# Supplemental Mathematical Operators

## N-ary operators

`2A00` ⨀ N-Ary Circled Dot Operator
`2299` ⊙ circled dot operator
`25C9` ◉ fisheye
`2A01` ⨁ N-Ary Circled Plus Operator
`2295` ⊕ circled plus
`2A02` ⨂ N-Ary Circled Times Operator
`2297` ⊗ circled times
`2B59` ⭙ heavy circled saltire
`2A03` ⨃ N-Ary Union Operator With Dot
`228D` ⊍ multiset multiplication
`2A04` ⨄ N-Ary Union Operator With Plus
`228E` ⊎ multiset union
`2A05` ⨅ N-Ary Square Intersection Operator
`2293` ⊓ square cap
`2A06` ⨆ N-Ary Square Union Operator
`2294` ⊔ square cup
`2A07` ⨇ Two Logical And Operator
=merge
`2A55` ⩕ two intersecting logical and
`2A08` ⨈ Two Logical Or Operator
`2A56` ⩖ two intersecting logical or
`2A09` ⨉ N-Ary Times Operator
`00D7` × multiplication sign

## Summations and integrals

`2A0A` ⨊ Modulo Two Sum
`2211` ∑ n-ary summation
`2A0B` ⨋ Summation With Integral
`2A0C` ⨌ Quadruple Integral Operator
`222D` ∭ triple integral
`222B` ∫ `222B` ∫ `222B` ∫ `222B` ∫
`2A0D` ⨍ Finite Part Integral
`2A0E` ⨎ Integral With Double Stroke
`2A0F` ⨏ Integral Average With Slash
`2A10` ⨐ Circulation Function
`2A11` ⨑ Anticlockwise Integration
`2A12` ⨒ Line Integration With Rectangular Path Around Pole
`2A13` ⨓ Line Integration With Semicircular Path Around Pole
`2A14` ⨔ Line Integration Not Including The Pole
`2A15` ⨕ Integral Around A Point Operator
`222E` ∮ contour integral
`2A16` ⨖ Quaternion Integral Operator
`2A17` ⨗ Integral With Leftwards Arrow With Hook
`2A18` ⨘ Integral With Times Sign
`2A19` ⨙ Integral With Intersection
`2A1A` ⨚ Integral With Union
`2A1B` ⨛ Integral With Overbar
=upper integral
`2A1C` ⨜ Integral With Underbar
=lower integral

## Miscellaneous large operators

`2A1D` ⨝ Join
=large bowtie
relational database theory
`22C8` ⋈ bowtie
`27D7` ⟗ full outer join
`2A1E` ⨞ Large Left Triangle Operator
relational database theory
`25C1` ◁ white left-pointing triangle
`2A1F` ⨟ Z Notation Schema Composition
`2A3E` ⨾ z notation relational composition
`2A20` ⨠ Z Notation Schema Piping
`226B` ≫ much greater-than
`2A21` ⨡ Z Notation Schema Projection
`21BE` ↾ upwards harpoon with barb rightwards

## Plus and minus sign operators

`2A22` ⨢ Plus Sign With Small Circle Above
`2A23` ⨣ Plus Sign With Circumflex Accent Above
`2A24` ⨤ Plus Sign With Tilde Above
=positive difference or sum
`2A25` ⨥ Plus Sign With Dot Below
`2214` ∔ dot plus
`2A26` ⨦ Plus Sign With Tilde Below
=sum or positive difference
`2A27` ⨧ Plus Sign With Subscript Two
`2A28` ⨨ Plus Sign With Black Triangle
`2A29` ⨩ Minus Sign With Comma Above
`2A2A` ⨪ Minus Sign With Dot Below
`2238` ∸ dot minus
`2A2B` ⨫ Minus Sign With Falling Dots
`2A2C` ⨬ Minus Sign With Rising Dots
`2A2D` ⨭ Plus Sign In Left Half Circle
`2A2E` ⨮ Plus Sign In Right Half Circle

