;
U+2276   ≶   less than or greater than ON 1.1
sgml &LessGreater; &lessgtr; &lg;
U+2277   ≷   greater than or less than ON 1.1
sgml &GreaterLess; &gl; &gtrless;
U+2278   ≸   neither less than nor greater than ON 1.1
sgml &NotLessGreater; &ntlg; &ntvlg;
U+2279   ≹   neither greater than nor less than ON 1.1
sgml &NotGreaterLess; &ntgl; &ntvgl;
U+227A   ≺   precedes ON 1.1
sgml &Precedes; &pr; &prec;
aka lower rank than
ref U+22B0   ⊰   precedes under relation (Mathematical Operators)
U+227B   ≻   succeeds ON 1.1
sgml &Succeeds; &sc; &succ;
aka higher rank than
ref U+22B1   ⊱   succeeds under relation (Mathematical Operators)
U+227C   ≼   precedes or equal to ON 1.1
sgml &PrecedesEqual; &PrecedesSlantEqual; &cupre; &prE; &prcue; &pre; &preccurlyeq; &preceq;
U+227D   ≽   succeeds or equal to ON 1.1
sgml &SucceedsEqual; &SucceedsSlantEqual; &sccue; &sce; &succcurlyeq; &succeq;
U+227E   ≾   precedes or equivalent to ON 1.1
sgml &PrecedesTilde; &prap; &precapprox; &precsim; &prsim; &scE;
U+227F   ≿   succeeds or equivalent to ON 1.1
sgml &SucceedsTilde; &scap; &scsim; &succapprox; &succsim;
U+2280   ⊀   does not precede ON 1.1
sgml &NotPrecedes; &npr; &nprec;
U+2281   ⊁   does not succeed ON 1.1
sgml &NotSucceeds; &nsc; &nsucc;
U+2282   ⊂   subset of ON 1.1
html &sub;
sgml &sub; &subset;
aka included in set
ref U+2E26   ⸦   left sideways u bracket (Supplemental Punctuation)
U+2283   ⊃   superset of ON 1.1
html &sup;
sgml &Superset; &sup; &supset;
aka includes in set
ref U+2E27   ⸧   right sideways u bracket (Supplemental Punctuation)
U+2284   ⊄   not a subset of ON 1.1
html &nsub;
sgml &NotSubset; &nsub; &nsubset; &vnsub;
U+2285   ⊅   not a superset of ON 1.1
sgml &NotSuperset; &nsup; &nsupset; &vnsup;
U+2286   ⊆   subset of or equal to ON 1.1
html &sube;
sgml &SubsetEqual; &subE; &sube; &subseteq; &subseteqq;
U+2287   ⊇   superset of or equal to ON 1.1
html &supe;
sgml &SupersetEqual; &supE; &supe; &supseteq; &supseteqq;
U+2288   ⊈   neither a subset of nor equal to ON 1.1
sgml &nsubE; &nsube; &nsubseteq; &nsubseteqq;
U+2289   ⊉   neither a superset of nor equal to ON 1.1
sgml &nsupE; &nsupe; &nsupseteq; &nsupseteqq;
U+228A   ⊊   subset of with not equal to ON 1.1
sgml &subnE; &subne; &subsetneq; &subsetneqq; &vsubnE; &vsubne;
U+228B   ⊋   superset of with not equal to ON 1.1
sgml &supnE; &supne; &supsetneq; &supsetneqq; &vsupnE; &vsupne;

     Operators

U+228C   ⊌   multiset ON 1.1
U+228D   ⊍   multiset multiplication ON 1.1
sgml &cupdot;
ref U+2A03   ⨃   n ary union operator with dot (Supplemental Mathematical Operators)
ref U+2A40   ⩀   intersection with dot (Supplemental Mathematical Operators)
U+228E   ⊎   multiset union ON 1.1
sgml &UnionPlus; &biguplus; &uplus; &xuplus;
aka z notation bag addition
ref U+2A04   ⨄   n ary union operator with plus (Supplemental Mathematical Operators)

     Relations

U+228F   ⊏   square image of ON 1.1
sgml &SquareSubset; &sqsub; &sqsubset;
U+2290   ⊐   square original of ON 1.1
sgml &SquareSuperset; &sqsup; &sqsupset;
U+2291   ⊑   square image of or equal to ON 1.1
sgml &SquareSubsetEqual; &sqsube; &sqsubseteq;
U+2292   ⊒   square original of or equal to ON 1.1
sgml &SquareSupersetEqual; &sqsupe; &sqsupseteq;

