Math Symbols

2000-03-14

ISO
INTERNATIONAL ORGANIZATION FOR STANDARDIZATIONORGANISATION INTERNATIONALE DE NORMALISATION
ISO/IEC JTC1/SC2/WG2Universal Multiple-Octet Coded Character Set (UCS)
ISO/IEC JTC1/SC2/WG2 N2191
Date: 2000-03-14

Title:
Source:Status:Action:Distribution:

Proposal for Encoding Additional Mathematical Symbols in the BMP
U.S. National Body
Working Document of JTC1/SC2/WG2 (and Summary Proposal Form)
For review and comment by JTC1/SC2/WG2Members of JTC1/SC2/WG2Introduction
This document constitutes the consolidated proposal for completion of the set of mathematical symbols encoded in
ISO/IEC 10646.
Additional alphanumeric symbols were added to the CD for 10646-2, and have been under ballot. This proposal
provides for the complementary set – those math symbols, operators, and delimiters that are currently missing from therepertoire of math symbols encoded in the BMP of 10646-1.
This proposal is the culmination of a several-year process of collation and review of mathematical symbols, with close
cooperation between the Unicode Technical Committee and the STIX Project, involving extensive expertise from themathematical, scientific, and technical publishing industry. In our opinion, this proposal is now quite mature, having
passed the technical scrutiny of the mathematicians and technical publishing experts of the STIX Project, and thecharacter encoding scrutiny of the UTC. It is now ready for review and comment by WG2. We urge consideration for a
new subdivision of work for an Amendment to 10646-1 to add this repertoire to the UCS, to meet the expressed needsof the international mathematical, scientific, and technical publishing industry for the representation of mathematics
using the ISO/IEC 10646 character encoding.
The document we present here is divided into six parts:• Introduction, background, rationale, and references• Annex 1: Proposal summary form
• Annex 2: Draft charts and names list, enumerating the proposed repertoire• Annex 3: Relevant excerpts from L2/00-002, to illustrate glyphs currently missing from Annex 2• Annex 4: Symbol variants defined using a Variation Selector (VS)• Annex 5: Letters of support from major mathematical organizations

Background
This proposal originated as 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 andtechnical publishing. This set of fonts should be adopted and supported by all major STM (scientific, technical, andmathematics) publishers internationally. It 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 worldwide.

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The symbol complement of the STIX font set will be based on the symbols in this proposal along with many othersymbols already encoded in ISO/IEC 10646, as well as variant forms not included here (because they are required bypublishing house styles without different meaning from symbols included above). Additional technical symbols fromareas other than mathematics will also be included in the font definitions.
More information about the STIX Project can be found at the STIX web site, hosted by the American MathematicalSociety (AMS): http://www.ams.org/STIX/The Unicode Technical Committee worked closely with the STIX Project over the past two years, to refine the proposal
into a character encoding proposal, suitable for addition to ISO/IEC 10646. During this process, duplicates have been
identified and removed, and clarification of distinctions between characters, glyphs, and variants has been made. The
original proposal was divided into two large portions: a proposal for the addition of alphanumeric symbols (under ballot
for the CD for 10646-2), and this proposal for the addition of other mathematical symbols.
As this proposal has developed, it has been connected to other standardization efforts, which are now interdependent on
the completion of mathematical symbol encoding in ISO/IEC 10646. In particular, the special problems of handlingtechnical texts have been examined in detail by the W3C HTML Math Working Group; their MathML proposal, whichis interdependent with this proposed repertoire of math symbols for ISO/IEC 10646, was accepted as a W3C
Recommendation on 7 April 1998 [see http://www.w3c.org/Math ].The work of the HTML Math Working Group isalso related to the work of the OpenMath Consortium. Major vendors of mathematical formatting software are also
dependent on the resolution of the encoding of additional mathematical symbols in ISO/IEC 10646-1.

Rationale
Scientific communication and publication via the World Wide Web are currently hindered by the absence both ofsuitable symbol fonts and of recognized methods of indicating particular symbols and their relationships to one another.
The availability of a complete UCS character encoding of mathematical symbols, and of a correlated universal font set
for their rendering will benefit scientific and technical publishing in several ways:•••

Elimination of certain legal problems with distributing PDF files and publishing on the World Wide Web
Ease of exchange of documents from different publishers
Simpler and more robust re-use of archived material

The STIX Project group has agreed that the basis for the organization of such a font set should be ISO/IEC
10646/Unicode. ISO/IEC 10646 is the reference character set for XML, and therefore for MathML as well. It is thecharacter set of the programming language Java and underlies all current Windows operating systems, as well as manyothers. In XML documents, and most importantly for use in MathML, one must be able to identify all notation, either bynumerical character reference or by entity reference. But numerical character references are ISO/IEC 10646 numbers,
since that is the character set underlying XML. If entity names are used, they must still be mapped to something thatapplications will be able to handle and render. All of these considerations argue very strongly that the set ofmathematical symbols encoded in the UCS should be completed, so as to enable the representation and presentation ofmathematics and other technical materials dependent on mathematics – both for the World Wide Web and for datainterchange dependent on XML.
In the charts and lists shown in the Annexes, we have included only what we believe to be unique symbols not currently
covered by the repertoire of ISO/IEC 10646. 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 severalalphabets, whose members can be distinguished from one another, to represent various classes of variables andconstants, and a fairly extensive collection of similarly-sized shapes to represent various operations or delimitation of
expressions. 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 andredefined to have some other particular meaning. For this reason, the names suggested for the symbols listed here are insome cases not functionally precise; where multiple varying meanings are possible, or a single precise meaning is notavailable, the name simply describes the shape of the proposed character.

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Math Symbols

2000-03-14

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
Variation Selector (VS) is recommended, to be applied to a fixed list of symbols with predetermined results. The
Variation Selector follows the symbol whose variant it specifies. As a character by itself, the Variation Selector has no
independent appearance; it only functions to choose a particular variant for the character it follows. Only combinations
defined by the standard should be meaningful. In any other context, the Variation Selector character should be ignored.
The Variation Selector (VS) in this proposal is completely analogous to the Mongolian Free Variation Selector (MVS)
characters already in ISO/IEC 10646. The difference is merely that the MVS characters are only meaningful in
combination with other Mongolian characters, to select variants of those characters. The VS is separately proposed, foruse in combination with mathematical symbol characters, to select variants of those characters.
The exact list of variants currently known to be required for mathematical, scientific, and technical publishing is shownin Annex 4.

Letter-like Symbols
For a mathematician or other scientist, alphabets provide the symbols to represent ad hoc variables as well as a numberof more well-defined concepts. Different styles of alphabets have different meanings, some of which have been formallystandardized in some disciplines, but many of which follow only the strength of custom, or even current necessity.
The CD for ISO/IEC 10646-2 includes sets of mathematical alphanumeric symbols that are regularly used inmathematical and technical literature; those 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 orinverted orientation, as well as a few symbols in the style of a particular math alphabet but not part of its normalalphabetic complement. These are considered distinct letter-like symbols, and are therefore candidates for code
assignments. They are included in this proposal, along with the larger collection of general mathematical symbols andoperators.

Brace Parts
A small collection of brace and bracket parts has also been included in this proposal. These characters are intended tocomplete the coverage of the PostScript symbol set, as well as some character-like entities used by TeX and othertechnical typesetting systems. These brace parts are explicitly intended as compatibility characters to match thosepreexisting repertoires. Their inclusion facilitates the interconversion of data from such systems with systems using the
ISO/IEC 10646 character encoding.

Explanation of Conventions in the Annexes
In Annex 3, four data elements are given for each symbol:• an arbitrary reference ID indicating location in the corresponding chart• an asterisk (*) 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• a proposed name for the symbol (usually based on form; occasionally based on meaning, if dominant)Note: the proposed name shown in Annex 3 may have been superseded by the name shown in Annex 2. In all cases, thename shown in Annex 2 should take precedence for this proposal. Annex 3 is only attached because of the difficulty ofcompleting a high-quality font for Annex 2 in time to meet the deadline for consideration at the Beijing WG2 meeting.
The one-letter codes indicating the class of the symbol are as follows:
N: normal or ordinary; e.g., symbol used as a variable
A: alphabetic; subclass of ordinary
D: diacritic or combining symbol

3Math Symbols

2000-03-14

P: punctuation
B: binary operator, e.g., <math>a + b</math>R: relation, e.g., <math>a = b</math>
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)
In Annex 3, the two white and two black squares shown as DXEC, DXED, DXF0 and DXF1 are meant to form a sizegraded sequence with the present ISO/IEC 10646 squares 25A0, 25A1, 25AA and 25AB. Ideally, the largest should bejust 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.)References
International Organization for Standardization, ISO 31/XI-1992. Mathematical signs and symbols for use in thephysical 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 physicalsciences 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
SC2 N3393, Committee Draft ISO/IEC CD 10646-2.
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)

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Math Symbols

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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
L2/99-346, Mathematical brace pieces.
L2/00-002, 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)

5

ISO/IEC JTC 1/SC 2/WG 2
PROPOSAL SUMMARY FORM TO
ACCOMPANY SUBMISSIONSFOR ADDITIONS TO THE REPERTOIREOF ISO/IEC 10646
Please fill Sections A, B and C below. Section D will be filled by SC 2/WG 2.
For instructions and guidance for filling in the form please see the document " Principles and Procedures for
Allocation of New Characters and Scripts" (http://www.dkuug.dk/JTC1/SC2/WG2/prot)

A. Administrative
1. Title: Proposal for Encoding Additional Mathematical Symbols in the BMP

2. Requester's name: U.S.

3. Requester type (Member body/Liaison/Individual contribution): Member body

4. Submission date: 2000-03-14

5. Requester's reference (if applicable): WG2 N2191

6. This is a complete proposal.

B. Technical - General
1. (Choose one of the following:)

b. The proposal is for addition of character(s) to an existing block.
Name of the existing block:
Greek and Coptic (3)General Punctuation (14)Combining Diacritical Marks for Symbols (4)Letterlike Symbols (15)Arrows (12)Mathematical Operators (14)Miscellaneous Technical (29)
Geometric Shapes (8)Supplemental Arrows [New block 2900..297F] (128)
Miscellaneous Math Symbols [New block 2980..29FF] (117)
Supplemental Math Operators [New block 2A00..2AFF] (247)Note that the proposed new blocks are conceptually extensions of the existing Arrows and Mathematical
Operators blocks, and do not constitute new scripts.