## Multiplication and division sign operators

`2A2F` ⨯ Vector Or Cross Product
`00D7` × multiplication sign
`2A30` ⨰ Multiplication Sign With Dot Above
`2A31` ⨱ Multiplication Sign With Underbar
`2A32` ⨲ Semidirect Product With Bottom Closed
`2A33` ⨳ Smash Product
`2A34` ⨴ Multiplication Sign In Left Half Circle
`2A35` ⨵ Multiplication Sign In Right Half Circle
`2A36` ⨶ Circled Multiplication Sign With Circumflex Accent
`2A37` ⨷ Multiplication Sign In Double Circle
`2A38` ⨸ Circled Division Sign

## Miscellaneous mathematical operators

`2A39` ⨹ Plus Sign In Triangle
`2A3A` ⨺ Minus Sign In Triangle
`2A3B` ⨻ Multiplication Sign In Triangle
`2A3C` ⨼ Interior Product
`230B` ⌋ right floor
`2A3D` ⨽ Righthand Interior Product
`230A` ⌊ left floor
`2319` ⌙ turned not sign
`2A3E` ⨾ Z Notation Relational Composition
`2A1F` ⨟ z notation schema composition
`2A3F` ⨿ Amalgamation Or Coproduct
`2210` ∐ n-ary coproduct

## Intersections and unions

`2A40` ⩀ Intersection With Dot
`2227` ∧ logical and
`27D1` ⟑ and with dot
`2A41` ⩁ Union With Minus Sign
=z notation bag subtraction
`228E` ⊎ multiset union
`2A42` ⩂ Union With Overbar
`2A43` ⩃ Intersection With Overbar
`2A44` ⩄ Intersection With Logical And
`2A45` ⩅ Union With Logical Or
`2A46` ⩆ Union Above Intersection
`2A47` ⩇ Intersection Above Union
`2A48` ⩈ Union Above Bar Above Intersection
`2A49` ⩉ Intersection Above Bar Above Union
`2A4A` ⩊ Union Beside And Joined With Union
`2A4B` ⩋ Intersection Beside And Joined With Intersection
`2A4C` ⩌ Closed Union With Serifs
`222A` ∪ union
`2A4D` ⩍ Closed Intersection With Serifs
`2229` ∩ intersection
`2A4E` ⩎ Double Square Intersection
`2A4F` ⩏ Double Square Union
`2A50` ⩐ Closed Union With Serifs And Smash Product

## Logical ands and ors

`2A51` ⩑ Logical And With Dot Above
`2A52` ⩒ Logical Or With Dot Above
`2A53` ⩓ Double Logical And
`2A54` ⩔ Double Logical Or
`2A55` ⩕ Two Intersecting Logical And
`2A07` ⨇ two logical and operator
`2A56` ⩖ Two Intersecting Logical Or
`2A08` ⨈ two logical or operator
`2A57` ⩗ Sloping Large Or
`2A58` ⩘ Sloping Large And
`2A59` ⩙ Logical Or Overlapping Logical And
`2A5A` ⩚ Logical And With Middle Stem
`2A5B` ⩛ Logical Or With Middle Stem
`2A5C` ⩜ Logical And With Horizontal Dash
`2A5D` ⩝ Logical Or With Horizontal Dash
`2A5E` ⩞ Logical And With Double Overbar
`2306` ⌆ perspective
`2A5F` ⩟ Logical And With Underbar
`2A60` ⩠ Logical And With Double Underbar
`2259` ≙ estimates
`2A61` ⩡ Small Vee With Underbar
`225A` ≚ equiangular to
`2A62` ⩢ Logical Or With Double Overbar
`2A63` ⩣ Logical Or With Double Underbar
`225A` ≚ equiangular to

## Miscellaneous mathematical operators

`2A64` ⩤ Z Notation Domain Antirestriction
`2A65` ⩥ Z Notation Range Antirestriction
`2332` ⌲ conical taper

