L2/00-002
Date:
9 January 2000
To:
Unicode Technical Committee
ISO/IEC JTC1/SC2/WG2
From:
STIX Project of the STIPUB Consortium (a consortium of scientific societies
and scientific/technical publishers)
Subject:
Request for assignment of codes to mathematical and technical symbols that
do not appear in Unicode 2.0 or ISO/IEC 10646 (supersedes L2/99-244R)
References:
L2/98-405, Request for assignment of codes to mathematical and technical
symbols that do not appear in Unicode 2.0 or ISO/IEC 10646
L2/98-406, Proposal to encode mathematical variant tags
L2/99-045, Proposal to encode mathematical alphanumeric symbols
L2/99-049, Addendum to L2/98-405: Request for assignment of codes to
mathematical and technical symbols
L2/99-159, Request for assignment of codes to mathematical and technical
symbols that do not appear in Unicode 2.0 or ISO/IEC 10646 (revised)
L2/99-160, Proposal to encode mathematical variant tags
L2/99-195, Proposal to encode mathematical alphanumeric symbols
L2/99-199, Mathematical Alphabets (for L2/99-195)
L2/99-244R, Request for assignment of codes to mathematical and technical
symbols that do not appear in Unicode 2.0 or ISO/IEC 10646
This document is a revision of earlier documents of the same name, applying decisions communicated from the October 1999 UTC meeting. It incorporates material from the Proposal
to add the ISO Standard Z character set to Unicode/ISO-IEC 10646, transmitted by the UTC
chair.
Rationale
Scientific communication and publication via the Web are currently hindered by the absence
of both suitable symbol fonts and recognized methods of indicating particular symbols and
their relationships to one another. The font problems of ordinary text, which are considerable irrespective of language, have so far been addressed essentially only by the introduction
of the ISO 10646/Unicode standard. The special problems of handling technical texts have
been examined by the W3C Math Working Group, and their MathML proposal, which is interdependent with this request, was accepted as a W3C Recommendation on 7 April 1998 [see
http://www.w3c.org/Math]. The work of the HTML-Math WG is also related to the work of
the OpenMath consortium.
The present proposal is the work of the STIX Project (scientific and technical information
exchange), a working group reporting to STIPUB, a consortium of publishers of mathematical,
scientific, and technical books and journals. The ultimate product of the STIX group will be
the creation of one comprehensive set of fonts for scientific and technical publishing. This set
1
of fonts should be adopted and supported by all major STM publishers, and will also be made
available for general use under license but free of charge, with the explicit aim to ease and foster
the uninhibited flow, exchange, and linking of scientific information. The symbol complement
of the STIX font set will be based on the symbols in this proposal along with many already in
Unicode, as well as variant forms not included here (because they are required by publishing
house styles without different meaning from symbols included above) and additional technical
symbols from areas other than mathematics.
The availability of a universal font set will benefit scientific and technical publishing in several
ways:
• It will eliminate certain legal problems with distributing PDF files and publishing on the
World Wide Web.
• It will ease the exchange of documents from different publishers.
• It will make the re-use of archived material simpler and more robust.
The STIX group has agreed that the basis for the organization of such a font set should be
ISO 10646/Unicode. Some arguments in favor of ISO 10646/Unicode are: it is the basis for
XML, and therefore for MathML, and it is the character set of the programming language Java
and the operating system Windows NT. In XML documents, and most importantly for use in
MathML, one must be able to identify all notation, either by numerical character reference or
by entity reference. But numerical character references are ISO 10646/Unicode numbers, since
that is the character set underlying XML. If entity names are used, they must still be mapped
to something that applications will be able to handle and render.
In the attached charts and lists, we have included only what we believe to be unique symbols.
The language of mathematics is fluid, and symbols are defined in context to represent particular
mathematical concepts. The tool set of an active mathematician ideally consists of several
alphabets, whose members can be distinguished from one another, to represent various classes
of variables and constants, and a fairly extensive collection of similarly sized shapes to represent
various operations. There are of course many fully “standardized” shapes that are now used
almost exclusively to represent particular operations and relations, but even these are sometimes
adopted in fields where they are not already in use and redefined to have some other particular
meaning. For this reason, the “definitions” accompanying the symbols listed here are in some
cases not precise; where multiple varying meanings are possible, or a single precise meaning is
not available, the shape is described.
Variants
Many math symbols occur in two or more variant forms, with the same or similar meanings
usually, but not always, attached to both. In order to accommodate the (sometimes strong)
preferences of authors and publishers, a single Math Variant Tag (MVT) is recommended, to
be applied to a fixed list of symbols with predetermined results.
Two lists follow the tables of requested symbols:
2
• variant symbols composed of a base symbol plus a combining slash, followed by most of
these same variants further modified by application of the MVT to yield a vertical stroke
in place of the slash
• variants defined by a base symbol plus the MVT
Some symbols have been removed from the tables as a consequence of adding this MVT.
The case for alphabets
For a mathematician or other scientist, alphabets provide the symbols to represent ad hoc
variables as well as a number of more well-defined concepts. Different styles of alphabets have
different meanings, some of which have been formally standardized in some disciplines, but
many of which follow only the strength of custom, or even current necessity.
Document L2/99-195, Proposal to encode mathematical alphanumeric symbols, catalogues the
different styles of alphabets that are routinely used in mathematical and technical literature;
these alphabets and digits will not be further dealt with here.
There remain, however, some individual letters from or related to these alphabets that are
routinely used in a turned or inverted orientation, as well as a few symbols in the style of
a particular math alphabet but not part of its normal alphabetic complement. These are
considered distinct symbols, and are therefore candidates for code assignments.
Symbols
In the tables that follow, four data elements are given for each symbol:
• a reference ID indicating location in the corresponding chart
• a * if there is an existing symbol in Unicode or another symbol in this collection that
appears to be similar
• a one-letter code indicating the class of the symbol:
– N: normal or ordinary, e.g., symbol used as a variable
– A: alphabetic; subclass of ordinary
– D: diacritic or combining symbol
– P: punctuation
– B: binary operator, e.g., a + b
– R: relation, e.g., a = b
– L: large operator, e.g. sum, product
– O: opening delimiter (assuming left-to-right presentation)
– C: closing delimiter (assuming left-to-right presentation)
– F: nondirectional delimiter (fence post)
• description of the symbol, or meaning when dominant
3
Letter-like symbols; combining diacritics; punctuation
AX00
AX01
AX02
AX03
AX04
AX05
AX06
AX07
AX08
AX09
AX0A
AX0B
AX0C
AX0D
AX0E
AX0F
AX10
AX11
AX12
AX13
AX14
AX15
AX16
AX17
...
