# Miscellaneous Mathematical Symbols-A

Miscellaneous Mathematical Symbols-A is a Unicode block containing characters for mathematical, logical, and database notation.

## Character table

| Code | Result | Description |
| U+27C0 | ⟀ | Three dimensional angle |
| U+27C1 | ⟁ | White triangle containing small white triangle |
| U+27C2 | ⟂ | Perpendicular |
| U+27C3 | ⟃ | Open subset |
| U+27C4 | ⟄ | Open superset |
| U+27C5 | ⟅ | Left S-shaped bag delimiter |
| U+27C6 | ⟆ | Right S-shaped bag delimiter |
| U+27C7 | ⟇ | Or with dot inside |
| U+27C8 | ⟈ | Reverse solidus preceding subset |
| U+27C9 | ⟉ | Superset preceding solidus |
| U+27CA | ⟊ | Vertical bar with horizontal stroke |
| U+27CC | ⟌ | Long division |
| U+27D0 | ⟐ | White diamond with centered dot |
| U+27D1 | ⟑ | And with dot |
| U+27D2 | ⟒ | Element of opening upward |
| U+27D3 | ⟓ | Lower right corner with dot |
| U+27D4 | ⟔ | Upper left corner with dot |
| U+27D5 | ⟕ | Left outer join |
| U+27D6 | ⟖ | Right outer join |
| U+27D7 | ⟗ | Full outer join |
| U+27D8 | ⟘ | Large up tack |
| U+27D9 | ⟙ | Large down tack |
| U+27DA | ⟚ | Left and right double turnstile |
| U+27DB | ⟛ | Left and right tack |
| U+27DC | ⟜ | Left multimap |
| U+27DD | ⟝ | Long right tack |
| U+27DE | ⟞ | Long left tack |
| U+27DF | ⟟ | Up tack with circle above |
| U+27E0 | ⟠ | Lozenge divided by horizontal rule |
| U+27E1 | ⟡ | White concave-sided diamond |
| U+27E2 | ⟢ | White concave-sided diamond with leftward tick |
| U+27E3 | ⟣ | White concave-sided diamond with rightward tick |
| U+27E4 | ⟤ | White square with leftward tick |
| U+27E5 | ⟥ | White square with rightward tick |
| U+27E6 | ⟦ | Mathematical left white square bracket |
| U+27E7 | ⟧ | Mathematical right white square bracket |
| U+27E8 | ⟨ | Mathematical left angle bracket |
| U+27E9 | ⟩ | Mathematical right angle bracket |
| U+27EA | ⟪ | Mathematical left double angle bracket |
| U+27EB | ⟫ | Mathematical right double angle bracket |
| U+27EC | ⟬ | Mathematical left white tortoise shell bracket |
| U+27ED | ⟭ | Mathematical right white tortoise shell bracket |
| U+27EE | ⟮ | Mathematical left flattened parenthesis |
| U+27EF | ⟯ | Mathematical right flattened parenthesis |

## Compact table

Miscellaneous Mathematical Symbols-A 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.^ As of Unicode version 16.0 |||||||||||||||||