## Relational operators

`2A66` ⩦ Equals Sign With Dot Below
`2250` ≐ approaches the limit
`2A67` ⩧ Identical With Dot Above
`2A68` ⩨ Triple Horizontal Bar With Double Vertical Stroke
=identical and parallel to
`22D5` ⋕ equal and parallel to
`29E5` ⧥ identical to and slanted parallel
`2A69` ⩩ Triple Horizontal Bar With Triple Vertical Stroke
`2A6A` ⩪ Tilde Operator With Dot Above
`2A6B` ⩫ Tilde Operator With Rising Dots
`223B` ∻ homothetic
`2A6C` ⩬ Similar Minus Similar
`2A6D` ⩭ Congruent With Dot Above
`2245` ≅ approximately equal to
`2A6E` ⩮ Equals With Asterisk
`225B` ≛ star equals
`2A6F` ⩯ Almost Equal To With Circumflex Accent
`2A70` ⩰ Approximately Equal Or Equal To
`2245` ≅ approximately equal to
`2A71` ⩱ Equals Sign Above Plus Sign
black stands slightly better (chess notation)
`2A72` ⩲ Plus Sign Above Equals Sign
white stands slightly better (chess notation)
`2A73` ⩳ Equals Sign Above Tilde Operator
`2A74` ⩴ Double Colon Equal
`003A` : `003A` : `003D` =
`2A75` ⩵ Two Consecutive Equals Signs
`003D` = `003D` =
`2A76` ⩶ Three Consecutive Equals Signs
`003D` = `003D` = `003D` =
`2A77` ⩷ Equals Sign With Two Dots Above And Two Dots Below
`2A78` ⩸ Equivalent With Four Dots Above
`2A79` ⩹ Less-Than With Circle Inside
`2A7A` ⩺ Greater-Than With Circle Inside
`2A7B` ⩻ Less-Than With Question Mark Above
`2A7C` ⩼ Greater-Than With Question Mark Above
`2A7D` ⩽ Less-Than Or Slanted Equal To
`2264` ≤ less-than or equal to
`2A7E` ⩾ Greater-Than Or Slanted Equal To
`2265` ≥ greater-than or equal to
`2A7F` ⩿ Less-Than Or Slanted Equal To With Dot Inside
`2A80` ⪀ Greater-Than Or Slanted Equal To With Dot Inside
`2A81` ⪁ Less-Than Or Slanted Equal To With Dot Above
`2A82` ⪂ Greater-Than Or Slanted Equal To With Dot Above
`2A83` ⪃ Less-Than Or Slanted Equal To With Dot Above Right
`2A84` ⪄ Greater-Than Or Slanted Equal To With Dot Above Left
`2A85` ⪅ Less-Than Or Approximate
`2A86` ⪆ Greater-Than Or Approximate
`2A87` ⪇ Less-Than And Single-Line Not Equal To
`2268` ≨ less-than but not equal to
`2A88` ⪈ Greater-Than And Single-Line Not Equal To
`2269` ≩ greater-than but not equal to
`2A89` ⪉ Less-Than And Not Approximate
`2A8A` ⪊ Greater-Than And Not Approximate
`2A8B` ⪋ Less-Than Above Double-Line Equal Above Greater-Than
`22DA` ⋚ less-than equal to or greater-than
`2A8C` ⪌ Greater-Than Above Double-Line Equal Above Less-Than
`22DB` ⋛ greater-than equal to or less-than
`2A8D` ⪍ Less-Than Above Similar Or Equal
`2A8E` ⪎ Greater-Than Above Similar Or Equal
`2A8F` ⪏ Less-Than Above Similar Above Greater-Than
`2A90` ⪐ Greater-Than Above Similar Above Less-Than
`2A91` ⪑ Less-Than Above Greater-Than Above Double-Line Equal
`2A92` ⪒ Greater-Than Above Less-Than Above Double-Line Equal
`2A93` ⪓ Less-Than Above Slanted Equal Above Greater-Than Above Slanted Equal
`2A94` ⪔ Greater-Than Above Slanted Equal Above Less-Than Above Slanted Equal
`2A95` ⪕ Slanted Equal To Or Less-Than
`22DC` ⋜ equal to or less-than
`2A96` ⪖ Slanted Equal To Or Greater-Than
`22DD` ⋝ equal to or greater-than
`2A97` ⪗ Slanted Equal To Or Less-Than With Dot Inside
`2A98` ⪘ Slanted Equal To Or Greater-Than With Dot Inside
`2A99` ⪙ Double-Line Equal To Or Less-Than
`22DC` ⋜ equal to or less-than
`2A9A` ⪚ Double-Line Equal To Or Greater-Than
`22DD` ⋝ equal to or greater-than
`2A9B` ⪛ Double-Line Slanted Equal To Or Less-Than
`2A9C` ⪜ Double-Line Slanted Equal To Or Greater-Than
`2A9D` ⪝ Similar Or Less-Than
`2A9E` ⪞ Similar Or Greater-Than
`2A9F` ⪟ Similar Above Less-Than Above Equals Sign
`2AA0` ⪠ Similar Above Greater-Than Above Equals Sign
`2AA1` ⪡ Double Nested Less-Than
=absolute continuity
`226A` ≪ much less-than
`2AA2` ⪢ Double Nested Greater-Than
`226B` ≫ much greater-than
`2AA3` ⪣ Double Nested Less-Than With Underbar
`2AA4` ⪤ Greater-Than Overlapping Less-Than
`2AA5` ⪥ Greater-Than Beside Less-Than
`2AA6` ⪦ Less-Than Closed By Curve
`2AA7` ⪧ Greater-Than Closed By Curve
`2AA8` ⪨ Less-Than Closed By Curve Above Slanted Equal
`2AA9` ⪩ Greater-Than Closed By Curve Above Slanted Equal
`2AAA` ⪪ Smaller Than
`2AAB` ⪫ Larger Than
`2AAC` ⪬ Smaller Than Or Equal To
`2AAD` ⪭ Larger Than Or Equal To
`2AAE` ⪮ Equals Sign With Bumpy Above
`224F` ≏ difference between
`2AAF` ⪯ Precedes Above Single-Line Equals Sign
`227C` ≼ precedes or equal to
`2AB0` ⪰ Succeeds Above Single-Line Equals Sign
`227D` ≽ succeeds or equal to
`2AB1` ⪱ Precedes Above Single-Line Not Equal To
`2AB2` ⪲ Succeeds Above Single-Line Not Equal To
`2AB3` ⪳ Precedes Above Equals Sign
`2AB4` ⪴ Succeeds Above Equals Sign
`2AB5` ⪵ Precedes Above Not Equal To
`2AB6` ⪶ Succeeds Above Not Equal To
`2AB7` ⪷ Precedes Above Almost Equal To
`2AB8` ⪸ Succeeds Above Almost Equal To
`2AB9` ⪹ Precedes Above Not Almost Equal To
`2ABA` ⪺ Succeeds Above Not Almost Equal To
`2ABB` ⪻ Double Precedes
`2ABC` ⪼ Double Succeeds