AX1A
AX1B
AX1C
AX1D
AX1E
AX1F
AX20
AX21
AX22
AX23
AX24
AX25
AX26
AX27
AX28
AX29
AX2A
AX2B
AX2C
N GREEK SYMBOL CAPITAL THETA WITH STRAIGHT BAR
→ 0472 cyrillic capital letter fita
N GREEK SYMBOL CURLY CAPITAL UPSILON
N GREEK SYMBOL STRAIGHT EPSILON
N GREEK SYMBOL REVERSED STRAIGHT EPSILON
N GREEK LETTER Q-KOPPA
N GREEK SMALL LETTER Q-KOPPA
N TURNED SANS SERIF CAPITAL G
= game
N TURNED SANS SERIF CAPITAL L
N REVERSED SANS SERIF CAPITAL L
N INVERTED SANS SERIF CAPITAL Y
N OPEN-FACE GREEK SMALL LETTER GAMMA
N OPEN-FACE GREEK CAPITAL GAMMA
N OPEN-FACE GREEK CAPITAL PI
L OPEN-FACE SUM
D COMBINING REVERSED SOLIDUS OVERLAY
D COMBINING DOUBLE VERTICAL STROKE OVERLAY
= Z NOTATION FINITE FUNCTION
D ANNUITY SYMBOL
= actuarial bend
N CAPITAL DIFFERENTIAL D
N DIFFERENTIAL D
N EXPONENTIAL E
N IMAGINARY I
N IMAGINARY J
D TRIPLE UNDERDOT
[removed]
N
P
N
B
B
N
N
N
[removed]
LOW ASTERISK
QUADRUPLE PRIME
[composed: U+2032 + U+2032 + U+2032 + U+2032]
[removed]
REVERSED SEMI-COLON
EM LEADER
TWO ASTERISKS ALIGNED VERTICALLY
SOLIDUS OVERBAR
REVERSED SOLIDUS WITH HORIZONTAL STROKE
BIG SOLIDUS
BIG REVERSED SOLIDUS
= Z NOTATION SCHEMA HIDING
TOP SQUARE BRACKET
BOTTOM SQUARE BRACKET
BOTTOM ABOVE TOP SQUARE BRACKET
TURNED AMPERSAND
[removed]
SIGNIFICANT BLANK SYMBOL
MEDIUM MATH SPACE
. four-eighteenths of an em
[removed: 2423]
4
BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8
AX0 AX1 AX2
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
A
A
B
B
C
C
D
D
E
E
F
F
Arrows and harpoons, combinations, fishtails
BX00
BX01
BX02
BX03
BX04
BX05
R
R
R
R
DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROW
THREE RIGHTWARDS ARROWS
LEFTWARDS ARROW WITH VERTICAL STROKE
RIGHTWARDS ARROW WITH VERTICAL STROKE
= Z NOTATION PARTIAL FUNCTION
R LEFT RIGHT ARROW WITH VERTICAL STROKE
= Z NOTATION PARTIAL RELATION
R LEFTWARDS ARROW WITH DOUBLE VERTICAL STROKE
5
BX06
BX07
BX08
BX09
BX0A
BX0B
BX0C
BX0D
BX0E
BX0F
BX10
BX11
BX12
BX13
BX14
BX15
BX16
BX17
BX18
BX19
BX1A
BX1B
BX1C
BX1D
BX1E
BX1F
BX20
BX21
BX22
BX23
BX24
BX25
BX26
BX27
BX28
BX29
BX2A
BX2B
BX2C
BX2D
BX2E
R RIGHTWARDS ARROW WITH DOUBLE VERTICAL STROKE
= Z NOTATION FINITE FUNCTION
R LEFT RIGHT ARROW WITH DOUBLE VERTICAL STROKE
= Z NOTATION FINITE RELATION
RULE-DELAYED
= colon right arrow
R LEFTWARDS OPEN-HEADED ARROW
R RIGHTWARDS OPEN-HEADED ARROW
R LEFT RIGHT OPEN-HEADED ARROW
R RIGHTWARDS TWO-HEADED ARROW WITH VERTICAL STROKE
= Z NOTATION PARTIAL SURJECTION
R RIGHTWARDS TWO-HEADED ARROW WITH DOUBLE VERTICAL STROKE
= Z NOTATION FINITE SURJECTION
R LEFTWARDS DOUBLE ARROW WITH VERTICAL STROKE
R RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKE
R LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKE
R RIGHTWARDS TWO-HEADED ARROW FROM BAR
= maps to
R LEFTWARDS DOUBLE ARROW FROM BAR
= maps from
R RIGHTWARDS DOUBLE ARROW FROM BAR
= maps to
R DOWNWARDS ARROW WITH HORIZONTAL STROKE
R UPWARDS ARROW WITH HORIZONTAL STROKE
R UPWARDS TRIPLE ARROW
R DOWNWARDS TRIPLE ARROW
R LEFTWARDS BROKEN ARROW
R RIGHTWARDS BROKEN ARROW
R LEFTWARDS DOUBLY BROKEN ARROW
R RIGHTWARDS DOUBLY BROKEN ARROW
R RIGHTWARDS TWO-HEADED BROKEN ARROW
R RIGHTWARDS ARROW WITH DOTTED STEM
R UPWARDS ARROW TO BAR
R DOWNWARDS ARROW TO BAR
R RIGHTWARDS ARROW WITH TAIL WITH VERTICAL STROKE
= Z NOTATION PARTIAL INJECTION
R RIGHTWARDS ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE
= Z NOTATION FINITE INJECTION
R RIGHTWARDS TWO-HEADED ARROW WITH TAIL
= bijective mapping
R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE
= Z NOTATION SURJECTIVE INJECTION
R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH DOUBLE VERTICAL STROKE
= Z NOTATION FINITE SURJECTIVE INJECTION
R LEFTWARDS ARROW-TAIL
R RIGHTWARDS ARROW-TAIL
R LEFTWARDS DOUBLE ARROW-TAIL
R RIGHTWARDS DOUBLE ARROW-TAIL
R LEFTWARDS ARROW TO FILLED DIAMOND
R RIGHTWARDS ARROW TO FILLED DIAMOND
R LEFTWARDS ARROW FROM BAR TO FILLED DIAMOND
R RIGHTWARDS ARROW FROM BAR TO FILLED DIAMOND
R NORTH WEST-SOUTH EAST ARROW
R NORTH EAST-SOUTH WEST ARROW
6
BX2F
BX30
BX31
BX32
BX33
BX34
BX35
BX36
BX37
BX38
BX39
BX3A
BX3B
BX3C
BX3D
BX3E
BX3F
R
R
R
R
R
R
R
R
N
N
N
N
N
N
N
N
R
BX40
BX41
BX42
BX43
BX44
BX45
BX46
BX47
BX48
BX49
BX4A
BX4B
BX4C
R
R
R
R
R
R
R
R
R
R
R
BX4D
R
BX4E
BX4F
BX50
BX51
BX52
BX53
BX54
BX55
BX56
BX57
BX58
BX59
BX5A
BX5B
BX5C
BX5D
BX5E
BX5F
BX60
BX61
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
NORTH WEST ARROW WITH HOOK
NORTH EAST ARROW WITH HOOK
SOUTH EAST ARROW WITH HOOK
SOUTH WEST ARROW WITH HOOK
NORTH WEST AND NORTH EAST ARROWS
NORTH EAST AND SOUTH EAST ARROWS
SOUTH EAST AND SOUTH WEST ARROWS
SOUTH WEST AND NORTH WEST ARROWS
RISING DIAGONAL CROSSING FALLING DIAGONAL
FALLING DIAGONAL CROSSING RISING DIAGONAL
SOUTH EAST ARROW CROSSING NORTH EAST ARROW
NORTH EAST ARROW CROSSING SOUTH EAST ARROW