2. Number of characters in proposal: 951

3. Proposed category (see section II, Character Categories):

4. Proposed Level of Implementation (see clause 15, ISO/IEC 10646-1): Level 3
Is a rationale provided for the choice? Yes
If Yes, reference:
The repertoire includes 4 combining characters, which can be used in free combinations with otherexisting 10646 characters. Many relational operators are intended to be usable with overlaid combining
marks U+0338 COMBINING LONG SOLIDUS OVERLAY or U+20D2 COMBINING LONG VERTICAL
LINE OVERLAY to productively indicate negation. Finally, the mathematical repertoire in general isintended for complex rendering, with the productive application of other combining marks to indicate
derivatives, vectors, and many other concepts.
Limited subsets of the mathematical symbols can, of course, be used for Level 1 implementations, but therepertoire addressed by this proposal is aimed at full and complete mathematical rendering andinterchange. (Note that this proposal encompasses the symbols needed for mathematical content, but is
not intended to cover mathematical markup languages or layout controls.)

5. Is a repertoire including character names provided? Yes. See Annex 2.
a.

If YES, are the names in accordance with the 'character naming guidelines' in Annex K of ISO/IEC 10646-1?
Yes

b. Are the character shapes attached in a reviewable form? Yes. See Annexes 2 and 3.

6. Who will provide the appropriate computerized font (ordered preference: True Type, PostScript or 96x96 bitmapped format) for publishing the standard?
The Unicode Consortium, working in collaboration with STIPUB and various professional font vendors.
If available now, identify source(s) for the font (include address, e-mail, ftp-site, etc.) and indicate the tools used:

7. References:a. Are references (to other character sets, dictionaries, descriptive texts etc.) provided? Yesc.

Are published examples (such as samples from newspapers, magazines, or other sources) of use of proposedcharacters attached?

No, not in WG2 N2191. However, a very large collection of source citations has been collected by the
STIX Project group of STIPUB. That group constitutes a consortium of mathematical, scientific, andtechnical publishers who have refined this repertoire on the basis of their publication requirements forsymbol usage.

8. Special encoding issues:
Use of a VARIATION SELECTOR. The use of this character is described in the proposal.
Does the proposal address other aspects of character data processing (if applicable) such as input, presentation,sorting, searching, indexing, transliteration etc. (if yes please enclose information)? Yes
There are no new input or presentation issues not already present for the existing repertoire of mathsymbols. Sorting, indexing, and transliteration are generally not an issue for math symbols. Some special
letterlike symbols are provided in the repertoire to facilitate searching for some common key mathematicalconcepts in text documents.

C. Technical - Justification
1. Has this proposal for addition of character(s) been submitted before? No (with a few exceptions)If YES explain.
Note that a few individual characters among the repertoire of 951 may appear in other proposals before
WG2. For example, the Q-shaped koppa letters have independently been requested. Several arrow
characters from a recent Japanese proposal for symbols to cover JIS X 0213 are also included. The vast
majority of the 951 characters in this proposal are requested here for the first time.

2. Has contact been made to members of the user community (for example: National Body, user groups of the scriptor characters, other experts, etc.)? Yes
If YES, with whom?

STIPUB (Scientific and Technical Information Publishing Consortium), representing mathematical andother major technical publishing interests. American Mathematical Society. International Mathematical
Union. major mathematical software vendors. W3C MathML participants.
If YES, available relevant documents? See the references and appended approval letters in the proposal.

3. Information on the user community for the proposed characters (for example: size, demographics, information
technology use, or publishing use) is included?
The repertoire is intended for all international mathematical information technology use and formathematical, scientific, and technical publishing worldwide. It is intended to complete the base symbol
set for MathML. It is also intended as the underlying symbol encoding for all major mathematical layout
software programs.
Reference:

4. The context of use for the proposed characters (type of use; common or rare):Common to rare, depending on the particular subfield of mathematics involved.
Reference:

5. Are the proposed characters in current use by the user community? Yes
If YES, where?
Books, journals, articles, online documents. Reference: STIPUB can provide voluminous references. This
constitutes the complete world community of mathematical users: all books, journals, magazines, andother publications in mathematics and scientific and technical disciplines that make use of mathematics,
worldwide.

6. After giving due considerations to the principles in N 1352 must the proposed characters be entirely in the BMP?
Yes
If YES, is a rationale provided? Yes
If YES, reference: See WG2 N2191.

7. Should the proposed characters be kept together in a contiguous range (rather thanbeing scattered)? Yes and No.
Exact details of the proposed distribution of the characters into existing and new blocks of 10646 areprovided in Annex 2.

8. Can any of the proposed characters be considered a presentation form of an existing character or charactersequence? Yes (a few)
If YES, is a rationale for its inclusion provided? No
In these instances, the precedents are already clearly established in the standard. For example, aquadruple integral character is requested; the double and triple integral are already encoded ascharacters.
If YES, reference:

9. Can any of the proposed character(s) be considered to be similar (in appearance or function) to an existing
character? Yes
If YES, is a rationale for its inclusion provided? No, not in detail.
There are numerous instances among mathematical symbols where one symbols is generically similar toanother in appearance, but where it is well understood in mathematical practice to not be the same
symbol. Annex 2 provides a number of cross-references, where there might be confusions regarding thedistinctiveness of a particular character, either with respect to existing encoded characters in 10646, orwith respect to other characters in this proposal. Mathematical symbols are also replete with examples
where the same function can be represented by different symbols. Multiplication, for example, canalready be represented by U+00D7 MULTIPLY or U+2219 BULLET OPERATOR. However, it can also be
represented by a zero-width operator, such as in xy where this expression represents the variable x
multiplied by the variable y. Multiple symbols corresponding to the same abstract mathematical functions
are requested for encoding as separate characters when their form is distinct in different mathematicaltraditions or subfields.
If YES, reference:
WG2 2191 does provide a detailed rationale for the request for two additional sets of squares asgeometric shape characters.

10. Does the proposal include use of combining characters and/or use of composite sequences (see clause 4.11 and4.13 in ISO/IEC 10646-1)? Yes
If YES, is a rationale for such use provided? Yes
If YES, reference: See B.4 above.
Is a list of composite sequences and their corresponding glyph images (graphic symbols) provided? No
Such a list would be unmanageably long, since combining marks are intended for productive use inmathematics.
If YES, reference:

11. Does the proposal contain characters with any special properties such as control function or similar semantics?
Yes
If YES, describe in detail (include attachment if necessary)
The VARIATION SELECTOR is described in WG2 N2191, and the list of variants it selects is detailed inAnnex 4.

D. SC 2/WG 2 Administrative (To be completed by SC
2/WG 2)
1. Relevant SC 2/WG 2 document numbers:

2. Status (list of meeting number and corresponding action or disposition):

3. Additional contact to user communities, liaison organizations etc:

4. Assigned category and assigned priority/time frame:Math Symbols Proposal
First Draft MTHM000307.lst
Created from L2/00-033R and L2/00-002.

File Statistics:
Total Characters: 591
Lines in file:746+ Generated:
86
Name lines:
677
Characters:
591
Reserved:
0
Unassigned:
86
Secondary lines: 102
Aliases:
33
Comments:
14
Cross Refs:
41
Can. Decomps:
0Compatibility: 14
Ignored:0
Header Lines:
53
Blocks:11
Subheaders:
40
Notices:0
Title lines:
1
Subtitles:
1
Page breaks:
0
Empty lines:0
Iso Comments
0
AnnexP Notes
0

0370

Greek and Coptic

037

038

039

03B

03C

03D

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ΐ Π ΰ π

0

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03A0

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1

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2

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03B1

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Β

β ς

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Γ Σ γ σ

3

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4

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5

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6

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7

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8

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9

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Printed 17-Mar-2000

2

03D8

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03F4

Archaic Greek Letters

03D8 ! GREEK LETTER Q-KOPPA
03D9 " GREEK SMALL LETTER Q-KOPPA

Greek symbol

03F4 # GREEK THETA SYMBOL WITH STRAIGHT
BAR
0472 cyrillic capital letter fita
03B8

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3

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2016
2017
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2020
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203D<reserved>
203E<reserved>
203F<reserved>
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2041<reserved>
2042<reserved>
2043<reserved>
2044<reserved>
2045<reserved>
2046<reserved>
2047<reserved>
2048<reserved>
2049<reserved>
204A<reserved>
204B<reserved>
204C<reserved>
204D<reserved>
204E $ LOW ASTERISK
204F % REVERSED SEMICOLON
2050 & EM LEADER
2051 ' TWO ASTERISKS ALIGNED VERTICALLY
2052 ( SOLIDUS OVERBAR
2053 ) REVERSE SOLIDUS WITH HORIZONTALSTROKE
2054 * BIG SOLIDUS
2055 + BIG REVERSE SOLIDUS= z notation schema hiding
2056 , TURNED AMPERSAND
2057 - QUADRUPLE PRIME
2035 2035 2035
2058
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2059<reserved>
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205C<reserved>
205D<reserved>
205E<reserved>
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0020
2060
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2061 / FUNCTION APPLICATION• contiguity operator indicating application of afunction
2062 0 INVISIBLE TIMES• contiguity operator indicating multiplication
2063 1 VARIATION SELECTOR• in conjunction with preceding character indicatesvariant choice

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5

20E5

3

6

20E6

4

7

20E7

8

5
20E8

9

A

B

C

D

E

F

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

6

20E5

Combining Diacritical Marks for Symbols

20E8

Combining Symbols

2 COMBINING REVERSE SOLIDUS OVERLAY
3 COMBINING DOUBLE VERTICAL STROKE

20E5
20E6

4

20E7
20E8

5

OVERLAY= z notation finite function
ANNUITY SYMBOL= actuarial bend
TRIPLE UNDERDOTPFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

7

2100

Letterlike Symbols

210

211

212

213

214F

214

;

0

2140

<

1

2141

2

3

™

=

2122

2142

ℓ

>

2113

2143

?

