Important Codes / Mathematical Operators List

Common Arithmetic & Alebgra

Character Name Character
LESS THAN <
GREATER THAN >
LESS THAN OR EQUAL TO ≤
GREATER THAN OR EQUAL TO ≥
PLUS OR MINUS ±
NOT EQUALS ≠
DIVISION SIGN ÷
TIMES X ×
MINUS −
DIVISION SLASH ∕
FRACTION SLASH ⁄
SQUARE ROOT RADICAL √
CUBE ROOT ∛
FOURTH ROOT ∜
INFINITY ∞
ALEF INFINITY SYMBOL ℵ
FUNCTION ITALIC F ƒ
PRIME (single quote) ′
DOUBLE PRIME (double quote) ″
TRIPLE PRIME (triple quote) ‴
THEREFORE (Triangular Dots) ∴
DOT OPERATOR ⋅
SUPERSCRIPT TWO ¹
SUPERSCRIPT TWO ²
SUPERSCRIPT THREE ³
LEFT ANGLE BRACKET ⟨
RIGHT ANGLE BRACKET ⟩
LEFT CEILING BRACKET ⌈
RIGHT CEILING BRACKET ⌉
LEFT FLOOR BRACKET ⌊
RIGHT FLOOR BRACKET ⌋
CIRCLED PLUS (Direct Sum) ⊕
CIRCLED TIMES (Vector Product) ⊗

Statistical operators

Character Name Character
LOWER CASE MU (Mean) μ
LOWER CASE SIGMA (Standard Deviation) σ
LOWER CASE CHI χ
CAPITAL SIGMA N-ARY SUMMATION ∑
CAPITAL PI N-ARY PRODUCT ∏
N-ARY COPRODUCT (upside down capital pi) ∐

Statistics Symbols using Combining Diacritics (X-Bar, P-Hat and D-Bar)

Character Name Character
X-Bar (Average) x̄
P-Hat p̂
D-Bar D̄

 

Measurement Symbols

Character Name Character
DEGREE SYMBOL °
MICRO MU SYMBOL µ
SINGLE PRIME (feet, degree minutes) ′
DOUBLE PRIME (inches, degree seconds) ″
PER MILLE (1/1000th) ‰

Calculus Symbols and Integration

Character Name Character
INTEGRAL ∫
PARTIAL DIFFERENTIAL ∂
INCREMENT (Difference or capital Delta) Δ
NABLA (Backward Difference, Grad or upside down triangle) ∇
DOUBLE INTEGRAL ∬
TRIPLE INTEGRAL ∭
QUADRUPLE INTEGRAL ⨌
CONTOUR INTEGRAL ∮
SURFACE INTEGRAL ∯
VOLUME INTEGRAL ∰
CLOCKWISE INTEGRAL ∱
ANTICLOCKWISE INTEGRAL ⨑
CLOCKWISE CONTOUR INTEGRAL ∲
ANTICLOCKWISE CONTOUR INTEGRAL ∳

Letter Symbols

Character Name Character
INFINITY (Sideways 8) ∞
ALEF INFINITY SYMBOL ℵ
WEIERSTRASS POWER SET (Script Capital P) ℘
IMAGINARY Part (Blackletter I) ℑ
REAL NUMBER (Blackletter R) ℜ
DOUBLE-STRUCK REAL NUMBER (Doublestruck R) ℝ
COMPLEX NUMBERS (Doublestruck C) ℂ
NATURAL NUMBERS (Doublestruck N) ℕ
PRIME NUMBERS (Doublestruck P) ℙ
RATIONAL NUMBERS (Doublestruck Q) ℚ
INTEGERS (Doublestruck Z) ℤ