FALLING DIAGONAL CROSSING NORTH EAST ARROW
RISING DIAGONAL CROSSING SOUTH EAST ARROW
NORTH EAST ARROW CROSSING NORTH WEST ARROW
NORTH WEST ARROW CROSSING NORTH EAST ARROW
WAVE ARROW POINTING DIRECTLY TO THE RIGHT
→ 219D rightwards wave arrow
[fill with arrow requested by Japanese, per Ken W]
[fill with arrow requested by Japanese, per Ken W]
ARROW POINTING DOWNWARDS THEN CURVING LEFTWARDS
ARROW POINTING DOWNWARDS THEN CURVING RIGHTWARDS
RIGHT-SIDE ARC CLOCKWISE ARROW
LEFT-SIDE ARC ANTICLOCKWISE ARROW
TOP ARC ANTICLOCKWISE ARROW
BOTTOM ARC ANTICLOCKWISE ARROW
TOP ARC CLOCKWISE ARROW WITH MINUS
TOP ARC ANTICLOCKWISE ARROW WITH PLUS
LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROW
LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROW
ANTICLOCKWISE CLOSED CIRCLE ARROW
→ 20DA combining anticlockwise ring overlay
CLOCKWISE CLOSED CIRCLE ARROW
→ 20D9 combining clockwise ring overlay
RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROW
LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROW
SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROW
RIGHTWARDS ARROW WITH PLUS BELOW
LEFTWARDS ARROW WITH PLUS BELOW
RIGHTWARDS ARROW THROUGH X
SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROW
UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLE
RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROW
LEFT-UP-RIGHT-DOWN HARPOON
LEFT-DOWN-RIGHT-UP HARPOON
UP-RIGHT-DOWN-LEFT HARPOON
UP-LEFT-DOWN-RIGHT HARPOON
LEFT-UP-RIGHT-UP HARPOON
UP-RIGHT-DOWN-RIGHT HARPOON
LEFT-DOWN-RIGHT-DOWN HARPOON
UP-LEFT-DOWN-LEFT HARPOON
LEFTWARDS HARPOON-UP TO BAR
RIGHTWARDS HARPOON-UP TO BAR
UPWARDS HARPOON-RIGHT TO BAR
7
BX62
BX63
BX64
BX65
BX66
BX67
BX68
BX69
BX6A
BX6B
BX6C
BX6D
BX6E
BX6F
BX70
BX71
BX72
BX73
BX74
BX75
BX76
BX77
BX78
BX79
BX7A
BX7B
BX7C
BX7D
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
BX7E
BX7F
BX80
BX81
BX82
BX83
BX84
BX85
BX86
BX87
BX88
BX89
BX8A
BX8B
BX8C
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
DOWNWARDS HARPOON-RIGHT TO BAR
LEFTWARDS HARPOON-DOWN TO BAR
RIGHTWARDS HARPOON-DOWN TO BAR
UPWARDS HARPOON-LEFT TO BAR
DOWNWARDS HARPOON-LEFT TO BAR
LEFTWARDS HARPOON-UP FROM BAR
RIGHTWARDS HARPOON-UP FROM BAR
UPWARDS HARPOON-RIGHT FROM BAR
DOWNWARDS HARPOON-RIGHT FROM BAR
LEFTWARDS HARPOON-DOWN FROM BAR
RIGHTWARDS HARPOON-DOWN FROM BAR
UPWARDS HARPOON-LEFT FROM BAR
DOWNWARDS HARPOON-LEFT FROM BAR
LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWN
UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHT
RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWN
DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHT
LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UP
LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWN
RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UP
RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWN
LEFTWARDS HARPOON-UP ABOVE LONG DASH
LEFTWARDS HARPOON-DOWN BELOW LONG DASH
RIGHTWARDS HARPOON-UP ABOVE LONG DASH
RIGHTWARDS HARPOON-DOWN BELOW LONG DASH
UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHT
DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHT
RIGHT DOUBLE ARROW WITH ROUNDED HEAD
. looks like thin superset
EQUAL ABOVE RIGHTWARDS ARROW
TILDE OPERATOR ABOVE RIGHTWARDS ARROW
LEFTWARDS ARROW ABOVE TILDE OPERATOR
RIGHTWARDS ARROW ABOVE TILDE OPERATOR
RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATOR
LESS THAN ABOVE LEFTWARDS ARROW
LEFTWARDS ARROW THROUGH LESS-THAN
GREATER-THAN ABOVE RIGHTWARDS ARROW
SUBSET ABOVE RIGHTWARDS ARROW
LEFTWARDS ARROW THROUGH SUBSET
SUPERSET ABOVE LEFTWARDS ARROW
LEFT FISH TAIL
RIGHT FISH TAIL
UP FISH TAIL
DOWN FISH TAIL
8
CX0 CX1 CX2 CX3 CX4 CX5 CX6 CX7 CX8 CX9 CXA CXB CXC CXD CXE CXF
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Large operators, binary operators; relational operators
CX00
CX01
CX02
CX03
CX04
CX05
CX06
CX0C
R
R
R
R
R
R
R
R
ELEMENT OF WITH LONG HORIZONTAL STROKE
ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
ELEMENT OF WITH DOT ABOVE
ELEMENT OF WITH OVERBAR
SMALL ELEMENT OF WITH OVERBAR
ELEMENT OF WITH UNDERBAR
ELEMENT OF WITH TWO HORIZONTAL STROKES
9
CX0E
CX0F
CX10
CX11
CX12
CX17
CX18
R
R
R
R
R
R
L
CX19
L
CX1A
L
CX1B
CX1C
L
L
CX1D
L
CX1E
L
CX1F
L
CX20
L
CX21
CX22
CX23
CX24
L
L
L
L
CX25
CX26
CX27
CX28
CX29
CX2A
CX2B
CX2C
CX2D
CX2E
CX2F
CX30
CX31
CX32
CX33
CX34
CX35
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
CX36
L
CX37
L
CX38
L
CONTAINS WITH LONG HORIZONTAL STROKE
CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE
CONTAINS WITH OVERBAR
SMALL CONTAINS WITH OVERBAR
Z NOTATION BAG MEMBERSHIP
N-ARY CIRCLED DOT OPERATOR
→ 2299 circled dot operator
N-ARY CIRCLED PLUS OPERATOR
→ 2295 circled plus
N-ARY CIRCLED TIMES OPERATOR
→ 2297 circled times
N-ARY UNION OPERATOR WITH DOT
N-ARY UNION OPERATOR WITH PLUS
→ 228E multiset union