4

2144

5

6

℅

@

2105

2145

A

№ Ω
2116

2126

2146

B

7

2147

C

8

2148

D

9

2149

A

6

B

213B

7

C

213C

8

D

213D

E

℮ 9
212E

F

213E

:
213F

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

8

213B

Letterlike Symbols

2149

Letterlike symbols

213B 6 GREEK SYMBOL STRAIGHT EPSILON<font> 03B5
213C 7 GREEK SYMBOL REVERSED STRAIGHTEPSILON
213D 8 OPEN-FACE GREEK SMALL LETTER GAMMA<font> 03B3
213E 9 OPEN-FACE GREEK CAPITAL GAMMA<font> 0393
213F : OPEN-FACE GREEK CAPITAL PI<font> 03A0
2140 ; OPEN-FACE SUM<font> 03A3
2141 < TURNED SANS SERIF CAPITAL G= game2142 = TURNED SANS SERIF CAPITAL L
2143 > REVERSED SANS SERIF CAPITAL L
2144 ? INVERTED SANS SERIF CAPITAL Y
2145 @ CAPITAL DIFFERENTIAL D<font> 0044 D
2146 A DIFFERENTIAL D<font> 0064 d
2147 B EXPONENTIAL E<font> 0065 e
2148 C IMAGINARY I<font> 0069 i
2149 D IMAGINARY J<font> 006A j

≈

ε

≈
≈
≈
≈

γ
Γ
Π
Σ

≈
≈
≈
≈
≈

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

9

2190

Arrows

219
0

21A

21B

21C

21D

21FF

21E

21F

←
2190

1

↑
2191

2

→
2192

3

↓
2193

4

5

↔

E

2194

21F4

↕

F

2195

21F5

G

6

21F6

H

7

21F7

8

↨

I

21A8

21F8

J

9

21F9

K

A

21FA

L

B

21FB

M

C

21FC

N

D

21FD

O

E

21FE

P

F

21FF

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

10

21F4

Arrows21FF

Arrows

21F4 E DOWNWARDS WHITE ARROW WITH CORNERLEFTWARDS= return
21F5 F DOWNWARDS ARROW LEFTWARDS OF
UPWARDS ARROW
21F6 G THREE RIGHTWARDS ARROWS
21F7 H LEFTWARDS ARROW WITH VERTICALSTROKE
21F8 I RIGHTWARDS ARROW WITH VERTICALSTROKE= z notation partial function
21F9 J LEFT RIGHT ARROW WITH VERTICALSTROKE= z notation partial relation
21FA K LEFTWARDS ARROW WITH DOUBLEVERTICAL STROKE
21FB L RIGHTWARDS ARROW WITH DOUBLEVERTICAL STROKE= z notation finite function
21FC M LEFT RIGHT ARROW WITH DOUBLEVERTICAL STROKE= z notation finite relation
21FD N LEFTWARDS OPEN-HEADED ARROW
21FE O RIGHTWARDS OPEN-HEADED ARROW
21FF P LEFT RIGHT OPEN-HEADED ARROWPFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

11

2200

Mathematical Operators

220

221

222

223

224

225

226

227F

227

≠

0

2260

1

2

∑

≡

2211

2261

∂ −
2202

2212

3

≤

4

2264

5

6

⁄

≥

2215

2265

∆
2206

7

≈

8

2248

· ∩

9

2219

2229

√

A

221A

∫

B

222B

C

D

∞

E

221E

F

∏ ∟
220F

PFS: amstt fonts Version 1fixed

221F

Printed 17-Mar-2000

12

2280

Mathematical Operators

228

229

22A

22B

22C

22D

22E

22FF

22F

0

1

Q

2

22F2

R

3

22F3

S

4

22F4

T

5

22F5

U

6

22F6

V

7

22F7

W

8

22F8

X

9

22F9

Y

A

22FA

Z

B

22FB

[

C

22FC

\

D

22FD

]

E

22FE

^

F

22FF

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

13

22F2

Mathematical Operators

22FF

Mathematical operators

22F2 Q ELEMENT OF WITH LONG HORIZONTALSTROKE
22F3 R ELEMENT OF WITH VERTICAL BAR AT END
OF HORIZONTAL STROKE
22F4 S SMALL ELEMENT OF WITH VERTICAL BAR
AT END OF HORIZONTAL STROKE
22F5 T ELEMENT OF WITH DOT ABOVE
22F6 U ELEMENT OF WITH OVERBAR
22F7 V SMALL ELEMENT OF WITH OVERBAR
22F8 W ELEMENT OF WITH UNDERBAR
22F9 X ELEMENT OF WITH TWO HORIZONTALSTROKES
22FA Y CONTAINS WITH LONG HORIZONTALSTROKE
22FB Z CONTAINS WITH VERTICAL BAR AT END OFHORIZONTAL STROKE
22FC [ SMALL CONTAINS WITH VERTICAL BAR AT
END OF HORIZONTAL STROKE
22FD \ CONTAINS WITH OVERBAR
22FE ] SMALL CONTAINS WITH OVERBAR
22FF ^ Z NOTATION BAG MEMBERSHIPPFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

14

2300

Miscellaneous Technical

230

231

232

233

234

235

236

237F

237

⌐ ⌠

0

2310

2320

⌡

1

2321

2

⌂
2302

3

4

5

6

7

8

9

A

B

_

C

237C

D

E

F

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

15

2380

Miscellaneous Technical

238

239

23A

23B

23C

23D

23E

23FF

23F



0

23A0



1

23A1



2

23A2



3

23A3

 y

4

23A4

23B4

 z

5

23A5

23B5

 {

6

23A6

23B6



7

23A7



8

23A8



9

23A9



A

23AA

B

 
239B

C

 
239C

D

23AD

 
239E

F

23AC

 
239D

E

23AB

23AE


239F

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

16

237C

Miscellaneous Technical

23B6

Miscellaneous technical

237C _ RIGHT ANGLE WITH DOWNWARDS ZIGZAG
ARROW

Brace pieces
239B  LEFT PARENTHESIS UPPER HOOK
239C  LEFT PARENTHESIS EXTENSION
239D  LEFT PARENTHESIS LOWER HOOK
239E  RIGHT PARENTHESIS UPPER HOOK
239F  RIGHT PARENTHESIS EXTENSION
23A0  RIGHT PARENTHESIS LOWER HOOK
23A1  LEFT BRACKET UPPER CORNER
23A2  LEFT BRACKET EXTENSION
23A3  LEFT BRACKET LOWER CORNER
23A4  RIGHT BRACKET UPPER CORNER
23A5  RIGHT BRACKET EXTENSION
23A6  RIGHT BRACKET LOWER CORNER
23A7  LEFT CURLY BRACE UPPER HOOK
23A8  LEFT CURLY BRACE MIDDLE PIECE
23A9  LEFT CURLY BRACE LOWER HOOK
23AA  CURLY BRACE EXTENSION
23AB  RIGHT CURLY BRACE UPPER HOOK
23AC  RIGHT CURLY BRACE MIDDLE PIECE
23AD  RIGHT CURLY BRACE LOWER HOOK
23AE  INTEGRAL EXTENSION
23AF
HORIZONTAL LINE EXTENSION
23B0
UPPER LEFT OR LOWER RIGHT BRACESECTION
23B1
UPPER RIGHT OR LOWER LEFT BRACESECTION

Summation sign parts
23B2
23B3

SUMMATION SYMBOL TOP
SUMMATION SYMBOL BOTTOM

Vertical brackets

23B4 y TOP SQUARE BRACKET
23B5 z BOTTOM SQUARE BRACKET
23B6 { BOTTOM ABOVE TOP SQUARE BRACKETPFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

17

25A0

Geometric Shapes

25A
0

25B

25C

25D

25E

25FF

25F

■
25A0

1

□
25A1

▲

2

25B2

3

◄

4

25C4

5

◦

6

25E6

7

8

9

A

C

|

25D8

25F8

◙

}

25D9

25F9

▪ ► ◊

~

25BA

25CA

25FA

▫

○



25AB

25CB

25FB

25AA

B

◘

▬ ▼
25AC

¡

25BC

25FC

¢

D

25FD

£

E

25FE

F

PFS: amstt fonts Version 1fixed

●

¤

25CF

25FF

Printed 17-Mar-2000

18

25F8

Geometric Shapes

25FF

Geometric shapes

25F8 | UPPER LEFT TRIANGLE
25F9 } UPPER RIGHT TRIANGLE
25FA ~ LOWER LEFT TRIANGLE
25FB  WHITE MEDIUM SQUARE
25FC ¡ BLACK MEDIUM SQUARE
25FD ¢ WHITE VERY SMALL SQUARE
25FE £ BLACK VERY SMALL SQUARE
25FF ¤ WHITE DIAMOND WITH CENTERED DOT