## Subset and superset relations

`2ABD` ⪽ Subset With Dot
`2ABE` ⪾ Superset With Dot
`2ABF` ⪿ Subset With Plus Sign Below
`2AC0` ⫀ Superset With Plus Sign Below
`2AC1` ⫁ Subset With Multiplication Sign Below
`2AC2` ⫂ Superset With Multiplication Sign Below
`2AC3` ⫃ Subset Of Or Equal To With Dot Above
`2AC4` ⫄ Superset Of Or Equal To With Dot Above
`2AC5` ⫅ Subset Of Above Equals Sign
`2AC6` ⫆ Superset Of Above Equals Sign
`2AC7` ⫇ Subset Of Above Tilde Operator
`2AC8` ⫈ Superset Of Above Tilde Operator
`2AC9` ⫉ Subset Of Above Almost Equal To
`2ACA` ⫊ Superset Of Above Almost Equal To
`2ACB` ⫋ Subset Of Above Not Equal To
`2ACC` ⫌ Superset Of Above Not Equal To
`2ACD` ⫍ Square Left Open Box Operator
`2ACE` ⫎ Square Right Open Box Operator
`2ACF` ⫏ Closed Subset
`2282` ⊂ subset of
`2AD0` ⫐ Closed Superset
`2283` ⊃ superset of
`2AD1` ⫑ Closed Subset Or Equal To
`2AD2` ⫒ Closed Superset Or Equal To
`2AD3` ⫓ Subset Above Superset
`2AD4` ⫔ Superset Above Subset
`2AD5` ⫕ Subset Above Subset
`2AD6` ⫖ Superset Above Superset
`2AD7` ⫗ Superset Beside Subset
`2AD8` ⫘ Superset Beside And Joined By Dash With Subset