N-ARY SQUARE INTERSECTION OPERATOR
→ 2293 square cap
N-ARY SQUARE UNION OPERATOR
→ 2294 square cup
TWO LOGICAL AND OPERATOR
= merge
→ CX76 two intersecting logical and
TWO LOGICAL OR OPERATOR
→ CX77 two intersecting logical or
N-ARY TIMES OPERATOR
MODULO TWO SUM
SUMMATION WITH INTEGRAL
QUADRUPLE INTEGRAL OPERATOR
[composed: U+222B + U+222B + U+222B + U+222B]
FINITE PART INTEGRAL
INTEGRAL WITH DOUBLE STROKE
INTEGRAL AVERAGE WITH SLASH
CIRCULATION FUNCTION
ANTICLOCKWISE INTEGRATION
LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLE
LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLE
LINE INTEGRATION NOT INCLUDING THE POLE
INTEGRAL AROUND A POINT OPERATOR
QUATERNION INTEGRAL OPERATOR
INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOK
INTEGRAL OVERPRINTED WITH TIMES SIGN
INTEGRAL OVERPRINTED WITH CAP
INTEGRAL OVERPRINTED WITH CUP
UPPER INTEGRAL WITH OVERBAR
LOWER INTEGRAL WITH UNDERBAR
JOIN
= large bowtie (relational database theory)
→ 22C8 BOWTIE
LARGE LEFT TRIANGLE OPERATOR
. relational database theory
Z NOTATION SCHEMA COMPOSITION
→ CX5A Z notation relational composition
Z NOTATION SCHEMA PIPING
→ 226B much greater-than
10
CX39
CX3A
CX3B
CX3C
CX3D
CX3E
CX3F
CX40
CX41
CX42
CX43
CX44
CX47
CX48
CX49
CX4A
CX4B
CX4C
CX4D
CX4E
CX4F
CX50
CX51
CX52
CX53
CX54
CX55
CX56
CX57
CX5A
CX5B
CX5C
CX5D
CX5E
CX5F
CX60
CX61
CX62
CX63
CX64
CX65
CX66
CX67
CX68
CX6B
CX6C
CX6D
L Z NOTATION SCHEMA PROJECTION
→ 21BE upwards harpoon with barb rightwards
B PLUS SIGN WITH SMALL CIRCLE ABOVE
B PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVE
B PLUS SIGN WITH TILDE ABOVE
B PLUS SIGN WITH DOT BELOW
B PLUS SIGN WITH TILDE BELOW
B PLUS SIGN WITH SUBSCRIPT TWO
= nim-addition
B FILLED TRIANGLE WITH PLUS
B MINUS SIGN WITH COMMA ABOVE
B MINUS SIGN WITH DOT BELOW
B FALLING DOTS MINUS
B RISING DOTS MINUS
B PLUS SIGN IN LEFT HALF CIRCLE
B PLUS SIGN IN RIGHT HALF CIRCLE
B VECTOR OR CROSS PRODUCT
→ 00D7 multiplication sign
B MULTIPLICATION SIGN WITH DOT ABOVE
B MULTIPLICATION SIGN WITH UNDERBAR
B SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSED
B SMASH PRODUCT
B MULTIPLICATION SIGN IN LEFT HALF CIRCLE
B MULTIPLICATION SIGN IN RIGHT HALF CIRCLE
B CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT
B MULTIPLICATION SIGN IN DOUBLE CIRCLE
B CIRCLED DIVISION SIGN
B PLUS IN TRIANGLE
B MINUS IN TRIANGLE
B MULTIPLICATION SIGN IN TRIANGLE
B INTERIOR PRODUCT
B RIGHTHAND INTERIOR PRODUCT
→ 2319 turned not sign
B Z NOTATION RELATIONAL COMPOSITION
→ CX37 Z notation schema composition
[removed: 2040]
B AMALGAMATION OR COPRODUCT
→ 2210 n-ary coproduct
B INTERSECTION WITH DOT
B UNION WITH MINUS
= Z NOTATION BAG SUBTRACTION
B UNION WITH OVERBAR
B INTERSECTION WITH OVERBAR
B INTERSECTION WITH LOGICAL AND
B UNION WITH LOGICAL OR
B UNION ABOVE INTERSECTION
B INTERSECTION ABOVE UNION
B UNION ABOVE BAR ABOVE INTERSECTION
B INTERSECTION ABOVE BAR ABOVE UNION
B UNION BESIDE AND JOINED WITH UNION
B INTERSECTION BESIDE AND JOINED WITH INTERSECTION
B CLOSED UNION WITH SERIFS
B CLOSED INTERSECTION WITH SERIFS
B DOUBLE SQUARE INTERSECTION
11
CX6E
CX71
CX72
CX73
CX74
CX75
CX76 *
B
B
B
B
B
B
B
CX77 * B
CX78
CX79
CX7A
CX7B
CX7C
CX7D
CX7E
CX7F
B
B
R
B
B
B
B
B
CX80
CX81
B
B
CX82
CX83
CX84
B
B
B
CX85
CX86
CX87
CX8B
CX8D
B
B
R
R
R
CX8E
CX92
CX94
R
R
R
CX97
CX9E
CXA0
CXA1
CXA2
CXA6
CXA7
CXA8
CXA9
CXAA
CXAB
CXAC
CXAD
CXAE
CXAF
CXB0
CXB1
CXB2
R
R
R
R
R
B
B
R
R
R
R
R
R
R
R
R
R
R
DOUBLE SQUARE UNION
CLOSED UNION WITH SERIFS AND SMASH PRODUCT
LOGICAL AND WITH DOT ABOVE
LOGICAL OR WITH DOT ABOVE
DOUBLE LOGICAL AND
DOUBLE LOGICAL OR
TWO INTERSECTING LOGICAL AND
→ CX1F two logical and operator
TWO INTERSECTING LOGICAL OR
→ CX20 two logical or operator
SLOPING LARGE OR
SLOPING LARGE AND
LOGICAL OR OVERLAPPING LOGICAL AND
LOGICAL AND WITH MIDDLE STEM
LOGICAL OR WITH MIDDLE STEM
LOGICAL AND WITH HORIZONTAL DASH
LOGICAL OR WITH HORIZONTAL DASH
LOGICAL AND WITH DOUBLE OVERBAR
→ 2306 perspective
LOGICAL AND WITH UNDERBAR
LOGICAL AND WITH DOUBLE UNDERBAR
→ 2259 estimates
SMALL VEE WITH UNDERBAR
LOGICAL OR WITH DOUBLE OVERBAR
LOGICAL OR WITH DOUBLE UNDERBAR
→ 225A equiangular to
Z NOTATION DOMAIN ANTIRESTRICTION
Z NOTATION RANGE ANTIRESTRICTION
EQUAL SIGN WITH DOT BELOW
IDENTICAL WITH DOT ABOVE
TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE
= identical and parallel to
TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKE
TILDE OPERATOR WITH DOT
TILDE OPERATOR WITH RISING DOTS
→ 223B homothetic
SIMILAR MINUS SIMILAR
CONGRUENT WITH OVERDOT
REVERSED CONGRUENT
DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENT
APPROXIMATELY EQUAL OR EQUAL TO
EQUAL ABOVE PLUS
PLUS ABOVE EQUAL
EQUAL ABOVE TILDE OPERATOR
DOUBLE COLON EQUAL
TWO CONSECUTIVE EQUAL SIGNS
THREE CONSECUTIVE EQUAL SIGNS
EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOW
EQUIVALENT WITH FOUR DOTS ABOVE
LESS-THAN WITH CIRCLE INSIDE
GREATER-THAN WITH CIRCLE INSIDE
LESS-THAN WITH QUESTION MARK ABOVE
GREATER-THAN WITH QUESTION MARK ABOVE
LESS-THAN OR SLANTED EQUAL TO
12
CXB3
CXB4
CXB5
CXB6
CXB7
CXB8
CXB9
CXBC
CXBD
CXBE
CXBF
CXC2
CXC3
CXD2
CXD3
CXD4
CXD5
CXD6
CXD7
CXD8
CXD9
CXDA
CXDB
CXDE
CXDF
CXE4
CXE5
CXE6
CXE7
CXE8
CXE9
CXEE
CXEF
CXF2
CXF3
CXF4
CXF5
CXF6
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
GREATER-THAN OR SLANTED EQUAL TO
LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDE
GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDE
LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE
GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE
LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHT
GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFT
LESS-THAN OR APPROXIMATE
GREATER-THAN OR APPROXIMATE
LESS-THAN AND NOT ONE-LINE EQUAL TO
GREATER-THAN AND NOT ONE-LINE EQUAL TO
LESS-THAN AND NOT APPROXIMATE
GREATER-THAN AND NOT APPROXIMATE
LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THAN
GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THAN
LESS-THAN ABOVE SIMILAR OR EQUAL
GREATER-THAN ABOVE SIMILAR OR EQUAL
LESS-THAN ABOVE SIMILAR ABOVE GREATER-THAN
GREATER-THAN ABOVE SIMILAR ABOVE LESS-THAN
LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUAL
GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUAL
LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUAL
GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUAL
SLANTED EQUAL TO OR LESS-THAN
SLANTED EQUAL TO OR GREATER-THAN
SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDE
SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDE
TWO-LINE EQUAL TO OR LESS-THAN
TWO-LINE EQUAL TO OR GREATER-THAN
TWO-LINE SLANTED EQUAL TO OR LESS-THAN
TWO-LINE SLANTED EQUAL TO OR GREATER-THAN
SIMILAR OR LESS-THAN
SIMILAR OR GREATER-THAN
SIMILAR ABOVE LESS-THAN ABOVE EQUAL
SIMILAR ABOVE GREATER-THAN ABOVE EQUAL
DOUBLE NESTED LESS-THAN SIGN
= absolute continuity
R DOUBLE NESTED GREATER-THAN SIGN
R DOUBLE LESS-THAN WITH UNDERBAR
13
DX0 DX1 DX2 DX3 DX4 DX5 DX6 DX7 DX8 DX9 DXA DXB DXC DXD DXE DXF
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
The two white and two black squares shown as DXEC, DXED, DXF0 and DXF1 are meant to form a
size-graded sequence with the present Unicode squares 25A0, 25A1, 25AA and 25AB. Ideally, the
largest should be just a bit larger than 25A0 (but not as large as 2588), and the smallest, just
a bit smaller than 25AA (but not quite as small as the dot operator, 22C5). These are used ad
hoc to define various operations, with different sizes often indicating the degree of conformity
to a particular notion. (Several different geometric shapes are used in this manner, the most
common being squares and circles.)
14
More relations
DX00
DX01
DX02
DX03
DX04
DX05
DX06
DX07
DX08
DX09
DX0E
DX0F
DX10
DX11
DX12
DX13
DX14
DX15
DX16
DX17
DX18
DX19
DX1A
DX25
DX26
DX29
DX2A
DX2B
DX2C
DX2D
DX2E
DX31
DX32
DX33
DX34
DX35
DX36
DX37
DX38
DX3B
DX3C
DX45
DX46
DX47
DX48
DX49
DX4A
DX4B
DX4C
DX4D
DX4E
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
GREATER-THAN OVERLAPPING LESS-THAN
GREATER-THAN BESIDE LESS-THAN
LESS-THAN CLOSED BY CURVE
GREATER-THAN CLOSED BY CURVE
LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUAL
GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUAL
SMALLER THAN
LARGER THAN
SMALLER THAN OR EQUAL
LARGER THAN OR EQUAL
BUMPY ABOVE TWO-LINE EQUAL
PRECEDES ABOVE ONE-LINE EQUAL
SUCCEEDS ABOVE ONE-LINE EQUAL
PRECEDES ABOVE NOT ONE-LINE EQUAL
SUCCEEDS ABOVE NOT ONE-LINE EQUAL
PRECEDES ABOVE TWO-LINE EQUAL
SUCCEEDS ABOVE TWO-LINE EQUAL
PRECEDES ABOVE NOT TWO-LINE EQUAL
SUCCEEDS ABOVE NOT TWO-LINE EQUAL
PRECEDES ABOVE DOUBLE TILDE OPERATOR
SUCCEEDS ABOVE DOUBLE TILDE OPERATOR
PRECEDES ABOVE NOT DOUBLE TILDE OPERATOR
SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATOR
DOUBLE PRECEDES
DOUBLE SUCCEEDS
SUBSET WITH DOT
SUPERSET WITH DOT
SUBSET WITH PLUS BELOW
SUPERSET WITH PLUS BELOW
SUBSET WITH MULTIPLICATION SIGN BELOW
SUPERSET WITH MULTIPLICATION SIGN BELOW
SUBSET OF OR EQUAL TO WITH DOT ABOVE
SUPERSET OF OR EQUAL TO WITH DOT ABOVE
SUBSET OF OR TWO-LINE EQUAL
SUPERSET OF OR TWO-LINE EQUAL
SUBSET OF ABOVE TILDE OPERATOR
SUPERSET OF ABOVE TILDE OPERATOR
SUBSET OF ABOVE DOUBLE TILDE OPERATOR
SUPERSET OF ABOVE DOUBLE TILDE OPERATOR
SUBSET OF OR NOT TWO-LINE EQUAL
SUPERSET OF OR NOT TWO-LINE EQUAL
SQUARE LEFT OPEN BOX OPERATOR
SQUARE RIGHT OPEN BOX OPERATOR
CLOSED SUBSET
CLOSED SUPERSET
CLOSED SUBSET OR EQUAL
CLOSED SUPERSET OR EQUAL
SUBSET ABOVE SUPERSET
SUPERSET ABOVE SUBSET
SUBSET ABOVE SUBSET
SUPERSET ABOVE SUPERSET
15
DX4F
DX50
DX51
DX52
DX53
R
R
R
R
R
DX54
R
DX55
R
DX56
DX57
DX58
DX59
DX5A
R
R
R
R