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

19

2900

Supplemental Arrows

290
0

2911

2912

¨ ·
2903

4

2910

§ ¶
2902

3

2913

2914

2915

2941

2951

% 5
2961

2971

Æ Ö å õ & 6
2922

2932

2942

2952

2962

2972

Ç × æ ö ' 7
2923

2933

2943

2953

2963

2973

2924

2934

2944

2954

2925

2935

2945

2955

2964

2974

) 9
2965

2975

2916

2926

2936

2946

2956

2966

2976

2917

2927

2918

2928

2937

2947

2957

2967

2977

Ü ë û , <
2938

2948

2958

2968

2978

ì

ü - =
2959

2919

2969

2979

® ¾ Î Þ í ý . >
291A

292A

293A

294A

295A

296A

297A

¯ ¿ Ï ß î þ / ?
291B

292B

293B

294B

295B

291C

292C

293C

294C

295C

292D

293D

294D

297B

296C

297C

! 1 A

± Á Ñ á ð
291D

296B

ÿ 0 @

° À Ð à ï

295D

296D

297D

² Â Ò â ñ " 2 B
290E

291E

292E

³ Ã Ó
290F

PFS: amstt fonts Version 1fixed

2931

2970

2949

290D

F

2921

2960

Ý

290C

E

2950

2939

290B

D

2940

2929

290A

C

2930

­ ½ Í
2909

B

2920

¬ ¼ Ì
2908

A

297

« » Ë Û ê ú + ;
2907

9

296

ª º Ê Ú é ù * :
2906

8

295

¹ É Ù è ø

5

7

294

© ¸ È Ø ç ÷ ( 8
2904

6

293

¦ µ Å Õ ä ô
2901

2

292

¥ ´ Ä Ô ã ó $ 4
2900

1

291

297F

291F

292F

293E

294E

295E

296E

297E

ò # 3 C
294F

295F

Printed 17-Mar-2000

296F

297F

20

2900

Supplemental Arrows

2946

2921 K NORTH WEST-SOUTH EAST ARROW
2922
L NORTH EAST-SOUTH WEST ARROW
2900 p RIGHTWARDS TWO-HEADED ARROW WITH
2923
M
NORTH WEST ARROW WITH HOOK
VERTICAL STROKE
2924
N
NORTH
EAST ARROW WITH HOOK
= z notation partial surjection
2925
O
SOUTH
EAST
ARROW WITH HOOK
2901 q RIGHTWARDS TWO-HEADED ARROW WITH
2926 P SOUTH WEST ARROW WITH HOOK
DOUBLE VERTICAL STROKE= z notation finite surjection
2927 Q NORTH WEST AND NORTH EAST ARROWS
2902 r LEFTWARDS DOUBLE ARROW WITH
2928 R NORTH EAST AND SOUTH EAST ARROWSVERTICAL STROKE
2929 S SOUTH EAST AND SOUTH WEST ARROWS
2903 s RIGHTWARDS DOUBLE ARROW WITH
292A T SOUTH WEST AND NORTH WEST ARROWSVERTICAL STROKE
292B U RISING DIAGONAL CROSSING FALLING
2904 t LEFT RIGHT DOUBLE ARROW WITHDIAGONALVERTICAL STROKE
292C V FALLING DIAGONAL CROSSING RISING
2905
RIGHTWARDS TWO-HEADED ARROW FROMDIAGONAL
BAR
292D W SOUTH EAST ARROW CROSSING NORTH= maps to
EAST ARROW
2906 u LEFTWARDS DOUBLE ARROW FROM BAR
292E X NORTH EAST ARROW CROSSING SOUTH= maps fromEAST ARROW
2907 v RIGHTWARDS DOUBLE ARROW FROM BAR
292F Y FALLING DIAGONAL CROSSING NORTH= maps to
EAST ARROW
2908 w DOWNWARDS ARROW WITH HORIZONTAL
2930 Z RISING DIAGONAL CROSSING SOUTH EASTSTROKE
ARROW
2909 x UPWARDS ARROW WITH HORIZONTAL
2931 [ NORTH EAST ARROW CROSSING NORTHSTROKE
WEST ARROW
290A y UPWARDS TRIPLE ARROW
2932 \ NORTH WEST ARROW CROSSING NORTH
290B z DOWNWARDS TRIPLE ARROW
EAST ARROW
290C { LEFTWARDS BROKEN ARROW
2933 ] WAVE ARROW POINTING DIRECTLY TO THE
RIGHT
290D | RIGHTWARDS BROKEN ARROW
219D rightwards wave arrow
290E } LEFTWARDS DOUBLY BROKEN ARROW
2934 ^ ARROW POINTING RIGHTWARDS THEN
290F ~ RIGHTWARDS DOUBLY BROKEN ARROWCURVING UPWARDS
2910  RIGHTWARDS TWO-HEADED BROKEN
2935
_
ARROW
POINTING RIGHTWARDS THENARROW
CURVINGDOWNWARDS
2911  RIGHTWARDS ARROW WITH DOTTED STEM
2936
`
ARROW
POINTING
DOWNWARDS THEN
2912  UPWARDS ARROW TO BARCURVING LEFTWARDS
2913  DOWNWARDS ARROW TO BAR
2937 a ARROW POINTING DOWNWARDS THEN
2914  RIGHTWARDS ARROW WITH TAIL WITHCURVING RIGHTWARDSVERTICAL STROKE
2938b
RIGHT-SIDE
ARC CLOCKWISE ARROW= z notation partial injection2939
cLEFT-SIDEARC
ANTICLOCKWISE ARROW
2915  RIGHTWARDS ARROW WITH TAIL WITH
293A d TOP ARC ANTICLOCKWISE ARROWDOUBLE VERTICAL STROKE
293B e BOTTOM ARC ANTICLOCKWISE ARROW= z notation finite injection
293C
f TOP ARC CLOCKWISE ARROW WITH MINUS
2916
RIGHTWARDS TWO-HEADED ARROW WITH
293D g TOP ARC ANTICLOCKWISE ARROW WITH
TAIL
PLUS
= bijective mapping
2917  RIGHTWARDS TWO-HEADED ARROW WITH 293E h LOWER RIGHT SEMICIRCULAR CLOCKWISE
ARROW
TAIL WITH VERTICAL STROKE
293F
LOWER LEFT SEMICIRCULAR= z notation surjective injection
ANTICLOCKWISE ARROW
2918  RIGHTWARDS TWO-HEADED ARROW WITH
2940 i ANTICLOCKWISE CLOSED CIRCLE ARROWTAIL WITH DOUBLE VERTICAL STROKE= z notation finite surjective injection
20DA
combining anticlockwise ring overlay
2919  LEFTWARDS ARROW-TAIL
2941 j CLOCKWISE CLOSED CIRCLE ARROW
20D9
combining clockwise ring overlay
291A  RIGHTWARDS ARROW-TAIL
2942 k RIGHTWARDS ARROW ABOVE SHORT
291B  LEFTWARDS DOUBLE ARROW-TAIL
LEFTWARDS ARROW
291C  RIGHTWARDS DOUBLE ARROW-TAIL
2943
l
LEFTWARDS
ARROW ABOVE SHORT
291D  LEFTWARDS ARROW TO FILLED DIAMOND
RIGHTWARDS
ARROW
291E  RIGHTWARDS ARROW TO FILLED DIAMOND
2944
m
SHORT
RIGHTWARDSARROW ABOVE
291F  LEFTWARDS ARROW FROM BAR TO FILLEDLEFTWARDS ARROWDIAMOND
2920  RIGHTWARDS ARROW FROM BAR TO FILLED 2945 n RIGHTWARDS ARROW WITH PLUS BELOW
2946 o LEFTWARDS ARROW WITH PLUS BELOWDIAMOND

Supplemental arrows→→→

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

21

2947

Supplemental Arrows

2947  RIGHTWARDS ARROW THROUGH X
2948  SMALL CIRCLE WITH SUPERIMPOSED LEFTRIGHT ARROW
2949  UPWARDS TWO-HEADED ARROW FROMSMALL CIRCLE
294A  LEFT-UP-RIGHT-DOWN HARPOON
294B  LEFT-DOWN-RIGHT-UP HARPOON
294C  UP-RIGHT-DOWN-LEFT HARPOON
294D  UP-LEFT-DOWN-RIGHT HARPOON
294E  LEFT-UP-RIGHT-UP HARPOON
294F  UP-RIGHT-DOWN-RIGHT HARPOON
2950  LEFT-DOWN-RIGHT-DOWN HARPOON
2951  UP-LEFT-DOWN-LEFT HARPOON
2952  LEFTWARDS HARPOON-UP TO BAR
2953  RIGHTWARDS HARPOON-UP TO BAR
2954  UPWARDS HARPOON-RIGHT TO BAR
2955  DOWNWARDS HARPOON-RIGHT TO BAR
2956  LEFTWARDS HARPOON-DOWN TO BAR
2957
RIGHTWARDS HARPOON-DOWN TO BAR
2958 ¡ UPWARDS HARPOON-LEFT TO BAR
2959 ¢ DOWNWARDS HARPOON-LEFT TO BAR
295A £ LEFTWARDS HARPOON-UP FROM BAR
295B ¤ RIGHTWARDS HARPOON-UP FROM BAR
295C ¥ UPWARDS HARPOON-RIGHT FROM BAR
295D ! DOWNWARDS HARPOON-RIGHT FROM BAR
295E " LEFTWARDS HARPOON-DOWN FROM BAR
295F # RIGHTWARDS HARPOON-DOWN FROM BAR
2960 $ UPWARDS HARPOON-LEFT FROM BAR
2961 % DOWNWARDS HARPOON-LEFT FROM BAR
2962 & LEFTWARDS HARPOON-UP ABOVELEFTWARDS HARPOON-DOWN
2963 ' UPWARDS HARPOON-LEFT BESIDEUPWARDS HARPOON-RIGHT
2964 ( RIGHTWARDS HARPOON-UP ABOVERIGHTWARDS HARPOON-DOWN
2965 ) DOWNWARDS HARPOON-LEFT BESIDEDOWNWARDS HARPOON-RIGHT
2966 * LEFTWARDS HARPOON-UP ABOVERIGHTWARDS HARPOON-UP
2967 + LEFTWARDS HARPOON-DOWN ABOVERIGHTWARDS HARPOON-DOWN
2968 , RIGHTWARDS HARPOON-UP ABOVELEFTWARDS HARPOON-UP
2969 - RIGHTWARDS HARPOON-DOWN ABOVELEFTWARDS HARPOON-DOWN
296A . LEFTWARDS HARPOON-UP ABOVE LONG
DASH
296B / LEFTWARDS HARPOON-DOWN BELOWLONG DASH
296C 0 RIGHTWARDS HARPOON-UP ABOVE LONG
DASH
296D 1 RIGHTWARDS HARPOON-DOWN BELOWLONG DASH
296E 2 UPWARDS HARPOON-LEFT BESIDEDOWNWARDS HARPOON-RIGHT
296F 3 DOWNWARDS HARPOON-LEFT BESIDEUPWARDS HARPOON-RIGHT
2970 4 RIGHT DOUBLE ARROW WITH ROUNDED
HEAD
2283 superset of297F

2971 5 EQUAL ABOVE RIGHTWARDS ARROW
2972 6 TILDE OPERATOR ABOVE RIGHTWARDS
ARROW
2973 7 LEFTWARDS ARROW ABOVE TILDEOPERATOR
2974 8 RIGHTWARDS ARROW ABOVE TILDEOPERATOR
2975 9 RIGHTWARDS ARROW ABOVE DOUBLETILDE OPERATOR
2976 : LESS THAN ABOVE LEFTWARDS ARROW
2977 ; LEFTWARDS ARROW THROUGH LESS-THAN
2978 < GREATER-THAN ABOVE RIGHTWARDS
ARROW
2979 = SUBSET ABOVE RIGHTWARDS ARROW
297A > LEFTWARDS ARROW THROUGH SUBSET
297B ? SUPERSET ABOVE LEFTWARDS ARROW
297C @ LEFT FISH TAIL
297D A RIGHT FISH TAIL
297E B UP FISH TAIL
297F C DOWN FISH TAIL→

