Mathematical operators and symbols in Unicode explained

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

See main article: Mathematical Operators (Unicode block). The Mathematical Operators block (U+2200 - U+22FF) contains characters for mathematical, logical, and set notation.

Supplemental Mathematical Operators block

See main article: Supplemental Mathematical Operators (Unicode block). 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.

Mathematical Alphanumeric Symbols block

See main article: Mathematical Alphanumeric Symbols (Unicode block). 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 ℎ / ℬ ℰ ℱ ℋ ℐ ℒ ℳ ℛ / ℯ ℊ ℴ / ℭ ℌ ℑ ℜ ℨ / ℂ ℍ ℕ ℙ ℚ ℝ ℤ.

Letterlike Symbols block

See main article: Letterlike Symbols (Unicode block). 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]

Miscellaneous Mathematical Symbols-A block

See main article: Miscellaneous Mathematical Symbols-A (Unicode block). The Miscellaneous Mathematical Symbols-A block (U+27C0 - U+27EF) contains characters for mathematical, logical, and database notation.

Miscellaneous Mathematical Symbols-B block

See main article: Miscellaneous Mathematical Symbols-B (Unicode block). The Miscellaneous Mathematical Symbols-B block (U+2980 - U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols.

Miscellaneous Technical block

See main article: Miscellaneous Technical (Unicode block). 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.

Geometric Shapes block

See main article: Geometric Shapes (Unicode block). 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.

Arrows block

See main article: Arrows (Unicode block). 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]

Supplemental Arrows-A block

See main article: Supplemental Arrows-A (Unicode block). The Supplemental Arrows-A block (U+27F0 - U+27FF) contains arrows and arrow-like operators.

Supplemental Arrows-B block

See main article: Supplemental Arrows-B (Unicode block). The Supplemental Arrows-B block (U+2900 - U+297F) contains arrows and arrow-like operators (arrow tails, crossing arrows, curved arrows, and harpoons).

Miscellaneous Symbols and Arrows block

See main article: Miscellaneous Symbols and Arrows (Unicode block). 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]

Combining Diacritical Marks for Symbols block

See main article: Combining Diacritical Marks for Symbols (Unicode block). 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.

Arabic Mathematical Alphabetic Symbols block

See main article: Arabic Mathematical Alphabetic Symbols block. The Arabic Mathematical Alphabetic Symbols block (U+1EE00 - U+1EEFF) contains characters used in Arabic mathematical expressions.

Characters in other blocks

Mathematical characters also appear in other blocks. Below is a list of these characters as of Unicode version version=15.1:

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

Notes and References

  1. Web site: Unicode Technical Report #25: Unicode Support for Mathematics . The Unicode Consortium . 2 April 2012 . PDF . 14 August 2014.
  2. Web site: Unicode Character Database: Derived Core Properties . The Unicode Consortium . 19 February 2014 . 14 August 2014 .
  3. Web site: Unicode Technical Annex #44: Unicode Character Database . The Unicode Consortium . 25 September 2013 . PDF . 14 August 2014.
  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 15.1.0, the ASCII hyphen-minus is not a mathematical symbol. To express the minus sign in math, is used instead.