Logic & Set Theory

Codes for Logic and Set Theory Symbols
Character Name Character
FOR ALL (Upside-down A) ∀
COMPLEMENT (Thin C) ∁
THERE EXISTS (Backwards E) ∃
THERE DOES NOT EXIST (Backwards E with slash) ∄
EMPTY SET (O slash) ∅
NOT SYMBOL (Corner) ¬
TILDE (Alternate Not Symbol) ˜
LOGICAL AND (Wedge or Upside down V Symbol) ∧
LOGICAL OR (V Symbol) ∨
XOR ⊻
NAND ⊼
NOR ⊽
INTERSECTION (Cap or Upside Down U) ∩
UNION (Cup or U Symbol) ∪
ELEMENT OF ∈
NOT AN ELEMENT OF ∉
SMALL ELEMENT OF ∊
CONTAINS AS MEMBER ∋
DOES NOT CONTAIN AS MEMBER ∌
SMALL CONTAINS AS MEMBER ∍
SET MINUS ∖
SUBSET OF (Sideways U with cap to left) ⊂
SUPERSET OF (Sideways U with cap to right) ⊃
NOT A SUBSET OF (Subset with Slash) ⊄
NOT A SUPERSET OF (Superset with slash) ⊅
SUBSET OF OR EQUAL TO (Subset with line below) ⊆
SUPERSET OF OR EQUAL TO (Superset with line below) ⊇
NEITHER A SUBSET OF NOR EQUAL TO ⊈
NEITHER A SUPERSET OF NOR EQUAL TO ⊉
SUBSET OF WITH NOT EQUAL TO ⊊
SUPERSET OF WITH NOT EQUAL TO ⊋
DIAMOND OPERATOR
(Possibility)		 ⋄
ASYMPTOTICALLY EQUAL TO
One to one Correspondence 		≃
NOT ASYMPTOTICALLY EQUAL TO ≄
MULTISET (U with arrow) ⊌
MULTISET MULTIPLICATION (U with dot in center) ⊍
MULTISET UNION (U with plus in center) ⊎
DOUBLE SUBSET ⋐
DOUBLE SUPERSET ⋑
DOUBLE INTERSECTION ⋒
DOUBLE UNION ⋓
N-ARY LOGICAL AND ⋀
N-ARY LOGICAL OR ⋁
N-ARY INTERSECTION/td> ⋂
N-ARY UNION ⋃
CURLY LOGICAL OR ⋎
CURLY LOGICAL AND ⋏
CIRCLED PLUS (Direct Sum) ⊕
CIRCLED TIMES (Vector Product) ⊗
CIRCLED MINUS ⊖
CIRCLED DIVISION SLASH ⊘

Other Element Of Symbols

Character Name Character
ELEMENT OF WITH LONG HORIZONTAL STROKE ⋲
ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE ⋳
SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE ⋴
ELEMENT OF WITH DOT ABOVE ⋵
ELEMENT OF WITH OVERBAR ⋶
SMALL ELEMENT OF WITH OVERBAR ⋷
ELEMENT OF WITH UNDERBAR ⋸
ELEMENT OF WITH TWO HORIZONTAL STROKES ⋹
CONTAINS WITH LONG HORIZONTAL STROKE ⋺
CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE ⋻
SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE ⋼
CONTAINS WITH OVERBAR ⋽
SMALL CONTAINS WITH OVERBAR ⋾
NOTATION BAG MEMBERSHIP ⋿

Geometric Symbols

Angles and Lines

Character Name Character
RIGHT ANGLE ∟
ANGLE
Entity Code = &ang;		 ∠
MEASURED ANGLE ∡
SPHERICAL ANGLE ∢
DIVIDES ∣
DOES NOT DIVIDE ∤
PARALLEL TO ∥
NOT PARALLEL TO ∦
RIGHT ANGLE WITH ARC ⊾
RIGHT TRIANGLE ⊿
UP TACK (Perpendicular)
Entity Code = &perp; 		⊥
RIGHT TACK ⊢
LEFT TACK ⊣
DOWN TACK ⊤

Logical Symbols

Character Name Character
THEREFORE (Triangular Dots)
Entity Code = &there4;		 ∴
BECAUSE (Upside down Triangular Dots) ∵
PROPORTIONAL TO
Entity Code = &prop;		 ∝
END OF PROOF (solid rectangle) ∎