## History

The following Unicode-related documents record the purpose and process of defining specific characters in the Miscellaneous Mathematical Symbols-A block:
| Version | Final code points | Count | L2 ID | WG2 ID | Document |
| 3.2 | U+27D0..27E5 | 22 | L2/01-142 | N2336 | Beeton, Barbara; Freytag, Asmus; Ion, Patrick (2001-04-02), Additional Mathematical Symbols |
| 3.2 | U+27D0..27E5 | 22 | L2/01-227 | | Whistler, Ken (2001-05-22), "ITEM 3", WG2 Consent Docket for UTC #87 |
| 3.2 | U+27D0..27E5 | 22 | L2/01-184R | | Moore, Lisa (2001-06-18), "Motion 87-M16, ITEM 3", Minutes from the UTC/L2 meeting |
| 3.2 | U+27D0..27E5 | 22 | L2/01-344 | N2353 (pdf, doc) | Umamaheswaran, V. S. (2001-09-09), "Resolution M40.4", Minutes from SC2/WG2 meeting #40 -- Mountain View, April 2001 |
| 3.2 | U+27E6..27EB | 6 | L2/99-052 | | Freytag, Asmus (1999-02-05), The math pieces from the symbol font |
| 3.2 | U+27E6..27EB | 6 | L2/01-033 | | Karlsson, Kent; Freytag, Asmus (2001-01-16), Disunify braces/brackets for math, computing science, and Z notation from similar-looking CJK braces/brackets |
| 3.2 | U+27E6..27EB | 6 | L2/01-159 | N2344 | Ad-hoc report on Mathematical Symbols, 2001-04-03 |
| 3.2 | U+27E6..27EB | 6 | L2/01-157 | N2345R | Karlsson, Kent (2001-04-04), Proposal to disunify certain fencing CJK punctuation marks from similar-looking Math fences |
| 3.2 | U+27E6..27EB | 6 | L2/01-168 | | Whistler, Ken (2001-04-10), Bracket Disunification & Normalization Hell |
| 3.2 | U+27E6..27EB | 6 | L2/01-012R | | Moore, Lisa (2001-05-21), "Disunifying Braces and Brackets", Minutes UTC #86 in Mountain View, Jan 2001 |
| 3.2 | U+27E6..27EB | 6 | L2/01-223 | | Suignard, Michel (2001-05-23), Discussion of Issues Regarding Bracket Disunification |
| 3.2 | U+27E6..27EB | 6 | L2/01-184R | | Moore, Lisa (2001-06-18), "Motion 87-M21", Minutes from the UTC/L2 meeting, Reverse the decision made in motion 86-M6 not to disunify brackets. |
| 3.2 | U+27E6..27EB | 6 | L2/01-317 | | Suignard, Michel (2001-08-14), Bracket Disunification & Normalization |
| 3.2 | U+27E6..27EB | 6 | L2/01-295R | | Moore, Lisa (2001-11-06), "Bracket Disunification and Normalization", Minutes from the UTC/L2 meeting #88 |
| 3.2 | U+27E6..27EB | 6 | L2/02-154 | N2403 | Umamaheswaran, V. S. (2002-04-22), "Resolution M41.1", Draft minutes of WG 2 meeting 41, Hotel Phoenix, Singapore, 2001-10-15/19 |
| 4.1 | U+27C0..27C1 | 2 | L2/03-187 | N2612-6 | Pantelia, Maria (2003-06-11), Proposal to encode ancient Greek mathematical characters in the UCS |
| 4.1 | U+27C2 | 1 | L2/03-194 | N2590 | Freytag, Asmus (2003-06-09), Additional Mathematical and Letterlike Characters |
| 4.1 | U+27C3..27C6 | 4 | L2/03-410 | N2680R | Freytag, Asmus (2003-10-30), Additional Mathematical Characters |
| 4.1 | U+27C3..27C6 | 4 | L2/04-098 | | Suignard, Michel (2004-02-04), "T.10 Miscellaneous Mathematical, item b", Comments accompanying the US positive vote on PDAM1 to ISO/IEC 10646:2003 |
| 4.1 | U+27C3..27C6 | 4 | L2/04-316 | | Moore, Lisa (2004-08-19), "100-C6", UTC #100 Minutes |
| 5.0 | U+27C7..27C9 | 3 | L2/04-406 | | Freytag, Asmus; Sargent, Murray; Beeton, Barbara; Carlisle, David (2004-11-15), Progress report on Mathematical Symbols |
| 5.0 | U+27C7..27C9 | 3 | L2/04-410 | | Freytag, Asmus (2004-11-18), Twenty six mathematical characters |