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

22

2980

Miscellaneous Math Symbols

298
0

1

2

3

8

9

A

B

29C0

29D0

29E0

29F0

29A1

29B1

29C1

29D1

29E1

29F1

F

V f v § · Ç Ú

2982

2992

29A2

29B2

29C2

29D2

29E2

29F2

G W g w ¨ ¸ È Û
2993

29A3

29B3

29C3

29D3

29E3

29F3

H X h x © ¹ É Ü
2994

29A4

29B4

29C4

29D4

29E4

29F4

I Y i y ª º Ê
2995

29A5

29B5

29C5

29D5

29E5

J Z j z « » Ë
29B6

29C6

29D6

29E6

2996

29A6

K

[

k { ¬ ¼ Ì

2987

2997

29A7

L

\

l | ­ ½ Í

2988

2998

29A8

M

]

m } ® ¾ Î

2989

2999

29A9

N

^

n ~ ¯ ¿ Ò

298A

299A

29AA

29B7

29B8

29B9

29BA

29C7

29C8

29C9

29CA

29D7

29D8

29D9

29DA

29E7

29E8

29E9

29EA

O _ o  ° À Ó
299B

29AB

29BB

29CB

29DB

29EB

P ` p ¡ ± Á Ô
299C

29AC

29BC

29CC

29DC

29EC

Q a q ¢ ² Â Õ
299D

29AD

29BD

29CD

29DD

29ED

R b r £ ³ Ã Ö
299E

29AE

29BE

29CE

29DE

29EE

S c s ¤ ´ Ä ×
298F

PFS: amstt fonts Version 1fixed

29B0

U e u ¦ ¶ Æ Ù

298E

F

29A0

2991

298D

E

29F

E

298C

D

29E

2981

298B

C

29D

T d t ¥ µ Å Ø

2986

7

29C

2990

2985

6

29B

D

2984

5

29A

2980

2983

4

299

29FF

299F

29AF

29BF

29CF

29DF

Printed 17-Mar-2000

29EF

23

2980

Miscellaneous Math Symbols

Miscellaneous math symbols

2980 D TRIPLE VERTICAL BAR DELIMITER
2AF4 triple vertical bar with horizontal stroke
2981 E Z NOTATION SPOT
• medium-sized filled circle
2982 F Z NOTATION TYPE COLON→

Brackets

2983 G LEFT WHITE BRACE
2984 H RIGHT WHITE BRACE
2985 I LEFT WHITE ANGULAR BRACKET
3108 left white tortoise shell bracket
2986 J RIGHT WHITE ANGULAR BRACKET
3109 right white tortoise shell bracket
2987 K Z NOTATION LEFT IMAGE BRACKET
2988 L Z NOTATION RIGHT IMAGE BRACKET
2989 M Z NOTATION LEFT BINDING BRACKET
298A N Z NOTATION RIGHT BINDING BRACKET
298B O LEFT BRACKET UNDERBAR
298C P RIGHT BRACKET UNDERBAR
298D Q LEFT BRACKET WITH REVERSE SOLIDUS
TOP CORNER
298E R RIGHT BRACKET WITH REVERSE SOLIDUS
BOTTOM CORNER
298F S LEFT BRACKET WITH SOLIDUS BOTTOM
CORNER
2990 T RIGHT BRACKET WITH SOLIDUS TOP
CORNER
2991 U LEFT ANGLE BRACKET WITH DOT
2992 V RIGHT ANGLE BRACKET WITH DOT
2993 W LEFT ARC LESS-THAN BRACKET
2994 X RIGHT ARC GREATER-THAN BRACKET
2995 Y DOUBLE LEFT ARC GREATER-THAN
BRACKET2996 Z DOUBLE RIGHT ARC LESS-THAN BRACKET
2997 [ RIGHT MOUSTACHE
2998 \ LEFT MOUSTACHE

→
→

Fence
2999

] DOTTED FENCE• four close dots vertical

Miscellaneous math symbol

299B _ MEASURED ANGLE OPENING LEFT
299C ` RIGHT ANGLE VARIANT WITH SQUARE
299D a MEASURED RIGHT ANGLE WITH DOT
299E b ANGLE WITH S INSIDE
299F c ACUTE ANGLE
29A0 d SPHERICAL ANGLE OPENING LEFT
29A1 e SPHERICAL ANGLE OPENING UP
29A2 f TURNED ANGLE
29A3 g REVERSED ANGLE
29A4 h ANGLE WITH UNDERBAR
29A5 i REVERSED ANGLE WITH UNDERBAR
29A6 j LARGE DOWNWARDS POINTING ANGLE
29A7 k LARGE UPWARDS POINTING ANGLEPFS: amstt fonts Version 1fixed

29A8 l MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING UP AND TO
THE RIGHT
29A9 m MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING UP AND TO
THE LEFT
29AA n MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING DOWN AND
TO THE RIGHT
29AB o MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING DOWN AND
TO THE LEFT
29AC p MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING RIGHT AND
UP
29AD q MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING LEFT AND UP
29AE r MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING RIGHT AND
DOWN
29AF s MEASURED ANGLE WITH OPEN ARM
ENDING IN ARROW POINTING LEFT AND
DOWN

Empty sets

29B0 t REVERSED EMPTY SET
2349 apl functional symbol circle backslash
29B1 u EMPTY SET OVERBAR
29B2 v EMPTY SET WITH SMALL CIRCLE ABOVE
29B3 w EMPTY SET RIGHT ARROW ABOVE
29B4 x EMPTY SET LEFT ARROW ABOVE→

Circle symbols

29B5 y CIRCLE WITH HORIZONTAL BAR
29B6 z CIRCLED VERTICAL BAR
29B7 { CIRCLED PARALLEL
29B8 | CIRCLED FALLING DIAGONAL
29B9 } CIRCLED PERPENDICULAR
29BA ~ CIRCLE DIVIDED BY HORIZONTAL BAR AND
TOP HALF DIVIDED BY VERTICAL
29BB  CIRCLE WITH SUPERIMPOSED X
29BC ¡ CIRCLED ANTICLOCKWISE-ROTATEDDIVISION SIGN
29BD ¢ UP ARROW THROUGH CIRCLE
29BE £ CIRCLED LARGE CIRCLE
233E apl functional symbol circle jot
29BF ¤ CIRCLED FILLED CIRCLE
29C0 ¥ CIRCLED LESS-THAN
29C1 ¦ CIRCLED GREATER-THAN
29C2 § CIRCLE WITH SMALL CIRCLE TO THE RIGHT
29C3 ¨ CIRCLE WITH TWO HORIZONTAL STROKESTO THE RIGHT→

299A ^ VERTICAL ZIGZAG LINE

Angles

29C7

Square symbols

29C4 © SQUARED RISING DIAGONAL SLASH
2341 apl functional symbol quad slash
29C5 ª SQUARED FALLING DIAGONAL SLASH
2342 apl functional symbol quad backslash
29C6 « SQUARED ASTERISK
29C7 ¬ SQUARED SMALL CIRCLE
233B apl functional symbol quad circle→→→

Printed 17-Mar-2000

24

29C8

Miscellaneous Math Symbols

29C8 ­ SQUARED SQUARE
29C9 ® TWO JOINED SQUARES

29F4Error bar symbols

Triangle symbols

29CA ¯ TRIANGLE WITH DOT OVER
29CB ° TRIANGLE WITH UNDERBAR
29CC ± S IN TRIANGLE
29CD ² TRIANGLE WITH SERIFS AT BOTTOM
29CE ³ RIGHT TRIANGLE ABOVE LEFT TRIANGLE
29CF ´ LEFT TRIANGLE BESIDE VERTICAL BAR
29D0 µ VERTICAL BAR BESIDE RIGHT TRIANGLE

29EE Ö ERROR-BARRED WHITE SQUARE
29EF × ERROR-BARRED FILLED SQUARE
29F0 Ø ERROR-BARRED WHITE DIAMOND
29F1 Ù ERROR-BARRED FILLED DIAMOND
29F2 Ú ERROR-BARRED WHITE CIRCLE
29F3 Û ERROR-BARRED FILLED CIRCLE

Miscellanous math symbol
29F4 Ü RULE-DELAYED= colon right arrow

Bowtie symbols

29D1 ¶ LEFT FILLED BOWTIE
29D2 · RIGHT FILLED BOWTIE
29D3 ¸ FILLED BOWTIE
29D4 ¹ LEFT FILLED TIMES
22C9 left normal factor semidirect product
29D5 º RIGHT FILLED TIMES
22CA right normal factor semidirect product
29D6 » WHITE HOURGLASS= vertical bowtie
29D7 ¼ FILLED HOURGLASS→→

Miscellaneous math symbols

29D8 ½ MOST POSITIVE
29D9 ¾ CONGRUENCE SIGN WITH LAZY S
29DA ¿ REVERSED MOST POSITIVE WITH LINE
BELOW
29DB À MOST POSITIVE WITH TWO LINES BELOW
29DC Á INFINITY SIGN WITH TOP RIGHT QUADRANTOMITTED
29DD Â TIE OVER INFINITY
29DE Ã INFINITY NEGATED WITH VERTICAL BAR
29DF Ä DOUBLE-ENDED MULTIMAP
29E0 Å SQUARE WITH CONTOURED OUTLINE= D'Alembertian
29E1 Æ INCREASES AS
29E2 Ç SHUFFLE PRODUCT
29E3 È SLANTED PARALLEL SUPERIMPOSED ON
EQUAL= homethetically congruent to29E4 É TILDE ABOVE SLANTED PARALLEL
SUPERIMPOSED ON EQUAL
29E5 Ê SLANTED PARALLEL SUPERIMPOSED ON
THREE-LINE EQUAL= congruent and parallel
29E6 Ë TOP ARC ABOVE BOTTOM ARC
29E7 Ì THERMODYNAMIC• vertical bar crossed by two horizontals
29E8 Í DOWN-POINTING TRIANGLE WITH LEFTHALF BLACK
29E9 Î DOWN-POINTING TRIANGLE WITH RIGHTHALF BLACK
29EA Ò FILLED DIAMOND WITH DOWN ARROW
29EB Ó FILLED LOZENGE
29EC Ô CIRCLE WITH DOWN ARROW
29ED Õ FILLED CIRCLE WITH DOWN ARROWPFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

25

2A00

Supplemental Math Operators

2A0

2A2

2A3

2A4

2A5

2A6

2A7

Ý í ý . > + ;

0

2A00

2A10

Þ î

1

2A01

2A11

2A20

2A30

2A40

2A50

2A60

þ / ? , <
2A21

2A31

2A41

2A51

2A61

ß ï ÿ 0 @ - =

2

2A02

2A12

à ð

3

2A03

2A13

2A22

2A32

2A42

2A52

2A62

! 1 A . >
2A23

2A33

2A43

2A53

2A63

á ñ " 2 B / ?

