Mathematical operators and symbols in Unicode

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Template:Short description

File:0009-cmls-2012 preview ecran.jpg
Blackboard at the Laurent Schwartz Center for Mathematics, École Polytechnique

Template:SpecialChars The Unicode Standard encodes almost all standard characters used in mathematics.[1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation.[1] Mathematical operators and symbols are in multiple Unicode blocks. Some of these blocks are dedicated to, or primarily contain, mathematical characters while others are a mix of mathematical and non-mathematical characters. This article covers all Unicode characters with a derived property of "Math".[2][3]

Dedicated blocks

Mathematical Operators block

Script error: No such module "Labelled list hatnote". The Mathematical Operators block (U+2200–U+22FF) contains characters for mathematical, logical, and set notation.

Mathematical Operators<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+220x
U+221x
U+222x
U+223x
U+224x
U+225x
U+226x
U+227x
U+228x
U+229x
U+22Ax
U+22Bx
U+22Cx
U+22Dx
U+22Ex
U+22Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Mathematical Operators block

Script error: No such module "Labelled list hatnote". The Supplemental Mathematical Operators block (U+2A00–U+2AFF) contains various mathematical symbols, including N-ary operators, summations and integrals, intersections and unions, logical and relational operators, and subset/superset relations.

Supplemental Mathematical Operators<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2A0x
U+2A1x
U+2A2x
U+2A3x ⨿
U+2A4x
U+2A5x
U+2A6x
U+2A7x ⩿
U+2A8x
U+2A9x
U+2AAx
U+2ABx ⪿
U+2ACx
U+2ADx
U+2AEx
U+2AFx ⫿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Mathematical Alphanumeric Symbols block

Script error: No such module "Labelled list hatnote". The Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The reserved code points (the "holes") in the alphabetic ranges up to U+1D551 duplicate characters in the Letterlike Symbols block. In order, these are: Template:Not a typo.

Template:Unicode chart Mathematical Alphanumeric Symbols

Letterlike Symbols block

Script error: No such module "Labelled list hatnote". The Letterlike Symbols block (U+2100–U+214F) includes variables. Most alphabetic math symbols are in the Mathematical Alphanumeric Symbols block shown above.

The math subset of this block is U+2102, U+2107, U+210A–U+2113, U+2115, U+2118–U+211D, U+2124, U+2128–U+2129, U+212C–U+212D, U+212F–U+2131, U+2133–U+2138, U+213C–U+2149, and U+214B.[4]

Letterlike Symbols<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+210x
U+211x
U+212x
U+213x
U+214x
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Mathematical Symbols-A block

Script error: No such module "Labelled list hatnote". The Miscellaneous Mathematical Symbols-A block (U+27C0–U+27EF) contains characters for mathematical, logical, and database notation.

Miscellaneous Mathematical Symbols-A<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Cx
U+27Dx
U+27Ex
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Mathematical Symbols-B block

Script error: No such module "Labelled list hatnote". The Miscellaneous Mathematical Symbols-B block (U+2980–U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols.

Miscellaneous Mathematical Symbols-B<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+298x
U+299x
U+29Ax
U+29Bx ⦿
U+29Cx
U+29Dx
U+29Ex
U+29Fx ⧿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Technical block

Script error: No such module "Labelled list hatnote". The Miscellaneous Technical block (U+2300–U+23FF) includes braces and operators.

The math subset of this block is U+2308–U+230B, U+2320–U+2321, U+237C, U+239B–U+23B5, 23B7, U+23D0, and U+23DC–U+23E2.

Miscellaneous Technical<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+230x
U+231x
U+232x
U+233x
U+234x
U+235x
U+236x
U+237x
U+238x
U+239x
U+23Ax
U+23Bx
U+23Cx
U+23Dx
U+23Ex
U+23Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Unicode code points U+2329 and U+232A are deprecated as of Unicode version 5.2

Geometric Shapes block

Script error: No such module "Labelled list hatnote". The Geometric Shapes block (U+25A0–U+25FF) contains geometric shape symbols.

The math subset of this block is U+25A0–25A1, U+25AE–25B7, U+25BC–25C1, U+25C6–25C7, U+25CA–25CB, U+25CF–25D3, U+25E2, U+25E4, U+25E7–25EC, and U+25F8–25FF.

Geometric Shapes<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+25Ax
U+25Bx
U+25Cx
U+25Dx
U+25Ex
U+25Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Arrows block

Script error: No such module "Labelled list hatnote". The Arrows block (U+2190–U+21FF) contains line, curve, and semicircle arrows and arrow-like operators.