| 5.0 | U+27CA | 1 | L2/05-189 | N2958 | Lehtiranta, Juhani; Ruppel, Klaas; Suutari, Toni; Trosterud, Trond (2005-07-22), Report on progress in implementing the Uralic Phonetic Alphabet with indication of the need for additional characters and symbols |
| 5.0 | U+27CA | 1 | L2/05-261 | N2989 | Ruppel, Klaas; Kolehmainen, Erkki I.; Everson, Michael; Freytag, Asmus; Whistler, Ken (2005-09-13), Proposal to add six additional Uralicist characters to the UCS |
| 5.0 | U+27CA | 1 | L2/05-270 | | Whistler, Ken (2005-09-21), "A. Uralicist character additions", WG2 Consent Docket (Sophia Antipolis) |
| 5.0 | U+27CA | 1 | L2/05-279 | | Moore, Lisa (2005-11-10), "Consensus 105-C29", UTC #105 Minutes |
| 5.0 | U+27CA | 1 | | N2953 (pdf, doc) | Umamaheswaran, V. S. (2006-02-16), "7.4.7", Unconfirmed minutes of WG 2 meeting 47, Sophia Antipolis, France; 2005-09-12/15 |
| 5.1 | U+27CC, 27EE..27EF | 3 | L2/07-011R | N3198R | Freytag, Asmus; Beeton, Barbara; Ion, Patrick; Sargent, Murray; Carlisle, David; Pournader, Roozbeh (2007-01-15), 29 Additional Mathematical and Symbol Characters |
| 5.1 | U+27CC, 27EE..27EF | 3 | L2/07-015 | | Moore, Lisa (2007-02-08), "Mathematical Characters and Symbols (C.4)", UTC #110 Minutes |
| 5.1 | U+27CC, 27EE..27EF | 3 | L2/07-268 | N3253 (pdf, doc) | Umamaheswaran, V. S. (2007-07-26), "M50.16", Unconfirmed minutes of WG 2 meeting 50, Frankfurt-am-Main, Germany; 2007-04-24/27 |
| 5.1 | U+27EC..27ED | 2 | L2/06-054R | N3040 | Freytag, Asmus; Beeton, Barbara; Sargent, Murray (2006-02-09), Proposal for the Addition of Two Mathematical Bracket Characters |
| 5.1 | U+27EC..27ED | 2 | L2/06-008R2 | | Moore, Lisa (2006-02-13), "C.21", UTC #106 Minutes |
| 5.1 | U+27EC..27ED | 2 | | N3103 (pdf, doc) | Umamaheswaran, V. S. (2006-08-25), "M48.22", Unconfirmed minutes of WG 2 meeting 48, Mountain View, CA, USA; 2006-04-24/27 |
| 6.0 | U+27CE..27CF | 2 | L2/09-273 | N3677 | Iancu, Laurențiu (2009-07-28), Proposal to Encode Two Mathematical Symbols |
| 6.0 | U+27CE..27CF | 2 | L2/09-225R | | Moore, Lisa (2009-08-17), "D.2.2", UTC #120 / L2 #217 Minutes |
| 6.0 | U+27CE..27CF | 2 | L2/09-359 | | Iancu, Laurențiu (2009-10-21), Follow-up on Action Item 120-A77 |
| 6.0 | U+27CE..27CF | 2 | | N3703 (pdf, doc) | Umamaheswaran, V. S. (2010-04-13), "M55.9b", Unconfirmed minutes of WG 2 meeting no. 55, Tokyo 2009-10-26/30 |
| 6.1 | U+27CB, 27CD | 2 | L2/09-397 | | Iancu, Laurențiu (2009-10-26), Proposal to Encode Mathematical Diagonals |
| 6.1 | U+27CB, 27CD | 2 | L2/09-335R | | Moore, Lisa (2009-11-10), "D.2.1", UTC #121 / L2 #218 Minutes |
| 6.1 | U+27CB, 27CD | 2 | L2/10-007R | N3763 | Anderson, Deborah; Beeton, Barbara; Iancu, Laurențiu (2010-01-12), Revised Proposal to Encode Mathematical Diagonals |
| 6.1 | U+27CB, 27CD | 2 | L2/10-010 | | Constable, Peter; Iancu, Laurențiu; Sargent, Murray (2010-01-13), Proposal to rename the diagonal symbols U+27CB and U+27CD in the pipeline |
| 6.1 | U+27CB, 27CD | 2 | L2/10-015R | | Moore, Lisa (2010-02-09), "Consensus 122-C11", UTC #122 / L2 #219 Minutes, Change the name of U+27CB from RISING DIAGONAL to MATHEMATICAL RISING DIAGONAL and U+27CD from FALLING DIAGONAL to MATHEMATICAL FALLING DIAGONAL. |
| 6.1 | U+27CB, 27CD | 2 | | N3803 (pdf, doc) | "M56.08c", Unconfirmed minutes of WG 2 meeting no. 56, 2010-09-24 |