Mathematical Operators (Unicode block)

Mathematical Operators
Mathematical Operators
Range	U+2200..U+22FF; (256 code points)
Plane	BMP
Scripts	Common
Symbol sets	Mathematical symbols; Logic and Set operators; Relation symbols
Assigned	256 code points
Unused	0 reserved code points
Unicode version history
1.0.0 (1991)	242 (+242)
3.2 (2002)	256 (+14)
Unicode documentation
	Code chart ∣ Web page
	Note:

Mathematical Operators
Range U+2200..U+22FF
(256 code points)
Plane BMP
Scripts Common
Symbol sets Mathematical symbols
Logic and Set operators
Relation symbols
Assigned 256 code points
Unused 0 reserved code points
Unicode version history
1.0.0 (1991) 242 (+242)
3.2 (2002) 256 (+14)

Unicode documentation
Code chart ∣ Web page
Note:

This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.

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
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.^ As of Unicode version 16.0

Variation sequences

The Mathematical Operators block has sixteen variation sequences defined for standardized variants. 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 points 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 L2/00-119 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

^ 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

References

^ "Unicode character database". The Unicode Standard. Retrieved 2023-07-26.
^ "Enumerated Versions of The Unicode Standard". The Unicode Standard. Retrieved 2023-07-26.
^ "Unicode Character Database: Standardized Variation Sequences". The Unicode Consortium.
^ Whistler, Ken; Freytag, Asmus (2000-04-19), "Symbol variants defined using a Variation Selector", L2/00-119: Encoding Additional Mathematical Symbols in Unicode (PDF)

[final-5] Proposed code points and characters names may differ from final code points and names

[mathdocs-6] Refer to the history section of the Miscellaneous Mathematical Symbols-B block for additional math-related documents

[1] "Unicode character database". The Unicode Standard. Retrieved 2023-07-26.

[2] "Enumerated Versions of The Unicode Standard". The Unicode Standard. Retrieved 2023-07-26.

[3] "Unicode Character Database: Standardized Variation Sequences". The Unicode Consortium.

[4] Whistler, Ken; Freytag, Asmus (2000-04-19), "Symbol variants defined using a Variation Selector", L2/00-119: Encoding Additional Mathematical Symbols in Unicode (PDF)

Mathematical Operators (Unicode block)
This article is about the Unicode block. For operators in mathematics, see Operator (mathematics). For mathematical symbols in Unicode, including other blocks, see Mathematical operators and symbols in Unicode.

Top View

Block

Variation sequences

History

See also

References

Mathematical Operators
Range	U+2200..U+22FF (256 code points)
Plane	BMP
Scripts	Common
Symbol sets	Mathematical symbols Logic and Set operators Relation symbols
Assigned	256 code points
Unused	0 reserved code points
Unicode version history

1.0.0 (1991)	242 (+242)
3.2 (2002)	256 (+14)

Unicode documentation
Code chart ∣ Web page
Note:

Mathematical Operators 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.^ As of Unicode version 16.0

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

Version	Final code points	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		L2/00-119	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
^ 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

Mathematical Operators (Unicode block) This article is about the Unicode block. For operators in mathematics, see Operator (mathematics). For mathematical symbols in Unicode, including other blocks, see Mathematical operators and symbols in Unicode.

Top View

Block

Variation sequences

History

See also

References

Premium Membership

€4.95

Create a Premium Account quick and easy

Save your Favourite Pages

Listen to any page in Audio

Colour Night Mode

Mathematical Operators (Unicode block)
This article is about the Unicode block. For operators in mathematics, see Operator (mathematics). For mathematical symbols in Unicode, including other blocks, see Mathematical operators and symbols in Unicode.