Equivalence and Proportion Operators

Character Name Character
NOT EQUALS ≠
APPROXIMATELY EQUAL ≅
ALMOST EQUAL (ASYMPTOTIC) ≈
NOT ALMOST EQUAL TO ≉
TILDE SIMILAR TO ∼
IDENTICAL TO (three lines) ≡
NOT IDENTICAL TO ≢

Other Equivalence Symbols

Character Name Character
STRICTLY EQUIVALENT TO ≣
NOT IDENTICAL TO ≢
LESS-THAN OVER EQUAL TO ≦
GREATER-THAN OVER EQUAL TO ≧
LESS-THAN BUT NOT EQUAL TO ≨
GREATER-THAN BUT NOT EQUAL TO ≩
MUCH LESS-THAN ≪
MUCH GREATER-THAN ≫
BETWEEN ≬
NOT EQUIVALENT TO ≭
NOT LESS-THAN ≮
NOT GREATER-THAN ≯
NEITHER LESS-THAN NOR EQUAL TO ≰
NEITHER GREATER-THAN NOR EQUAL TO ≱
LESS-THAN OR EQUIVALENT TO ≲
GREATER-THAN OR EQUIVALENT TO ≳
NEITHER LESS-THAN NOR EQUIVALENT TO ≴
NEITHER GREATER-THAN NOR EQUIVALENT TO ≵
LESS-THAN OR GREATER-THAN ≶
GREATER-THAN OR LESS-THAN ≷
NEITHER LESS-THAN NOR GREATER-THAN ≸
NEITHER GREATER-THAN NOR LESS-THAN ≹
NOT TILDE ≁
MINUS TILDE ≂
ASYMPTOTICALLY EQUAL TO ≃
NOT ASYMPTOTICALLY EQUAL TO ≄
APPROXIMATELY BUT NOT ACTUALLY EQUAL TO ≆
NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO ≇
NOT ALMOST EQUAL TO ≉
ALMOST EQUAL OR EQUAL TO ≊
TRIPLE TILDE ≋
ALL EQUAL TO ≌