     Operators

U+2293   ⊓   square cap ON 1.1
sgml &SquareIntersection; &sqcap;
ref U+2A05   ⨅   n ary square intersection operator (Supplemental Mathematical Operators)
U+2294   ⊔   square cup ON 1.1
sgml &SquareUnion; &bigsqcup; &sqcup; &xsqcup;
U+2295   ⊕   circled plus ON 1.1
html &oplus;
sgml &CirclePlus; &bigoplus; &oplus; &xoplus;
aka direct sum
aka vector pointing into page
ref U+2641   ♁   earth (Miscellaneous Symbols)
ref U+2A01   ⨁   n ary circled plus operator (Supplemental Mathematical Operators)
U+2296   ⊖   circled minus ON 1.1
sgml &CircleMinus; &ominus;
aka symmetric difference
ref U+29B5   ⦵   circle with horizontal bar (Miscellaneous Mathematical Symbols B)
U+2297   ⊗   circled times ON 1.1
html &otimes;
sgml &CircleTimes; &bigotimes; &otimes; &xotime;
aka tensor product
aka vector pointing into page
ref U+2A02   ⨂   n ary circled times operator (Supplemental Mathematical Operators)
U+2298   ⊘   circled division slash ON 1.1
sgml &oslash; &osol;
U+2299   ⊙   circled dot operator ON 1.1
sgml &CircleDot; &bigodot; &odot; &xodot;
aka direct product
aka vector pointing out of page
ref U+0298   ʘ   Latin letter bilabial click (IPA Extensions)
ref U+2609   ☉   sun (Miscellaneous Symbols)
ref U+2A00   ⨀   n ary circled dot operator (Supplemental Mathematical Operators)
U+229A   ⊚   circled ring operator ON 1.1
sgml &circledcirc; &ocir;
ref U+233E   ⌾   APL functional symbol circle jot (Miscellaneous Technical)
ref U+25CE   ◎   bullseye (Geometric Shapes)
U+229B   ⊛   circled asterisk operator ON 1.1
sgml &circledast; &oast;
ref U+235F   ⍟   APL functional symbol circle star (Miscellaneous Technical)
U+229C   ⊜   circled equals ON 1.1
U+229D   ⊝   circled dash ON 1.1
sgml &circleddash; &odash;
U+229E   ⊞   squared plus ON 1.1
sgml &boxplus; &plusb;
U+229F   ⊟   squared minus ON 1.1
sgml &boxminus; &minusb;
U+22A0   ⊠   squared times ON 1.1
sgml &boxtimes; &timesb;
ref U+2612   ☒   ballot box with x (Miscellaneous Symbols)
U+22A1   ⊡   squared dot operator ON 1.1
sgml &dotsquare; &sdotb;
U+22A2   ⊢   right tack ON 1.1
sgml &RightTee; &vdash;
aka turnstile
aka proves, implies, yields
aka reducible
U+22A3   ⊣   left tack ON 1.1
sgml &LeftTee; &dashv;
aka reverse turnstile
aka non-theorem, does not yield

     Miscellaneous mathematical symbols

U+22A4   ⊤   down tack ON 1.1
sgml &DownTee; &top;
aka top
ref U+2E06   ⸆   raised interpolation marker (Supplemental Punctuation)
U+22A5   ⊥   up tack ON 1.1
html &perp;
sgml &UpTee; &bot; &bottom; &perp;
aka base, bottom
ref U+27C2   ⟂   perpendicular (Miscellaneous Mathematical Symbols A)

     Relations

U+22A6   ⊦   assertion ON 1.1
aka reduces to
U+22A7   ⊧   models ON 1.1
sgml &models;
U+22A8   ⊨   true ON 1.1
sgml &DoubleRightTee; &vDash;
aka statement is true, valid
aka is a tautology
aka satisfies
aka results in
U+22A9   ⊩   forces ON 1.1
sgml &Vdash;
U+22AA   ⊪   triple vertical bar right turnstile ON 1.1
sgml &Vvdash;
U+22AB   ⊫   double vertical bar double right turnstile ON 1.1
sgml &VDash;
U+22AC   ⊬   does not prove ON 1.1
sgml &nvdash;
U+22AD   ⊭   not true ON 1.1
sgml &nvDash;
U+22AE   ⊮   does not force ON 1.1
sgml &nVdash;
U+22AF   ⊯   negated double vertical bar double right turnstile ON 1.1
sgml &nVDash;
U+22B0   ⊰   precedes under relation ON 1.1
sgml &prurel;
ref U+227A   ≺   precedes (Mathematical Operators)
U+22B1   ⊱   succeeds under relation ON 1.1
ref U+227B   ≻   succeeds (Mathematical Operators)
U+22B2   ⊲   normal subgroup of ON 1.1
sgml &LeftTriangle; &vartriangleleft; &vltri;
ref U+25C5   ◅   white left pointing pointer (Geometric Shapes)
U+22B3   ⊳   contains as normal subgroup ON 1.1
sgml &RightTriangle; &vartriangleright; &vrtri;
ref U+25BB   ▻   white right pointing pointer (Geometric Shapes)
U+22B4   ⊴   normal subgroup of or equal to ON 1.1
sgml &LeftTriangleEqual; &ltrie; &trianglelefteq;
U+22B5   ⊵   contains as normal subgroup or equal to ON 1.1
sgml &RightTriangleEqual; &rtrie; &trianglerighteq;
U+22B6   ⊶   original of ON 1.1
sgml &origof;
U+22B7   ⊷   image of ON 1.1
sgml &imof;
U+22B8   ⊸   multimap ON 1.1
sgml &multimap; &mumap;
U+22B9   ⊹   hermitian conjugate matrix ON 1.1
sgml &hercon;