The math subset of this block is U+2190–U+21A7, U+21A9–U+21AE, U+21B0–U+21B1, U+21B6–U+21B7, U+21BC–U+21DB, U+21DD, U+21E4–U+21E5, U+21F4–U+21FF.[5]

Arrows<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+219x
U+21Ax
U+21Bx
U+21Cx
U+21Dx
U+21Ex
U+21Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Arrows-A block

Script error: No such module "Labelled list hatnote". The Supplemental Arrows-A block (U+27F0–U+27FF) contains arrows and arrow-like operators.

Supplemental Arrows-A<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+27Fx
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Supplemental Arrows-B block

Script error: No such module "Labelled list hatnote". The Supplemental Arrows-B block (U+2900–U+297F) contains arrows and arrow-like operators (arrow tails, crossing arrows, curved arrows, and harpoons).

Supplemental Arrows-B<templatestyles src="Citation/styles.css"/>[1]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+290x
U+291x
U+292x
U+293x ⤿
U+294x
U+295x
U+296x
U+297x ⥿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version

Miscellaneous Symbols and Arrows block

Script error: No such module "Labelled list hatnote". The Miscellaneous Symbols and Arrows block (U+2B00–U+2BFF Arrows) contains arrows and geometric shapes with various fills.

The math subset of this block is U+2B30–U+2B44, U+2B47–U+2B4C.[6]

Miscellaneous Symbols and Arrows<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+2B0x
U+2B1x
U+2B2x
U+2B3x ⬿
U+2B4x
U+2B5x
U+2B6x
U+2B7x ⭿
U+2B8x
U+2B9x
U+2BAx
U+2BBx ⮿
U+2BCx
U+2BDx
U+2BEx
U+2BFx ⯿
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Grey areas indicate non-assigned code points

Combining Diacritical Marks for Symbols block

Script error: No such module "Labelled list hatnote". The Combining Diacritical Marks for Symbols block contains arrows, dots, enclosures, and overlays for modifying symbol characters.

The math subset of this block is U+20D0–U+20DC, U+20E1, U+20E5–U+20E6, and U+20EB–U+20EF.

Combining Diacritical Marks for Symbols<templatestyles src="Citation/styles.css"/>[1]<templatestyles src="Citation/styles.css"/>[2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+20Dx ◌⃐ ◌⃑ ◌⃒ ◌⃓ ◌⃔ ◌⃕ ◌⃖ ◌⃗ ◌⃘ ◌⃙ ◌⃚ ◌⃛ ◌⃜ ◌⃝ ◌⃞ ◌⃟
U+20Ex ◌⃠ ◌⃡ ◌⃢ ◌⃣ ◌⃤ ◌⃥ ◌⃦ ◌⃧ ◌⃨ ◌⃩ ◌⃪ ◌⃫ ◌⃬ ◌⃭ ◌⃮ ◌⃯
U+20Fx ◌⃰
Notes
1.<templatestyles src="Citation/styles.css"/>^ Template:Unicode version
2.<templatestyles src="Citation/styles.css"/>^ Grey areas indicate non-assigned code points

Arabic Mathematical Alphabetic Symbols block

Script error: No such module "Labelled list hatnote". The Arabic Mathematical Alphabetic Symbols block (U+1EE00–U+1EEFF) contains characters used in Arabic mathematical expressions. Template:Unicode chart Arabic Mathematical Alphabetic Symbols

Characters in other blocks

Mathematical characters also appear in other blocks. Below is a list of these characters as of Unicode version Template:Unicode version:

U+002B + PLUS SIGN
U+002D - HYPHEN-MINUS[7]
U+003C < LESS-THAN SIGN
U+003D = EQUALS SIGN
U+003E > GREATER-THAN SIGN
U+005E ^ CIRCUMFLEX ACCENT
U+007C | VERTICAL LINE
U+007E ~ TILDE
U+00AC ¬ NOT SIGN
U+00B0 ° DEGREE SIGN[8]
U+00B1 ± PLUS-MINUS SIGN
U+00D7 × MULTIPLICATION SIGN
U+00F7 ÷ DIVISION SIGN
U+03D0 ϐ GREEK BETA SYMBOL
U+03D1 ϑ GREEK THETA SYMBOL
U+03D2 ϒ GREEK UPSILON WITH HOOK SYMBOL
U+03D5 ϕ GREEK PHI SYMBOL
U+03F0 ϰ GREEK KAPPA SYMBOL
U+03F1 ϱ GREEK RHO SYMBOL
U+03F4 ϴ GREEK CAPITAL THETA SYMBOL
U+03F5 ϵ GREEK LUNATE EPSILON SYMBOL
U+03F6 ϶ GREEK REVERSED LUNATE EPSILON SYMBOL
U+0606 ؆ ARABIC-INDIC CUBE ROOT
U+0607 ؇ ARABIC-INDIC FOURTH ROOT
U+0608 ؈ ARABIC RAY
U+2016 DOUBLE VERTICAL LINE
U+2032 PRIME
U+2033 DOUBLE PRIME
U+2034 TRIPLE PRIME
U+2040 CHARACTER TIE
U+2044 FRACTION SLASH
U+2052 COMMERCIAL MINUS SIGN
U+2061 noteScript error: No such module "Check for unknown parameters". FUNCTION APPLICATION
U+2062 noteScript error: No such module "Check for unknown parameters". INVISIBLE TIMES
U+2063 noteScript error: No such module "Check for unknown parameters". INVISIBLE SEPARATOR
U+2064 noteScript error: No such module "Check for unknown parameters". INVISIBLE PLUS