R
DX5B
DX5C
DX5D
DX5E
R
R
R
R
DX61
R
DX62
R
DX63
DX64
DX65
R
R
R
DX66
DX67
DX68
R
R
F
DX69
F
DX6A
DX6B
DX6C
DX6D
F
O
C
O
DX6E
C
DX6F
DX70
DX71
DX72
DX73
DX74
DX75
DX76
DX77
DX78
DX79
DX7A
O
C
O
C
O
C
O
C
O
C
O
C
SUPERSET BESIDE SUBSET
SUPERSET BESIDE AND JOINED BY DASH WITH SUBSET
ELEMENT OF OPENING DOWNWARDS
PITCHFORK WITH TEE TOP
TRANSVERSAL INTERSECTION
→ 22D4 proper intersection
FORKING
. symbol is slashed although positive
NONFORKING
. negative symbol - has no slash
SHORT LEFT TACK
SHORT DOWN TACK
SHORT UP TACK
PERPENDICULAR WITH S
VERTICAL BAR TRIPLE RIGHT TURNSTILE
= ordinarily satisfies
DOUBLE VERTICAL BAR LEFT TURNSTILE
VERTICAL BAR DOUBLE LEFT TURNSTILE
DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILE
LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL
→ 22A9 forces
SHORT DOWN TACK OVERBAR
→ 22A4 down tack
SHORT UP TACK WITH UNDERBAR
→ 22A5 up tack
SHORT UP TACK OVER SHORT DOWN TACK
DOUBLE DOWN TACK
DOUBLE UP TACK
= independence (probability theory)
NOT WITH TWO HORIZONTAL STROKES
REVERSED NOT WITH TWO HORIZONTAL STROKES
TRIPLE VERTICAL BAR DELIMITER
→ DX8B triple vertical bar binary relation
Z NOTATION SPOT
. medium-sized filled circle
Z NOTATION TYPE COLON
LEFT WHITE BRACE
RIGHT WHITE BRACE
LEFT WHITE ANGULAR BRACKET
→ 3108 left white tortoise shell bracket
RIGHT WHITE ANGULAR BRACKET
→ 3109 right white tortoise shell bracket
Z NOTATION LEFT IMAGE BRACKET
Z NOTATION RIGHT IMAGE BRACKET
Z NOTATION LEFT BINDING BRACKET
Z NOTATION RIGHT BINDING BRACKET
LEFT BRACKET UNDERBAR
RIGHT BRACKET UNDERBAR
LEFT BRACKET WITH REVERSED SOLIDUS TOP CORNER
RIGHT BRACKET WITH REVERSED SOLIDUS BOTTOM CORNER
LEFT BRACKET WITH SOLIDUS BOTTOM CORNER
RIGHT BRACKET WITH SOLIDUS TOP CORNER
LEFT ANGLE BRACKET WITH DOT
RIGHT ANGLE BRACKET WITH DOT
16
DX7B
DX7C
DX7D
DX7E
DX7F
DX80
DX81
DX82
DX83
DX84
DX85
DX86
DX87
DX88
DX89
DX8A
DX8B
DX8C
DX8D
DX8E
DX8F
DX90
DX91
DX92
DX93
DX94
DX95
DX96
DX97
DX98
DX99
DX9A
DX9B
DX9C
DX9D
DX9E
DX9F
DXA0
DXA1
DXA2
DXA3
DXA4
DXA5
DXA6
DXA7
DXA8
DXA9
DXAA
DXAB
O LEFT ARC LESS-THAN BRACKET
C RIGHT ARC GREATER-THAN BRACKET
DOUBLE LEFT ARC GREATER-THAN BRACKET
DOUBLE RIGHT ARC LESS-THAN BRACKET
RIGHT MOUSTACHE
LEFT MOUSTACHE
[removed: AX25]
[removed: AX26]
R DOES NOT DIVIDE WITH REVERSED NEGATION SLASH
R CIRCLE WITH VERTICAL LINE BELOW
R VERTICAL LINE WITH CIRCLE BELOW
N TOP WITH CIRCLE BELOW
B PARALLEL WITH HORIZONTAL STROKE
R PARALLEL WITH OVERPRINTED TILDE OPERATOR
[removed]
[removed]
B TRIPLE VERTICAL BAR BINARY RELATION
= interleave
→ DX68 triple vertical bar delimiter
[removed]
B TRIPLE VERTICAL BAR WITH HORIZONTAL STROKE
[removed: 2506]
B TRIPLE COLON
. logic
F DOTTED FENCE
. four close dots vertical
VERTICAL ZIG-ZAG LINE
MEASURED ANGLE OPENING LEFT
RIGHT ANGLE VARIANT WITH SQUARE
MEASURED RIGHT ANGLE WITH DOT
ANGLE WITH S INSIDE
ACUTE ANGLE
SPHERICAL ANGLE OPENING LEFT
SPHERICAL ANGLE OPENING UP
TURNED ANGLE
REVERSED ANGLE
ANGLE WITH UNDERBAR
REVERSED ANGLE WITH UNDERBAR
[removed]
LARGE DOWNWARDS POINTING ANGLE
LARGE UPWARDS POINTING ANGLE
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW
[removed: 2205]
N REVERSED EMPTY SET
→ 2349 APL functional symbol circle backslash
N EMPTY SET OVERBAR
N EMPTY SET WITH SMALL CIRCLE ABOVE
17
POINTING
POINTING
POINTING
POINTING
POINTING
POINTING
POINTING
POINTING
UP AND TO THE RIGHT
UP AND TO THE LEFT
DOWN AND TO THE RIGHT
DOWN AND TO THE LEFT
RIGHT AND UP
LEFT AND UP
RIGHT AND DOWN
LEFT AND DOWN
DXAC
DXAD
DXAE
DXB0
DXB1
DXB2
DXB3
DXB4
DXB5
DXB6
DXB7
DXB8
DXB9
DXBA
DXBB
DXBC
DXBD
DXBE
DXBF
DXC0
DXC1
DXC2
DXC3
DXC4
DXC5
DXC6
DXC7
DXCA
DXCB
DXCC
DXCF
DXD0
DXD1
DXD2
DXD3
DXD4
DXD5
DXD6
DXD7
DXD8
DXD9
DXDA
DXDB
DXDC
DXDD
DXDE
N EMPTY SET RIGHT ARROW ABOVE
N EMPTY SET LEFT ARROW ABOVE
CIRCLE WITH HORIZONTAL BAR
B CIRCLED VERTICAL BAR
B CIRCLED PARALLEL
B CIRCLED FALLING DIAGONAL
B CIRCLED PERPENDICULAR
CIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICAL
CIRCLE WITH SUPERIMPOSED X
CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGN
UP ARROW THROUGH CIRCLE
CIRCLED LARGE CIRCLE
→ 233E APL functional symbol circle jot
CIRCLED FILLED CIRCLE
CIRCLED LESS-THAN
CIRCLED GREATER-THAN
CIRCLE WITH SMALL CIRCLE TO THE RIGHT
CIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHT
SQUARED RISING DIAGONAL SLASH
→ 2341 APL functional symbol quad slash
SQUARED FALLING DIAGONAL SLASH
→ 2342 APL functional symbol quad backslash
SQUARED ASTERISK
SQUARED SMALL CIRCLE
→ 233B APL functional symbol quad circle
B SQUARED SQUARE
TWO JOINED SQUARES
TRIANGLE WITH DOT OVER
TRIANGLE WITH UNDERBAR
S IN TRIANGLE
B TRIANGLE WITH SERIFS AT BOTTOM
R RIGHT TRIANGLE ABOVE LEFT TRIANGLE
R LEFT TRIANGLE BESIDE VERTICAL BAR
R VERTICAL BAR BESIDE RIGHT TRIANGLE
R LEFT FILLED BOWTIE
R RIGHT FILLED BOWTIE
R FILLED BOWTIE