4

2A04

2A14

2A24

2A34

2A44

2A54

2A64

â ò # 3 C 0 @

5

2A05

2A15

ã ó

6

2A06

2A16

ä ô

7

2A07

2A17

2A25

2A35

2A45

2A55

2A65

$ 4 ! 1 A
2A26

2A36

2A46

2A56

2A66

% 5 " 2 B
2A27

2A37

2A47

2A57

2A67

å õ & 6 # 3 C

8

2A08

2A18

2A28

2A38

2A48

2A58

2A68

æ ö ' 7 $ 4 D

9

2A09

2A19

2A29

2A39

2A49

2A59

2A69

ç ÷ ( 8 % 5 E

A

2A0A

2A1A

2A2A

2A3A

2A4A

2A5A

2A6A

è ø ) 9 & 6 F

B

2A0B

C

2A1

2A7F

2A1B

é ù
2A0C

D

2A5B

2A6B

* : ' 7 G
2A2C

2A3C

2A4C

2A5C

2A6C

2A1D

2A2D

2A3D

2A4D

2A5D

2A6D

2A1E

2A2E

2A3E

2A4E

2A5E

2A6E

ì ü - = * :2A0F

PFS: amstt fonts Version 1fixed

2A4Bë û , < ) 9 I
2A0E

F

2A3B

ê ú + ; ( 8 H
2A0D

E

2A1C

2A2B

2A1F

2A2F

2A3F

2A4F

2A5F

Printed 17-Mar-2000

26

2A80

Supplemental Math Operators

2A8

2A9

2AA

2AB

2AC

2AD

2AE

2AFF

2AF

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

PFS: amstt fonts Version 1fixed

Printed 17-Mar-2000

27

2A00

Supplemental Math Operators

N-ary operators

2A00 Ý N-ARY CIRCLED DOT OPERATOR
2299 circled dot operator
2A01 Þ N-ARY CIRCLED PLUS OPERATOR
2295 circled plus
2A02  N-ARY CIRCLED TIMES OPERATOR
2297 circled times
2A03  N-ARY UNION OPERATOR WITH DOT
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

→
→
→

→
→
→

→

0

2A55
two intersecting logical and
2A08 ¤ TWO LOGICAL OR OPERATOR→ 2A56 1 two intersecting logical or

2A0A ¦ MODULO TWO SUM
2A0B § SUMMATION WITH INTEGRAL
2A0C¨ QUADRUPLE INTEGRAL OPERATOR
222B 222B 222B 222B
2A0D © FINITE PART INTEGRAL
2A0E ª 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 SEMICIRCULARPATH AROUND POLE
2A14 ° LINE INTEGRATION NOT INCLUDING THE
POLE
2A15 ± INTEGRAL AROUND A POINT OPERATOR
2A16 ² QUATERNION INTEGRAL OPERATOR
2A17 ³ INTEGRAL OPERPRINTED WITH LEFTWARDSARROW WITH HOOK
2A18 ´ INTEGRAL OVERPRINTED WITH TIMES SIGN
2A19 µ INTEGRAL OVERPRINTED WITH CAP
2A1A ¶ INTEGRAL OVERPRINTED WITH CUP
2A1B · UPPER INTEGRAL WITH OVERBAR
2A1C ¸ LOWER INTEGRAL WITH UNDERBAR

∫

∫

∫

2A1D ¹ JOIN
= large bowtie• relational database theory
2A1E º LARGE LEFT TRIANGLE OPERATOR• relational database theory
2A1F  Z NOTATION SCHEMA COMPOSITION
2A3E  z notation relational composition
2A20 » Z NOTATION SCHEMA PIPING
226B much greater-than
PFS: amstt fonts Version 1fixed

Plus and minus sign operators

2A22 ÿ PLUS SIGN WITH SMALL CIRCLE ABOVE
2A23 ! PLUS SIGN WITH CIRCUMFLEX ACCENT
ABOVE
2A24 " PLUS SIGN WITH TILDE ABOVE
2A25 # PLUS SIGN WITH DOT BELOW
2A26 $ PLUS SIGN WITH TILDE BELOW
2A27 % PLUS SIGN WITH SUBSCRIPT TWO= nim-addition
2A28 & FILLED TRIANGLE WITH PLUS
2A29 ' MINUS SIGN WITH COMMA ABOVE
2A2A ( MINUS SIGN WITH DOT BELOW
2A2B ) FALLING DOTS MINUS
2A2C * RISING DOTS MINUS
2A2D + PLUS SIGN IN LEFT HALF CIRCLE
2A2E , PLUS SIGN IN RIGHT HALF CIRCLE
2A2F - VECTOR OR CROSS PRODUCT
00D7 × multiplication sign
2A30 . MULTIPLICATION SIGN WITH DOT ABOVE
2A31 / MULTIPLICATION SIGN WITH UNDERBAR
2A32 0 SEMIDIRECT PRODUCT MULTIPLICATIONSIGN WITH BOTTOM CLOSED
2A33 1 SMASH PRODUCT
2A34 2 MULTIPLICATION SIGN IN LEFT HALF
CIRCLE
2A35 3 MULTIPLICATION SIGN IN RIGHT HALF
CIRCLE
2A36 4 CIRCLED MULTIPLICATION SIGN WITH
CIRCUMFLEX ACCENT
2A37 5 MULTIPLICATION SIGN IN DOUBLE CIRCLE
2A38 6 CIRCLED DIVISION SIGN

Miscellaneous math operators

2A39 7 PLUS IN TRIANGLE
2A3A 8 MINUS IN TRIANGLE
2A3B 9 MULTIPLICATION SIGN IN TRIANGLE
2A3C : INTERIOR PRODUCT
2A3D ; RIGHTHAND INTERIOR PRODUCT2319 turned not sign
2A3E < Z NOTATION RELATIONAL COMPOSITION
2A1F ü z notation schema composition
2A3F = AMALGAMATION OR COPRODUCT2210 n-ary coproduct→→→Intersections and unions

Miscellaneous operators

→
→

→

→

Summations and integrals∫

2A21 þ Z NOTATION SCHEMA PROJECTION
21BE upwards harpoon with bar rightwards

Multiplication and division sign operators

2A09 ¥ N-ARY TIMES OPERATOR

≈

2A47

2A40 > INTERSECTION WITH DOT
2A41 ? UNION WITH MINUS= z notation bag subtraction
2A42 @ UNION WITH OVERBAR
2A43 A INTERSECTION WITH OVERBAR
2A44 B INTERSECTION WITH LOGICAL AND
2A45 C UNION WITH LOGICAL OR
2A46 ! UNION ABOVE INTERSECTION
2A47 " INTERSECTION ABOVE UNION

Printed 17-Mar-2000

28

2A48

Supplemental Math Operators# UNION ABOVE BAR ABOVE INTERSECTION$ INTERSECTION ABOVE BAR ABOVE UNION% UNION BESIDE AND JOINED WITH UNION& INTERSECTION BESIDE AND JOINED WITH
INTERSECTION
2A4C ' CLOSED UNION WITH SERIFS
2A4D ( CLOSED INTERSECTION WITH SERIFS
2A4E ) DOUBLE SQUARE INTERSECTION
2A4F * DOUBLE SQUARE UNION
2A50 + CLOSED UNION WITH SERIFS AND SMASH
2A48
2A49
2A4A
2A4B

PRODUCT

Logical ands and ors, LOGICAL AND WITH DOT ABOVE- LOGICAL OR WITH DOT ABOVE. DOUBLE LOGICAL AND/ DOUBLE LOGICAL OR
0 TWO INTERSECTING LOGICAL AND→ 2A07 £ two logical and operator
2A56 1 TWO INTERSECTING LOGICAL OR→ 2A08 ¤ two logical or operator
2A57 2 SLOPING LARGE OR
2A58 3 SLOPING LARGE AND
2A59 4 LOGICAL OR OVERLAPPING LOGICAL AND
2A5A 5 LOGICAL AND WITH MIDDLE STEM
2A5B 6 LOGICAL OR WITH MIDDLE STEM
2A5C 7 LOGICAL AND WITH HORIZONTAL DASH
2A5D 8 LOGICAL OR WITH HORIZONTAL DASH
2A5E 9 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
2A62 = LOGICAL OR WITH DOUBLE OVERBAR
2A63 > LOGICAL OR WITH DOUBLE UNDERBAR
2A51
2A52
2A53
2A54
2A55

→ 225A equiangular to? Z NOTATION DOMAIN ANTIRESTRICTION@ Z NOTATION RANGE ANTIRESTRICTION

Relational operators
2A66
2A67
2A68

A EQUAL SIGN WITH DOT BELOWB IDENTICAL WITH DOT ABOVEC TRIPLE HORIZONTAL BAR WITH DOUBLEVERTICAL STROKE= identical and parallel to
TRIPLE HORIZONTAL BAR WITH TRIPLE
VERTICAL STROKETILDE OPERATOR WITH DOTTILDE OPERATOR WITH RISING DOTS
223B homothetic
SIMILAR MINUS SIMILAR
CONGRUENT WITH OVERDOTREVERSED CONGRUENTDOUBLE TILDE OPERATOR WITH
CIRCUMFLEX ACCENT
APPROXIMATELY EQUAL OR EQUAL TO

