Mathematical Operators is a Unicode block containing characters for mathematical, logical, and set notation.
Notably absent are the plus sign (+), greater than sign (>) and less than sign (<), due to them already appearing in the Basic Latin Unicode block, and the plus-or-minus sign (±), multiplication sign (×) and obelus (÷), due to them already appearing in the Latin-1 Supplement block, although a distinct minus sign (−) is included, semantically different from the Basic Latin hyphen-minus (-).
Block
| Mathematical Operators[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 | ⋰ | ⋱ | ⋲ | ⋳ | ⋴ | ⋵ | ⋶ | ⋷ | ⋸ | ⋹ | ⋺ | ⋻ | ⋼ | ⋽ | ⋾ | ⋿ |
| Notes1.^ As of Unicode version 16.0 | ||||||||||||||||
Variation sequences
The Mathematical Operators block has sixteen variation sequences defined for standardized variants.12 They use U+FE00 VARIATION SELECTOR-1 (VS01) to denote variant symbols (depending on the font):
Variation sequences| Base character | Base | +VS01 | Description |
|---|---|---|---|
| U+2205 EMPTY SET | ∅ | ∅︀ | zero with long diagonal stroke overlay form |
| U+2229 INTERSECTION | ∩ | ∩︀ | with serifs |
| U+222A UNION | ∪ | ∪︀ | with serifs |
| U+2268 LESS-THAN BUT NOT EQUAL TO | ≨ | ≨︀ | with vertical stroke |
| U+2269 GREATER-THAN BUT NOT EQUAL TO | ≩ | ≩︀ | with vertical stroke |
| U+2272 LESS-THAN OR EQUIVALENT TO | ≲ | ≲︀ | following the slant of the lower leg |
| U+2273 GREATER-THAN OR EQUIVALENT TO | ≳ | ≳︀ | following the slant of the lower leg |
| U+228A SUBSET OF WITH NOT EQUAL TO | ⊊ | ⊊︀ | with stroke through bottom members |
| U+228B SUPERSET OF WITH NOT EQUAL TO | ⊋ | ⊋︀ | with stroke through bottom members |
| U+2293 SQUARE CAP | ⊓ | ⊓︀ | with serifs |
| U+2294 SQUARE CUP | ⊔ | ⊔︀ | with serifs |
| U+2295 CIRCLED PLUS | ⊕ | ⊕︀ | with white rim |
| U+2297 CIRCLED TIMES | ⊗ | ⊗︀ | with white rim |
| U+229C CIRCLED EQUALS | ⊜ | ⊜︀ | with equal sign touching the circle |
| U+22DA LESS-THAN EQUAL TO OR GREATER-THAN | ⋚ | ⋚︀ | with slanted equal |
| U+22DB GREATER-THAN EQUAL TO OR LESS-THAN | ⋛ | ⋛︀ | with slanted equal |
History
The following Unicode-related documents record the purpose and process of defining specific characters in the Mathematical Operators block:
| Version | Final code points3 | Count | UTC ID | L2 ID | WG2 ID | Document |
|---|---|---|---|---|---|---|
| 1.0.0 | U+2200..22F1 | 242 | (to be determined) | |||
| UTC/1999-013 | Karlsson, Kent (1999-05-27), Tildes and micro sign decompositions | |||||
| L2/99-176R | Moore, Lisa (1999-11-04), "Not Tilde", Minutes from the joint UTC/L2 meeting in Seattle, June 8-10, 1999 | |||||
| L2/00-115R2 | Moore, Lisa (2000-08-08), "Motion 83-M21", Minutes Of UTC Meeting #83 | |||||
| L2/01-342 | Suignard, Michel (2001-09-10), "T.9 B.1 List of combining characters/Variation selectors", Comments accompanying the US positive vote on the FPDAM 1 to ISO/IEC 10646-1:2001 | |||||
| L2/07-268 | N3253 (pdf, doc) | Umamaheswaran, V. S. (2007-07-26), "M50.7 (Math symbol glyph correction) [U+22C4]", Unconfirmed minutes of WG 2 meeting 50, Frankfurt-am-Main, Germany; 2007-04-24/27 | ||||
| L2/15-268 | Beeton, Barbara; Freytag, Asmus; Iancu, Laurențiu; Sargent, Murray (2015-10-30), Proposal to Represent the Slashed Zero Variant of Empty Set | |||||
| L2/15-254 | Moore, Lisa (2015-11-16), "B.12.1.2 Proposal to Represent the Slashed Zero Variant of Empty Set", UTC #145 Minutes | |||||
| L2/24-173 | Pentzlin, Karl (2024-06-06), Proposal to encode a Middle Asterisk as referred to in the German standard DIN 2137 [Affects U+2217] | |||||
| L2/24-166 | Anderson, Deborah; Goregaokar, Manish; Kučera, Jan; Whistler, Ken; Pournader, Roozbeh; Constable, Peter (2024-07-18), "20. Middle Asterisk [Affects U+2217]", Recommendations to UTC #180 July 2024 on Script Proposals | |||||
| L2/24-159 | Constable, Peter (2024-07-29), "Section 20. Middle Asterisk", UTC #180 Minutes, Consider adding an annotation to U+2217 that it may be used to represent the telephony asterisk | |||||
| 3.2 | U+22F2..22FF | 14 | L2/00-1194 | N2191R | Whistler, Ken; Freytag, Asmus (2000-04-19), Encoding Additional Mathematical Symbols in Unicode | |
| L2/00-234 | N2203 (rtf, txt) | Umamaheswaran, V. S. (2000-07-21), "8.18", Minutes from the SC2/WG2 meeting in Beijing, 2000-03-21 -- 24 | ||||
| L2/00-115R2 | Moore, Lisa (2000-08-08), "Motion 83-M11", Minutes Of UTC Meeting #83 | |||||
See also
References
"Unicode Character Database: Standardized Variation Sequences". The Unicode Consortium. https://www.unicode.org/Public/UNIDATA/StandardizedVariants.txt ↩
Whistler, Ken; Freytag, Asmus (2000-04-19), "Symbol variants defined using a Variation Selector", L2/00-119: Encoding Additional Mathematical Symbols in Unicode (PDF) https://www.unicode.org/L2/L2000/00119-math.pdf ↩
Proposed code points and characters names may differ from final code points and names ↩
Refer to the history section of the Miscellaneous Mathematical Symbols-B block for additional math-related documents /wiki/Miscellaneous_Mathematical_Symbols-B#History ↩