R LEFT FILLED TIMES
→ 22C9 left normal factor semidirect product
R RIGHT FILLED TIMES
→ 22CA right normal factor semidirect product
WHITE HOURGLASS
. vertical bowtie
FILLED HOURGLASS
MOST POSITIVE
CONGRUENCE SIGN WITH LAZY S
REVERSED MOST POSITIVE WITH LINE BELOW
MOST POSITIVE WITH TWO LINES BELOW
[removed: 221D]
N INFINITY SIGN WITH TOP RIGHT QUADRANT OMITTED
N TIE OVER INFINITY
N INFINITY NEGATED WITH VERTICAL BAR
R DOUBLE-ENDED MULTIMAP
18
DXDF
N SQUARE WITH CONTOURED OUTLINE
= D’Alembertian
R INCREASES AS
SHUFFLE PRODUCT
R SLANTED PARALLEL SUPERIMPOSED ON EQUAL
= homothetically congruent to
R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUAL
R SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL
= congruent and parallel
R TOP ARC OVER BOTTOM ARC
N THERMODYNAMIC
. vertical bar crossed by two horizontals
N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACK
N DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACK
UPPER LEFT TRIANGLE
UPPER RIGHT TRIANGLE
LOWER LEFT TRIANGLE
N WHITE MEDIUM SQUARE
N BLACK MEDIUM SQUARE
[removed]
[removed]
N WHITE VERY SMALL SQUARE
N BLACK VERY SMALL SQUARE
N WHITE DIAMOND WITH CENTERED DOT
N FILLED DIAMOND WITH DOWN ARROW
FILLED LOZENGE
[removed]
[removed: 2736]
N CIRCLE WITH DOWN ARROW
N FILLED CIRCLE WITH DOWN ARROW
N ERROR-BARRED WHITE SQUARE
N ERROR-BARRED FILLED SQUARE
N ERROR-BARRED WHITE DIAMOND
N ERROR-BARRED FILLED DIAMOND
N ERROR-BARRED WHITE CIRCLE
N ERROR-BARRED FILLED CIRCLE
DXE0
DXE1
DXE2
DXE3
DXE4
DXE5
DXE6
DXE7
DXE8
DXE9
DXEA
DXEB
DXEC
DXED
DXEE
DXEF
DXF0
DXF1
DXF2
DXF3
DXF4
DXF5
DXF6
DXF7
DXF8
DXF9
DXFA
DXFB
DXFC
DXFD
DXFE
Symbols defined using a Combining Character Sequence
Notes:
** The shape is incorrect, owing to unavailability of a suitable font; the correct shape will be
provided as soon as possible. The associated text correctly describes the desired shape.
•
•
•
•
•
•
219D
BX3F
220A
CX03
CX05
CX0C
¤ + 0338 / → § rightwards wave arrow - with slash
ⳡ
苸
苸̇
ⱬ
ã
+
+
+
+
+
0338
0338
0338
0338
0338
/
/
/
/
/
→
→
→
→
→
ⳡ
/
ⰻ
苸̇
/
ⱬ
ã
/
wave arrow pointing directly to the right - with slash
small element of - with slash
element of with dot above - with slash
element of with overbar - with slash
element of with two horizontal strokes - with slash
19
•
•
•
•
•
•
•
•
•
•
•
•
220D
CX11
2250
2263
CX97
2242
224B
CX9E
CXA2
CXB2
CXB3
2266
苹
Ⱬ
.
=
⭤
⳩
h
∼
˙
=
ⱁ
6
>
5
+
+
+
+
+
+
+
+
+
+
+
+
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
/
/
/
/
/
/
/
/
/
/
/
/
→
→
→
→
→
→
→
→
→
→
→
→
苹
Ⱬ
.
=
6
⭤
⳩
Ⲙ
/
∼
/˙
=
ⱁ
small contains with slash
contains with overbar - with slash
equal sign with overdot - with slash
strictly equivalent - with slash
similar minus similar - with slash
equal or similar - with slash
triple similar - with slash
congruent with overdot - with slash
approximately equal or equal to - with slash
less-than or slanted equal to - with slash
greater-than or slanted equal to - with slash
less-than or double equals - with slash
• 2267 = + 0338 / → greater-than or double equals - with slash
• CXDE 0 + 0338 / → ⱹ slanted equal to or less-than - with slash
• CXDF 1 + 0338 / → ⱸ slanted equal to or greater-than - with slash
5
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
0
1
Ⰶ
Ⰷ
≪
≫
m
l
%
2
3
j
k
@
A
9
œ

0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
two-line equal to or less-than - with slash
CXE7
CXE8
CXE9
CXF4
CXF5
226A
226B
22D8
22D9
224E
224F
DX0F
DX10
227E
227F
22DE
22DF
DX33
DX34
228F
2290
DX8B
DXCB
DXCC
=
•
** •
** •
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
+ 0338 / →
• CXE6
two-line equal to or greater-than - with slash
ⱹ two-line slanted equal to or less-than - with slash
ⱸ two-line slanted equal to or greater-than - with slash
/ double nested less-than - with slash
Ⰶ
/ double nested greater-than - with slash
Ⰷ
/ double less than - with slash
/ double greater than - with slash
≪
/ triple less than - with slash
≫
/ triple greater than - with slash
6m bumpy equal - with slash
6l bumpy above one-line equal - with slash
precedes above one-line equal - with slash
succeeds above one-line equal - with slash
6- precedes above tilde operator - with slash
6% succeeds above tilde operator - with slash
2
/ contour equals above precedes - with slash
3
/ contour equals above succeeds - with slash
" subset of or two-line equals - with slash
# superset of or two-line equals - with slash
6@ square subset - with slash
6A square superset - with slash
9 triple vertical bar - with slash
œ
/ left triangle beside vertical bar - with slash

/ vertical bar beside right triangle - with slash
20
• 003D = + 20E4 \ → =
\ equal - with reverse slash
• 2261 ≡ + 20E4 \ → ≡
\ equivalent - with reverse slash
• 2220 ∠ + 20D2 | → ∠| angle with vertical stroke
∈
ⱬ
3
Ⱬ
=
≡
⭤
∼
'
∼
=
⳩
h
≈
ⱁ
<
>
≤
≥
6
>
5
=
.