     Operators

U+22BA   ⊺   intercalate ON 1.1
sgml &intcal; &intercal;
U+22BB   ⊻   xor ON 1.1
sgml &veebar;
ref U+26BA   ⚺   semisextile (Miscellaneous Symbols)
U+22BC   ⊼   nand ON 1.1
sgml &barwed; &barwedge;
ref U+2305   ⌅   projective (Miscellaneous Technical)
ref U+26BB   ⚻   quincunx (Miscellaneous Symbols)
U+22BD   ⊽   nor ON 1.1
sgml &barvee;

     Miscellaneous mathematical symbols

U+22BE   ⊾   right angle with arc ON 1.1
sgml &angrtvb; &vangrt;
U+22BF   ⊿   right triangle ON 1.1
sgml &lrtri;

     N-ary operators

U+22C0   ⋀   n ary logical and ON 1.1
sgml &Wedge; &bigwedge; &xwedge;
* also used to denote the universal quantifier
ref U+2227   ∧   logical and (Mathematical Operators)
U+22C1   ⋁   n ary logical or ON 1.1
sgml &Vee; &bigvee; &xvee;
* also used to denote the existential quantifier
ref U+2228   ∨   logical or (Mathematical Operators)
U+22C2   ⋂   n ary intersection ON 1.1
sgml &Intersection; &bigcap; &xcap;
aka z notation generalised intersection
ref U+2229   ∩   intersection (Mathematical Operators)
U+22C3   ⋃   n ary union ON 1.1
sgml &Union; &bigcup; &xcup;
aka z notation generalised union
ref U+222A   ∪   union (Mathematical Operators)

     Operators

U+22C4   ⋄   diamond operator ON 1.1
sgml &diam; &diamond;
ref U+25C7   ◇   white diamond (Geometric Shapes)
ref U+2B29   ⬩   black small diamond (Miscellaneous Symbols and Arrows)
U+22C5   ⋅   dot operator ON 1.1
html &sdot;
sgml &cdot; &sdot;
ref U+00B7   ·   middle dot (Latin-1 Supplement)
U+22C6   ⋆   star operator ON 1.1
sgml &Star; &sstarf; &star;
* APL
ref U+066D   ٭   Arabic five pointed star (Arabic)
ref U+2605   ★   black star (Miscellaneous Symbols)
ref U+2B50   ⭐   white medium star (Miscellaneous Symbols and Arrows)
U+22C7   ⋇   division times ON 1.1
sgml &divideontimes; &divonx;

     Relation

U+22C8   ⋈   bowtie ON 1.1
sgml &bowtie;
ref U+2445   ⑅   OCR bow tie (Optical Character Recognition)

     Operators

U+22C9   ⋉   left normal factor semidirect product ON 1.1
sgml &ltimes;
U+22CA   ⋊   right normal factor semidirect product ON 1.1
sgml &rtimes;
U+22CB   ⋋   left semidirect product ON 1.1
sgml &leftthreetimes; &lthree;
U+22CC   ⋌   right semidirect product ON 1.1
sgml &rightthreetimes; &rthree;
ref U+2041   ⁁   caret insertion point (General Punctuation)

     Relation

U+22CD   ⋍   reversed tilde equals ON 1.1
sgml &backsimeq; &bsime;

     Logical operators

U+22CE   ⋎   curly logical or ON 1.1
sgml &curlyvee; &cuvee;
U+22CF   ⋏   curly logical and ON 1.1
sgml &curlywedge; &cuwed;

     Relations

U+22D0   ⋐   double subset ON 1.1
sgml &Sub; &Subset;
U+22D1   ⋑   double superset ON 1.1
sgml &Sup; &Supset;

     Operators

U+22D2   ⋒   double intersection ON 1.1
sgml &Cap;
U+22D3   ⋓   double union ON 1.1
sgml &Cup;