Note: non-marking character

U+207A SUPERSCRIPT PLUS SIGN
U+207B SUPERSCRIPT MINUS
U+207C SUPERSCRIPT EQUALS SIGN
U+207D SUPERSCRIPT LEFT PARENTHESIS
U+207E SUPERSCRIPT RIGHT PARENTHESIS
U+208A SUBSCRIPT PLUS SIGN
U+208B SUBSCRIPT MINUS
U+208C SUBSCRIPT EQUALS SIGN
U+208D SUBSCRIPT LEFT PARENTHESIS
U+208E SUBSCRIPT RIGHT PARENTHESIS
U+2605 BLACK STAR
U+2606 WHITE STAR
U+2640 FEMALE SIGN
U+2642 MALE SIGN
U+2660 BLACK SPADE SUIT
U+2661 WHITE HEART SUIT
U+2662 WHITE DIAMOND SUIT
U+2663 BLACK CLUB SUIT
U+266D MUSIC FLAT SIGN
U+266E MUSIC NATURAL SIGN
U+266F MUSIC SHARP SIGN
U+FB29 HEBREW LETTER ALTERNATIVE PLUS SIGN
U+FE61 SMALL ASTERISK
U+FE62 SMALL PLUS SIGN
U+FE63 SMALL HYPHEN-MINUS
U+FE64 SMALL LESS-THAN SIGN
U+FE65 SMALL GREATER-THAN SIGN
U+FE66 SMALL EQUALS SIGN
U+FE68 SMALL REVERSE SOLIDUS
U+FF0B FULLWIDTH PLUS SIGN
U+FF1C FULLWIDTH LESS-THAN SIGN
U+FF1D FULLWIDTH EQUALS SIGN
U+FF1E FULLWIDTH GREATER-THAN SIGN
U+FF3C FULLWIDTH REVERSE SOLIDUS
U+FF3E FULLWIDTH CIRCUMFLEX ACCENT
U+FF5C FULLWIDTH VERTICAL LINE
U+FF5E FULLWIDTH TILDE
U+FFE2 FULLWIDTH NOT SIGN
U+FFE9 HALFWIDTH LEFTWARDS ARROW
U+FFEA HALFWIDTH UPWARDS ARROW
U+FFEB HALFWIDTH RIGHTWARDS ARROW
U+FFEC HALFWIDTH DOWNWARDS ARROW
U+10D8E 𐶎 GARAY PLUS SIGN
U+10D8F 𐶏 GARAY MINUS SIGN

See also

References

<templatestyles src="Reflist/styles.css" />

  1. a b Script error: No such module "citation/CS1".
  2. Script error: No such module "citation/CS1".
  3. Script error: No such module "citation/CS1".
  4. See https://www.unicode.org/Public/UCD/latest/ucd/DerivedCoreProperties.txt
  5. More symbols are supported by TeX math packages, see e.g. Will Robertson, Symbols defined by unicode-math.
  6. The quadruple arrows U+2B45 and U+2B46 are supported by TeX math packages, per Will Robertson, Symbols defined by unicode-math.
  7. As per Unicode 16.0.0, the ASCII hyphen-minus is not a mathematical symbol. To express the minus sign in math, Template:Unichar is used instead.
  8. As per Unicode 16.0.0, the degree sign is not a mathematical symbol, since it is a measurement unit symbol rather than a math symbol. Consistently, TeX packages support many non-math symbols. But this article is designed to cover only Unicode characters with a derived property of "Math".

Script error: No such module "Check for unknown parameters".

External links

  • Script error: No such module "citation/CS1".
  • Images of glyphs in section 6.3.3 of the Script error: No such module "citation/CS1".

Template:Unicode navigation Template:Mathematical symbols notation language