&
≶
≷
0
1
5
=
2208
CX05
220B
CX11
003D
2261
2263
223C
2243
2245
CX97
2242
2248
CXA2
224D
003C
003E
2264
2265
CXB2
CXB3
2266
2267
2272
2273
2276
2277
CXDE
CXDF
CXE6
CXE7
CXE8
CXE9
CXF4
CXF5
227A
0
1
Ⰶ
Ⰷ
≺
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
僆
ⱬ
像
Ⱬ
⫽
⬅
⭤
⬃
⯝
⬵
菻
Ⲙ
⬇
ⱁ
ⱱ
⬍
⬎
ⱕ
ⱖ
⭐
⭓
⬉
⭌
.
|
&
|
≶
|
≷
|
ⱹ
ⱸ
⬉
⭌
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
** •
** •
•
•
•
0
|
1
|
|
Ⰶ
|
Ⰷ
Ɱ
element of with vertical stroke
element of with overbar - with vertical stroke
contains - with vertical stroke
contains with overbar - with vertical stroke
equal - with vertical stroke
equivalent - with vertical stroke
strictly equivalent - with vertical stroke
tilde operator - with vertical stroke
similar or equal - with vertical stroke
similar or double equal - with vertical stroke
similar minus similar - with vertical stroke
equal or similar - with vertical stroke
approximately equal to - with vertical stroke
approximately equal or equal to - with vertical stroke
asympototically equal to - with vertical stroke
less-than - with vertical stroke
greater-than - with vertical stroke
less-than or equal to - with vertical stroke
greater-than or equal to - with vertical stroke
less-than or slanted equal to - with vertical stroke
greater-than or slanted equal to - with vertical stroke
less-than or double equals - with vertical stroke
greater-than or double equals - with vertical stroke
less-than or similar - with vertical stroke
greater-than or similar - with vertical stroke
less-than or greater-than - with vertical stroke
greater-than or less-than - with vertical stroke
slanted equal to or less-than - with vertical stroke
slanted equal to or greater-than - with vertical stroke
two-line equal to or less-than - with vertical stroke
two-line equal to or greater-than - with vertical stroke
two-line slanted equal to or less-than - with vertical stroke
two-line slanted equal to or greater-than - with vertical stroke
double nested less-than - with vertical stroke
double nested greater-than - with vertical stroke
precedes with - vertical stroke
21
•
•
•
•
•
•
•
•
•
•
•
•
•
227B
227C
227D
22DE
22DF
2282
2283
2286
2287
DX33
DX34
2284
2285
4
<
2
3
⊂
⊃
⊆
⊇
j
k
E
D
+
+
+
+
+
+
+
+
+
+
+
+
+
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
0338
/
/
/
/
/
/
/
/
/
/
/
/
/
+
+
+
+
+
+
+
+
+
+
+
+
+
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
→
→
→
→
→
→
→
→
→
→
→
→
→
Ɑ
Ɐ
Ɒ
2
|
3
|
傺
傻
債
傶
Ⲵ
ⲵ
E
|
D
|
succeeds with - vertical stroke
precedes above contour equals - with vertical stroke
succeeds above contour equals - with vertical stroke
contour equals above precedes - with vertical stroke
contour equals above succeeds - with vertical stroke
subset - with vertical stroke
superset - with vertical stroke
subset of or equal to - with vertical stroke
superset of or equal to - with vertical stroke
subset of or two-line equals - with vertical stroke
superset of or two-line equals - with vertical stroke
left triangle underbar - with vertical stroke
right triangle underbar - with vertical stroke
Symbol variants defined using a Math Variant Tag
• 2268 + MVT →
less-than and not double equal - with vertical stroke
• 2269 + MVT → greater-than and not double equal - with vertical stroke
•
•
•
•
•
•
•
•
22DA
22DB
2272
2273
CXEE
CXEF
DX08
DX09
Q
R
.
&
Ȿ
Ɀ
o
p
+
+
+
+
+
+
+
+
MVT
MVT
MVT
MVT
MVT
MVT
MVT
MVT
→
→
→
→
→
→
→
→
_
`
ⱳ
ⱜ
ⱽ
ⱚ
q
r
less-than above slanted equal above greater-than
greater-than above slanted equal above less-than
less-than or similar - following the slant of the lower leg
greater-than or similar - following the slant of the lower leg
similar - following the slant of the upper leg - or less-than
similar - following the slant of the upper leg - or greater-than
smaller than or slanted equal
larger than or slanted equal
• 228A ( + MVT →
subset not equals - variant with stroke through bottom members
• 228B ) + MVT → ! superset not equals - variant with stroke through bottom members
• DX3B $ + MVT → & subset not two-line equals - variant with stroke through bottom
members
• DX3C % + MVT → ' superset not two-line equals - variant with stroke through bottom
members
• CX56 ´ + MVT → ² interior product - tall variant with narrow foot
• CX57 µ + MVT → ³ righthand interior product - tall variant with narrow foot
L
• 2295
+ MVT → 䊝 circled plus with white rim
N
• 2297
+ MVT → 䊟 circled times with white rim
22
• 229C 䊠 + MVT → equal sign inside and touching a circle
• 2225 k + MVT → // slanted parallel
•
// + MVT + 20E4 \ → /\/ slanted parallel with reverse slash
**
**
**
**
•
•
•
•
222A
2229
2293
2294
∪
∩
u
t
+
+
+
+
MVT
MVT
MVT
MVT
→
→
→
→
∪
∩
u
t
union with serifs
intersection with serifs
square intersection with serifs
square union with serifs
References
International Organization for Standardization, ISO 31/XI-1992. Mathematical signs and symbols for use in the physical sciences and technology, 2nd edition, 1992. (by ref. in ANSI/IEEE
P1324)
American Society of Mechanical Engineers, ANSI Y10.20-1975. Mathematical signs and symbols for use in physical sciences and technology, 1975.
Institute of Electrical and Electronics Engineers, ANSI/IEEE P1324 (draft revision of Y10.20),
Draft standard mathematical signs and symbols for use in physical sciences and technology,
1992.
ISO/IEC 8879:1986, Information Processing — Text and Office Systems — Standard Generalized Markup Language (SGML), Annex D: Public text
ISO/IEC 9573-13, Information Technology — SGML Support Facilities — Techniques for Using
SGML — Part 13: Public entity sets for mathematics and science
Stepney, Susan (editor), Proposal to add the ISO Standard Z character set to Unicode/ISO-IEC
10646
23