Other Mathematical Symbols

Character Name Character
MINUS-OR-PLUS SIGN ∓
DOT PLUS ∔
ASTERISK OPERATOR ∗
RING OPERATOR ∘
BULLET OPERATOR ∙
PROPORTIONAL TO ∝
RATIO ∶
PROPORTION ∷
DOT MINUS ∸
EXCESS ∹
GEOMETRIC PROPORTION ∺
HOMOTHETIC ∻
TILDE OPERATOR ∼
REVERSED TILDE ∽
INVERTED LAZY S ∾
SINE WAVE ∿
WREATH PRODUCT ≀
EQUIVALENT TO ≍
GEOMETRICALLY EQUIVALENT TO ≎
DIFFERENCE BETWEEN ≏
APPROACHES THE LIMIT ≐
GEOMETRICALLY EQUAL TO ≑
APPROXIMATELY EQUAL TO OR THE IMAGE OF ≒
IMAGE OF OR APPROXIMATELY EQUAL TO ≓
COLON EQUALS ≔
EQUALS COLON ≕
RING IN EQUAL TO ≖
RING EQUAL TO ≗
CORRESPONDS TO ≘
ESTIMATES ≙
EQUIANGULAR TO ≚
STAR EQUALS ≛
DELTA EQUAL TO ≜
EQUAL TO BY DEFINITION ≝
MEASURED BY ≞
QUESTIONED EQUAL TO ≟
PRECEDES ≺
SUCCEEDS ≻
PRECEDES OR EQUAL TO ≼
SUCCEEDS OR EQUAL TO ≽
PRECEDES OR EQUIVALENT TO ≾
SUCCEEDS OR EQUIVALENT TO ≿
DOES NOT PRECEDE ⊀
DOES NOT SUCCEED ⊁
SQUARE IMAGE OF ⊏
SQUARE ORIGINAL OF ⊐
SQUARE IMAGE OF OR EQUAL TO ⊑
SQUARE ORIGINAL OF OR EQUAL TO ⊒
SQUARE CAP ⊓
SQUARE CUP ⊔
CIRCLED PLUS ⊕
CIRCLED MINUS ⊖
CIRCLED TIMES ⊗
CIRCLED DIVISION SLASH ⊘
CIRCLED DOT OPERATOR ⊙
CIRCLED RING OPERATOR ⊚
CIRCLED ASTERISK OPERATOR ⊛
CIRCLED EQUALS ⊜
CIRCLED DASH ⊝
SQUARED PLUS ⊞
SQUARED MINUS ⊟
SQUARED TIMES ⊠
SQUARED DOT OPERATOR ⊪
ASSERTION ⊦
MODELS ⊧
TRUE ⊨
FORCES ⊩
TRIPLE VERTICAL BAR RIGHT TURNSTILE ⊪
DOUBLE VERTICAL BAR DOUBLE RIGHT TURNSTILE ⊫
DOES NOT PROVE ⊬
NOT TRUE ⊭
DOES NOT FORCE ⊮
NEGATED DOUBLE VERTICAL BAR DOUBLE RIGHT TURNSTILE ⊯
PRECEDES UNDER RELATION ⊰
SUCCEEDS UNDER RELATION ⊱
NORMAL SUBGROUP OF ⊲
CONTAINS AS NORMAL SUBGROUP ⊳
NORMAL SUBGROUP OF OR EQUAL TO ⊴
CONTAINS AS NORMAL SUBGROUP OR EQUAL TO ⊵
ORIGINAL OF ⊶
IMAGE OF ⊷
MULTIMAP ⊸
HERMITIAN CONJUGATE MATRIX ⊹
INTERCALATE ⊺
DIAMOND OPERATOR ⋄
DOT OPERATOR ⋅
STAR OPERATOR ⋆
DIVISION TIMES ⋇
BOWTIE ⋈
LEFT NORMAL FACTOR SEMIDIRECT PRODUCT ⋉
RIGHT NORMAL FACTOR SEMIDIRECT PRODUCT ⋊
LEFT SEMIDIRECT PRODUCT ⋋
RIGHT SEMIDIRECT PRODUCT ⋌
REVERSED TILDE EQUALS ⋍
PITCHFORK ⋔
EQUAL AND PARALLEL TO ⋕
LESS-THAN WITH DOT ⋖
GREATER-THAN WITH DOT ⋗
VERY MUCH LESS-THAN ⋘
VERY MUCH GREATER-THAN ⋙
LESS-THAN EQUAL TO OR GREATER-THAN ⋚
GREATER-THAN EQUAL TO OR LESS-THAN ⋛
EQUAL TO OR LESS-THAN ⋜
EQUAL TO OR GREATER-THAN ⋝
EQUAL TO OR PRECEDES ⋞
EQUAL TO OR SUCCEEDS ⋟
DOES NOT PRECEDE OR EQUAL ⋠
DOES NOT SUCCEED OR EQUAL ⋡
NOT SQUARE IMAGE OF OR EQUAL TO ⋢
NOT SQUARE ORIGINAL OF OR EQUAL TO ⋣
SQUARE IMAGE OF OR NOT EQUAL TO ⋤
SQUARE ORIGINAL OF OR NOT EQUAL TO ⋥
LESS-THAN BUT NOT EQUIVALENT TO ⋦
GREATER-THAN BUT NOT EQUIVALENT TO ⋧
PRECEDES BUT NOT EQUIVALENT TO ⋨
SUCCEEDS BUT NOT EQUIVALENT TO ⋩
NOT NORMAL SUBGROUP OF ⋪
DOES NOT CONTAIN AS NORMAL SUBGROUP ⋫
NOT NORMAL SUBGROUP OF OR EQUAL TO ⋬
DOES NOT CONTAIN AS NORMAL SUBGROUP OR EQUAL ⋭
VERTICAL ELLIPSIS ⋮
MIDLINE HORIZONTAL ELLIPSIS ⋯
UP RIGHT DIAGONAL ELLIPSIS ⋰
DOWN RIGHT DIAGONAL ELLIPSIS ⋱

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