D
2A6A E
2A6B F→
2A6C G
2A6D H
2A6E I
2A69

2A6F
2A70

PFS: amstt fonts Version 1fixed

2A78
2A79
2A7A
2A7B
2A7C
2A7D
2A7E
2A7F
2A80
2A81
2A82
2A83
2A84
2A85
2A86
2A87
2A88
2A89
2A8A
2A8B
2A8C

Miscellaneous math operators
2A64
2A65

2A71
2A72
2A73
2A74
2A75
2A76
2A77

2A8D
2A8E
2A8F
2A90
2A91
2A92
2A93
2A94
2A95
2A96
2A97

2A97

EQUAL ABOVE PLUS
PLUS ABOVE EQUAL
EQUAL ABOVE TILDE OPERATORDOUBLE COLON EQUALTWO CONSECUTIVE EQUAL SIGNSTHREE CONSECUTIVE EQUAL SIGNSEQUAL SIGN WITH TWO DOTS ABOVE AND
TWO DOTS BELOW
EQUIVALENT WITH FOUR DOTS ABOVE
LESS-THAN WITH CIRCLE INSIDEGREATER-THAN WITH CIRCLE INSIDE
LESS-THAN WITH QUESTION MARK ABOVEGREATER-THAN WITH QUESTION MARKABOVELESS-THAN OR SLANTED EQUAL TO
GREATER-THAN OR SLANTED EQUAL TO
LESS-THAN OR SLANTED EQUAL TO WITH
DOT INSIDEGREATER-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 RIGHTGREATER-THAN OR SLANTED EQUAL TO
WITH DOT ABOVE LEFT
LESS-THAN OR APPROXIMATEGREATER-THAN OR APPROXIMATE
LESS-THAN AND NOT ONE-LINE EQUAL TO
GREATER-THAN AND NOT ONE-LINE EQUAL
TO
LESS-THAN AND NOT APPROXIMATEGREATER-THAN AND NOT APPROXIMATE
LESS-THAN ABOVE TWO-LINE EQUALABOVE GREATER-THAN
GREATER-THAN ABOVE TWO-LINE EQUALABOVE LESS-THAN
LESS-THAN ABOVE SIMILAR OR EQUALGREATER-THAN ABOVE SIMILAR OR EQUAL
LESS-THAN ABOVE SIMILAR ABOVEGREATER-THAN
GREATER-THAN ABOVE SIMILAR ABOVE
LESS-THAN
LESS-THAN ABOVE GREATER-THAN ABOVE
TWO-LINE EQUALGREATER-THAN ABOVE LESS-THAN ABOVE
TWO-LINE EQUAL
LESS-THAN ABOVE SLANTED EQUALABOVE GREATER-THAN ABOVE SLANTEDEQUALGREATER-THAN ABOVE SLANTED EQUALABOVE LESS-THAN ABOVE SLANTEDEQUALSLANTED EQUAL TO OR LESS-THAN
SLANTED EQUAL TO OR GREATER-THAN
SLANTED EQUAL TO OR LESS-THAN WITH
DOT INSIDE

Printed 17-Mar-2000

29

2A98
2A98
2A99
2A9A
2A9B
2A9C
2A9D
2A9E
2A9F
2AA0
2AA1
2AA2
2AA3
2AA4
2AA5
2AA6
2AA7
2AA8
2AA9
2AAA
2AAB
2AAC
2AAD
2AAE
2AAF
2AB0
2AB1
2AB2
2AB3
2AB4
2AB5
2AB6
2AB7
2AB8
2AB9
2ABA
2ABB
2ABC

Supplemental Math Operators
SLANTED EQUAL TO OR GREATER-THAN
WITH DOT INSIDETWO-LINE EQUAL TO OR LESS-THAN
TWO-LINE EQUAL TO OR GREATER-THAN
TWO-LINE SLANTED EQUAL TO OR LESSTHAN
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 ABOVEEQUALDOUBLE NESTED LESS-THAN SIGN
= absolute continuity
DOUBLE NESTED GREATER-THAN SIGNDOUBLE LESS-THAN WITH UNDERBAR
GREATER-THAN OVERLAPPING LESS-THAN
GREATER-THAN BESIDE LESS-THAN
LESS-THAN CLOSED BY CURVEGREATER-THAN CLOSED BY CURVE
LESS-THAN CLOSED BY CURVE ABOVESLANTED EQUALGREATER-THAN CLOSED BY CURVE ABOVESLANTED EQUAL
SMALLER THAN
LARGER THAN
SMALLER THAN OR EQUAL
LARGER THAN OR EQUALBUMPY 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 TILDEOPERATOR
SUCCEEDS ABOVE DOUBLE TILDEOPERATORPRECEDES ABOVE NOT DOUBLE TILDEOPERATOR
SUCCEEDS ABOVE NOT DOUBLE TILDEOPERATORDOUBLE PRECEDESDOUBLE SUCCEEDS

2AC4
2AC5
2AC6
2AC7
2AC8
2AC9
2ACA
2ACB
2ACC
2ACD
2ACE
2ACF
2AD0
2AD1
2AD2
2AD3
2AD4
2AD5
2AD6
2AD7
2AD8

2AC2
2AC3

SUBSET WITH DOTSUPERSET WITH DOTSUBSET WITH PLUS BELOW
SUPERSET WITH PLUS BELOWSUBSET WITH MULTIPLICATION SIGN
BELOWSUPERSET WITH MULTIPLICATION SIGNBELOWSUBSET OF OR EQUAL TO WITH DOT ABOVEPFS: amstt fonts Version 1fixedSUPERSET OF OR EQUAL TO WITH DOTABOVESUBSET OF OR TWO-LINE EQUAL
SUPERSET OF OR TWO-LINE EQUAL
SUBSET OF ABOVE TILDE OPERATOR
SUPERSET OF ABOVE TILDE OPERATORSUBSET OF ABOVE DOUBLE TILDEOPERATORSUPERSET OF ABOVE DOUBLE TILDEOPERATORSUBSET OF OR NOT TWO-LINE EQUAL
SUPERSET OF OR NOT TWO-LINE EQUAL
SQUARE LEFT OPEN BOX OPERATORSQUARE RIGHT OPEN BOX OPERATOR
CLOSED SUBSET
CLOSED SUPERSETCLOSED SUBSET OR EQUAL
CLOSED SUPERSET OR EQUAL
SUBSET ABOVE SUPERSETSUPERSET ABOVE SUBSETSUBSET ABOVE SUBSET
SUPERSET ABOVE SUPERSETSUPERSET BESIDE SUBSET
SUPERSET BESIDE AND JOINED BY DASH
WITH SUBSET

Forks
2AD9
2ADA
2ADB
2ADC
2ADD

ELEMENT OF OPENING DOWNWARDSPITCHFORK WITH TEE TOP
TRANSVERSAL INTERSECTION
22D4 pitchfork
FORKING• symbol is slashed although positive
NONFORKING• negative symbol with no slash

→

Tacks
2ADE
2ADF
2AE0
2AE1
2AE2
2AE3
2AE4
2AE5
2AE6

Subset and superset relations
2ABD
2ABE
2ABF
2AC0
2AC1

2AEA

2AE7
2AE8
2AE9
2AEA

SHORT LEFT TACKSHORT DOWN TACKSHORT UP TACKPERPENDICULAR WITH S
VERTICAL BAR TRIPLE RIGHT TURNSTILE= ordinarily satisfies
DOUBLE VERTICAL BAR LEFT TURNSTILE
VERTICAL BAR DOUBLE LEFT TURNSTILEDOUBLE VERTICAL BAR DOUBLE LEFTTURNSTILE
LONG DASH FROM LEFT MEMBER OFDOUBLE VERTICAL
22A9 forces
SHORT DOWN TACK WITH OVERBAR
22A4 down tack
SHORT UP TACK WITH UNDERBAR
22A5 up tack
SHORT UP TACK ABOVE SHORT DOWNTACKDOUBLE DOWN TACK→→→

Printed 17-Mar-2000

30

Math Symbols

2000-03-14

Annex 3
Excerpts from L2/00-02

BX0 BX1 BX2 BX3 BX4 BX5 BX6 BX7 BX8AX0 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

Letter-like symbols; combining diacritics; punctuation
AX00

AX01
AX02

N GREEK THETA SYMBOL WITH STRAIGHT BAR→ 0472 cyrillic capital letter fita
→ 04E8 cyrillic capital letter barred o[removed: 03D2]
N GREEK SYMBOL STRAIGHT EPSILON

1

Math Symbols

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
A@XD
A@XE
A@XF

2000-03-14

N GREEK SYMBOL REVERSED STRAIGHT EPSILONN GREEK LETTER Q-KOPPA
N GREEK SMALL LETTER Q-KOPPA
N TURNED SANS SERIF CAPITAL G= gameN TURNED SANS SERIF CAPITAL LN REVERSED SANS SERIF CAPITAL LN INVERTED SANS SERIF CAPITAL Y
N OPEN-FACE GREEK SMALL LETTER GAMMAN OPEN-FACE GREEK CAPITAL GAMMAN OPEN-FACE GREEK CAPITAL PI
L OPEN-FACE SUM
D COMBINING REVERSE SOLIDUS OVERLAYD 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][removed]
LOW ASTERISKN QUADRUPLE PRIME[composed: U+2032 + U+2032 + U+2032 + U+2032][removed]
REVERSED SEMI-COLON
P EM LEADERN TWO ASTERISKS ALIGNED VERTICALLYSOLIDUS OVERBAR
REVERSE SOLIDUS WITH HORIZONTAL STROKEB BIG SOLIDUS
B BIG REVERSE SOLIDUS= Z NOTATION SCHEMA HIDING. visually distinguishably bigger than set minus
TOP SQUARE BRACKET
BOTTOM SQUARE BRACKET
BOTTOM ABOVE TOP SQUARE BRACKETN TURNED AMPERSAND[removed][removed]
N MEDIUM MATH SPACE. four-eighteenths of an em[removed: 2423]
FUNCTION APPLICATIONINVISIBLE TIMESVARIATION SELECTOR

2

Math Symbols

2000-03-14

Arrows and harpoons, combinations, fishtails
BX00
BX01
BX02
BX03
BX04
BX05
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