     Relations

U+22D4   ⋔   pitchfork ON 1.1
sgml &fork; &pitchfork;
aka proper intersection
U+22D5   ⋕   equal and parallel to ON 1.1
sgml &epar;
ref U+2317   ⌗   viewdata square (Miscellaneous Technical)
U+22D6   ⋖   less than with dot ON 1.1
sgml &ldot; &lessdot; &ltdot;
U+22D7   ⋗   greater than with dot ON 1.1
sgml &gsdot; &gtdot; &gtrdot;
U+22D8   ⋘   very much less than ON 1.1
sgml &Ll;
U+22D9   ⋙   very much greater than ON 1.1
sgml &Gg; &ggg;
U+22DA   ⋚   less than equal to or greater than ON 1.1
sgml &LessEqualGreater; &lEg; &leg; &lesseqgtr; &lesseqqgtr;
U+22DB   ⋛   greater than equal to or less than ON 1.1
sgml &GreaterEqualLess; &gEl; &gel; &gtreqless; &gtreqqless;
U+22DC   ⋜   equal to or less than ON 1.1
sgml &els; &eqslantless;
U+22DD   ⋝   equal to or greater than ON 1.1
sgml &egs; &eqslantgtr;
U+22DE   ⋞   equal to or precedes ON 1.1
sgml &cuepr; &curlyeqprec;
U+22DF   ⋟   equal to or succeeds ON 1.1
sgml &cuesc; &curlyeqsucc;
U+22E0   ⋠   does not precede or equal ON 1.1
sgml &NotPrecedesSlantEqual; &nprcue; &npre;
U+22E1   ⋡   does not succeed or equal ON 1.1
sgml &NotSucceedsSlantEqual; &nsccue; &nsce;
U+22E2   ⋢   not square image of or equal to ON 1.1
sgml &NotSquareSubsetEqual; &nsqsube;
U+22E3   ⋣   not square original of or equal to ON 1.1
sgml &NotSquareSupersetEqual; &nsqsupe;
U+22E4   ⋤   square image of or not equal to ON 1.1
U+22E5   ⋥   square original of or not equal to ON 1.1
U+22E6   ⋦   less than but not equivalent to ON 1.1
sgml &lnsim;
U+22E7   ⋧   greater than but not equivalent to ON 1.1
sgml &gnsim;
U+22E8   ⋨   precedes but not equivalent to ON 1.1
sgml &precnapprox; &precnsim; &prnap; &prnsim;
U+22E9   ⋩   succeeds but not equivalent to ON 1.1
sgml &scnap; &scnsim; &succnapprox; &succnsim;
U+22EA   ⋪   not normal subgroup of ON 1.1
sgml &NotLeftTriangle; &nltri; &ntriangleleft;
U+22EB   ⋫   does not contain as normal subgroup ON 1.1
sgml &NotRightTriangle; &nrtri; &ntriangleright;
U+22EC   ⋬   not normal subgroup of or equal to ON 1.1
sgml &NotLeftTriangleEqual; &nltrie; &ntrianglelefteq;
U+22ED   ⋭   does not contain as normal subgroup or equal ON 1.1
sgml &NotRightTriangleEqual; &nrtrie; &ntrianglerighteq;
U+22EE   ⋮   vertical ellipsis ON 1.1
sgml &vellip;
* these four ellipses are used for matrix row/column elision
ref U+205D   ⁝   tricolon (General Punctuation)
ref U+2026   …   horizontal ellipsis (General Punctuation)
ref U+FE19   ︙   presentation form for vertical horizontal ellipsis (Vertical Forms)
U+22EF   ⋯   midline horizontal ellipsis ON 1.1
sgml &ctdot;
U+22F0   ⋰   up right diagonal ellipsis ON 1.1
sgml &utdot;
U+22F1   ⋱   down right diagonal ellipsis ON 1.1
sgml &dtdot;
U+22F2   ⋲   element of with long horizontal stroke ON 3.2
sgml &disin;
U+22F3   ⋳   element of with vertical bar at end of horizontal stroke ON 3.2
sgml &isinsv;
U+22F4   ⋴   small element of with vertical bar at end of horizontal stroke ON 3.2
sgml &isins;
U+22F5   ⋵   element of with dot above ON 3.2
sgml &isindot;
U+22F6   ⋶   element of with overbar ON 3.2
sgml &notinvc;
U+22F7   ⋷   small element of with overbar ON 3.2
sgml &notinvb;
U+22F8   ⋸   element of with underbar ON 3.2
U+22F9   ⋹   element of with two horizontal strokes ON 3.2
sgml &isinE;
U+22FA   ⋺   contains with long horizontal stroke ON 3.2
sgml &nisd;
U+22FB   ⋻   contains with vertical bar at end of horizontal stroke ON 3.2
sgml &xnis;
U+22FC   ⋼   small contains with vertical bar at end of horizontal stroke ON 3.2
sgml &nis;
U+22FD   ⋽   contains with overbar ON 3.2
sgml &notnivc;
U+22FE   ⋾   small contains with overbar ON 3.2
sgml &notnivb;
U+22FF   ⋿   z notation bag membership ON 3.2

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