## Forks

`2AD9` ⫙ Element Of Opening Downwards
`2208` ∈ element of
`27D2` ⟒ element of opening upwards
`2ADA` ⫚ Pitchfork With Tee Top
`22D4` ⋔ pitchfork
`2ADB` ⫛ Transversal Intersection
`22D4` ⋔ pitchfork
`2ADC` ⫝̸ Forking
=not independent
an equational logic symbol, not a computing science symbol
non-independence (original concept) is related to forking
`2ADD` ⫝ `0338` ◌̸
`2ADD` ⫝ Nonforking
=independent
an equational logic symbol, not a computing science symbol
independence (original concept) is related to non-forking

## Tacks and turnstiles

`2ADE` ⫞ Short Left Tack
`22A3` ⊣ left tack
`2ADF` ⫟ Short Down Tack
`22A4` ⊤ down tack
`2AE0` ⫠ Short Up Tack
`22A5` ⊥ up tack
`2AE1` ⫡ Perpendicular With S
`2AE2` ⫢ Vertical Bar Triple Right Turnstile
=ordinarily satisfies
`2AE3` ⫣ Double Vertical Bar Left Turnstile
`22A9` ⊩ forces
`2AE4` ⫤ Vertical Bar Double Left Turnstile
`22A8` ⊨ true
`2AE5` ⫥ Double Vertical Bar Double Left Turnstile
`2AE6` ⫦ Long Dash From Left Member Of Double Vertical
`22A9` ⊩ forces
`2AE7` ⫧ Short Down Tack With Overbar
`22A4` ⊤ down tack
`2351` ⍑ apl functional symbol up tack overbar
`3012` 〒 postal mark
`2AE8` ⫨ Short Up Tack With Underbar
`22A5` ⊥ up tack
`234A` ⍊ apl functional symbol down tack underbar
`2AE9` ⫩ Short Up Tack Above Short Down Tack
`2AEA` ⫪ Double Down Tack
`2AEB` ⫫ Double Up Tack
=independence
probability theory
`2AEC` ⫬ Double Stroke Not Sign
`00AC` ¬ not sign
`2AED` ⫭ Reversed Double Stroke Not Sign
`2310` ⌐ reversed not sign

## Vertical line operators

`2AEE` ⫮ Does Not Divide With Reversed Negation Slash
`2224` ∤ does not divide
`2AEF` ⫯ Vertical Line With Circle Above
`2AF0` ⫰ Vertical Line With Circle Below
`2AF1` ⫱ Down Tack With Circle Below
=necessarily satisfies
`27DF` ⟟ up tack with circle above
`2AF2` ⫲ Parallel With Horizontal Stroke
`2226` ∦ not parallel to
`27CA` ⟊ vertical bar with horizontal stroke
`2AF3` ⫳ Parallel With Tilde Operator
`2AF4` ⫴ Triple Vertical Bar Binary Relation
=interleave
`2980` ⦀ triple vertical bar delimiter
`2AF5` ⫵ Triple Vertical Bar With Horizontal Stroke
`27CA` ⟊ vertical bar with horizontal stroke

## Miscellaneous mathematical operator

`2AF6` ⫶ Triple Colon Operator
logic
`205D` ⁝ tricolon
`22EE` ⋮ vertical ellipsis

## Relations

`2AF7` ⫷ Triple Nested Less-Than
`22D8` ⋘ very much less-than
`2AF8` ⫸ Triple Nested Greater-Than
`22D9` ⋙ very much greater-than
`2AF9` ⫹ Double-Line Slanted Less-Than Or Equal To
`2266` ≦ less-than over equal to
`2AFA` ⫺ Double-Line Slanted Greater-Than Or Equal To
`2267` ≧ greater-than over equal to
`2AFB` ⫻ Triple Solidus Binary Relation
`2AF4` ⫴ triple vertical bar binary relation

## Operators

`2AFC` ⫼ Large Triple Vertical Bar Operator
often n-ary
`2AF4` ⫴ triple vertical bar binary relation
`2980` ⦀ triple vertical bar delimiter
`2AFD` ⫽ Double Solidus Operator
`2225` ∥ parallel to
`2AFE` ⫾ White Vertical Bar
=Dijkstra choice
`2AFF` ⫿ N-Ary White Vertical Bar
=n-ary Dijkstra choice