R DOWNWARDS ARROW LEFTWARDS OF UPWARDS ARROWR THREE RIGHTWARDS ARROWS
R LEFTWARDS ARROW WITH VERTICAL STROKER 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 STROKER 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 ARROWR RIGHTWARDS OPEN-HEADED ARROWR LEFT RIGHT OPEN-HEADED ARROWR 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 STROKER RIGHTWARDS DOUBLE ARROW WITH VERTICAL STROKER LEFT RIGHT DOUBLE ARROW WITH VERTICAL STROKER RIGHTWARDS TWO-HEADED ARROW FROM BAR= maps to
R LEFTWARDS DOUBLE ARROW FROM BAR= maps fromR RIGHTWARDS DOUBLE ARROW FROM BAR= maps to
R DOWNWARDS ARROW WITH HORIZONTAL STROKER UPWARDS ARROW WITH HORIZONTAL STROKER UPWARDS TRIPLE ARROWR DOWNWARDS TRIPLE ARROWR LEFTWARDS BROKEN ARROWR RIGHTWARDS BROKEN ARROWR LEFTWARDS DOUBLY BROKEN ARROWR RIGHTWARDS DOUBLY BROKEN ARROWR RIGHTWARDS TWO-HEADED BROKEN ARROWR RIGHTWARDS ARROW WITH DOTTED STEMR UPWARDS ARROW TO BAR
R DOWNWARDS ARROW TO BARR 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= Z NOTATION BIJECTION
R RIGHTWARDS TWO-HEADED ARROW WITH TAIL WITH VERTICAL STROKE= Z NOTATION SURJECTIVE INJECTION

3

Math Symbols

BX24
BX25
BX26
BX27
BX28
BX29
BX2A
BX2B
BX2C
BX2D
BX2E
BX2F
BX30
BX31
BX32
BX33
BX34
BX35
BX36
BX37
BX38
BX39
BX3A
BX3B
BX3C
BX3D
BX3E
BX3F
BX40
BX41
BX42
BX43
BX44
BX45
BX46
BX47
BX48
BX49
BX4A
BX4B
BX4C
BX4D
BX4E
BX4F
BX50
BX51
BX52
BX53

2000-03-14

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 DIAMONDR NORTH WEST-SOUTH EAST ARROWR NORTH EAST-SOUTH WEST ARROWR NORTH WEST ARROW WITH HOOKR NORTH EAST ARROW WITH HOOK
R SOUTH EAST ARROW WITH HOOK
R SOUTH WEST ARROW WITH HOOKR NORTH WEST AND NORTH EAST ARROWSR NORTH EAST AND SOUTH EAST ARROWSR SOUTH EAST AND SOUTH WEST ARROWSR SOUTH WEST AND NORTH WEST ARROWSN RISING DIAGONAL CROSSING FALLING DIAGONALN FALLING DIAGONAL CROSSING RISING DIAGONALN SOUTH EAST ARROW CROSSING NORTH EAST ARROWN NORTH EAST ARROW CROSSING SOUTH EAST ARROWN FALLING DIAGONAL CROSSING NORTH EAST ARROWN RISING DIAGONAL CROSSING SOUTH EAST ARROWN NORTH EAST ARROW CROSSING NORTH WEST ARROWN NORTH WEST ARROW CROSSING NORTH EAST ARROWR WAVE ARROW POINTING DIRECTLY TO THE RIGHT→ 219D rightwards wave arrow
RIGHTWARDS ARROW CURVING UP. Japanese request
RIGHTWARDS ARROW CURVING DOWN
. Japanese request
R DOWNWARDS ARROW CURVING LEFTWARDSR DOWNWARDS ARROW CURVING RIGHTWARDSR RIGHT-SIDE ARC CLOCKWISE ARROWR LEFT-SIDE ARC ANTICLOCKWISE ARROWR TOP ARC ANTICLOCKWISE ARROWR BOTTOM ARC ANTICLOCKWISE ARROWR TOP ARC CLOCKWISE ARROW WITH MINUS
R TOP ARC ANTICLOCKWISE ARROW WITH PLUS
R LOWER RIGHT SEMICIRCULAR CLOCKWISE ARROWR LOWER LEFT SEMICIRCULAR ANTICLOCKWISE ARROWR ANTICLOCKWISE CLOSED CIRCLE ARROW→ 20DA combining anticlockwise ring overlay
R CLOCKWISE CLOSED CIRCLE ARROW→ 20D9 combining clockwise ring overlay
R RIGHTWARDS ARROW ABOVE SHORT LEFTWARDS ARROWR LEFTWARDS ARROW ABOVE SHORT RIGHTWARDS ARROWR SHORT RIGHTWARDS ARROW ABOVE LEFTWARDS ARROWR RIGHTWARDS ARROW WITH PLUS BELOW
R LEFTWARDS ARROW WITH PLUS BELOW
R RIGHTWARDS ARROW THROUGH X

4Math Symbols

BX54
BX55
BX56
BX57
BX58
BX59
BX5A
BX5B
BX5C
BX5D
BX5E
BX5F
BX60
BX61
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
BX7E
BX7F
BX80
BX81
BX82
BX83
BX84
BX85
BX86
BX87
BX88

2000-03-14

R SMALL CIRCLE WITH SUPERIMPOSED LEFT RIGHT ARROWR UPWARDS TWO-HEADED ARROW FROM SMALL CIRCLE
RIGHT ANGLE WITH DOWNWARDS ZIG-ZAG ARROWR LEFT-UP-RIGHT-DOWN HARPOONR LEFT-DOWN-RIGHT-UP HARPOON
R UP-RIGHT-DOWN-LEFT HARPOON
R UP-LEFT-DOWN-RIGHT HARPOONR LEFT-UP-RIGHT-UP HARPOON
R UP-RIGHT-DOWN-RIGHT HARPOONR LEFT-DOWN-RIGHT-DOWN HARPOON
R UP-LEFT-DOWN-LEFT HARPOONR LEFTWARDS HARPOON-UP TO BARR RIGHTWARDS HARPOON-UP TO BARR UPWARDS HARPOON-RIGHT TO BAR
R DOWNWARDS HARPOON-RIGHT TO BAR
R LEFTWARDS HARPOON-DOWN TO BARR RIGHTWARDS HARPOON-DOWN TO BARR UPWARDS HARPOON-LEFT TO BAR
R DOWNWARDS HARPOON-LEFT TO BAR
R LEFTWARDS HARPOON-UP FROM BAR
R RIGHTWARDS HARPOON-UP FROM BAR
R UPWARDS HARPOON-RIGHT FROM BAR
R DOWNWARDS HARPOON-RIGHT FROM BAR
R LEFTWARDS HARPOON-DOWN FROM BAR
R RIGHTWARDS HARPOON-DOWN FROM BAR
R UPWARDS HARPOON-LEFT FROM BAR
R DOWNWARDS HARPOON-LEFT FROM BAR
R LEFTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-DOWN
R UPWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTR RIGHTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-DOWN
R DOWNWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHT
R LEFTWARDS HARPOON-UP ABOVE RIGHTWARDS HARPOON-UP
R LEFTWARDS HARPOON-DOWN ABOVE RIGHTWARDS HARPOON-DOWN
R RIGHTWARDS HARPOON-UP ABOVE LEFTWARDS HARPOON-UP
R RIGHTWARDS HARPOON-DOWN ABOVE LEFTWARDS HARPOON-DOWN
R LEFTWARDS HARPOON-UP ABOVE LONG DASH
R LEFTWARDS HARPOON-DOWN BELOW LONG DASHR RIGHTWARDS HARPOON-UP ABOVE LONG DASHR RIGHTWARDS HARPOON-DOWN BELOW LONG DASHR UPWARDS HARPOON-LEFT BESIDE DOWNWARDS HARPOON-RIGHTR DOWNWARDS HARPOON-LEFT BESIDE UPWARDS HARPOON-RIGHTR RIGHT DOUBLE ARROW WITH ROUNDED HEAD
. looks like thin superset
R EQUAL ABOVE RIGHTWARDS ARROWR TILDE OPERATOR ABOVE RIGHTWARDS ARROWR LEFTWARDS ARROW ABOVE TILDE OPERATORR RIGHTWARDS ARROW ABOVE TILDE OPERATORR RIGHTWARDS ARROW ABOVE DOUBLE TILDE OPERATORR LESS THAN ABOVE LEFTWARDS ARROWR LEFTWARDS ARROW THROUGH LESS-THAN
R GREATER-THAN ABOVE RIGHTWARDS ARROWR SUBSET ABOVE RIGHTWARDS ARROWR LEFTWARDS ARROW THROUGH SUBSETR SUPERSET ABOVE LEFTWARDS ARROW

5

Math Symbols

BX89
BX8A
BX8B
BX8C

2000-03-14

R LEFT FISH TAIL
R RIGHT FISH TAIL
R UP FISH TAIL
R DOWN FISH TAILCX0 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

R ELEMENT OF WITH LONG HORIZONTAL STROKER ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKER SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKER ELEMENT OF WITH DOT ABOVE

6

Math Symbols

CX04
CX05
CX06
CX0C
CX0E
CX0F
CX10
CX11
CX12
CX17
CX18
CX19
CX1A
CX1B
CX1C
CX1D
CX1E
CX1F

CX20
CX21
CX22
CX23
CX24
CX25
CX26
CX27
CX28
CX29
CX2A
CX2B
CX2C
CX2D
CX2E
CX2F
CX30
CX31
CX32
CX33
CX34
CX35

CX36

2000-03-14

R ELEMENT OF WITH OVERBARR SMALL ELEMENT OF WITH OVERBARR ELEMENT OF WITH UNDERBARR ELEMENT OF WITH TWO HORIZONTAL STROKESR CONTAINS WITH LONG HORIZONTAL STROKER CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKER SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKER CONTAINS WITH OVERBARR SMALL CONTAINS WITH OVERBARR Z NOTATION BAG MEMBERSHIP
L N-ARY CIRCLED DOT OPERATOR→ 2299 circled dot operator
L N-ARY CIRCLED PLUS OPERATOR→ 2295 circled plus
L N-ARY CIRCLED TIMES OPERATOR→ 2297 circled times
L N-ARY UNION OPERATOR WITH DOT
L N-ARY UNION OPERATOR WITH PLUS
→ 228E multiset union
L N-ARY SQUARE INTERSECTION OPERATOR→ 2293 square cap
L N-ARY SQUARE UNION OPERATOR→ 2294 square cup
L TWO LOGICAL AND OPERATOR= merge→ CX76 two intersecting logical and
L TWO LOGICAL OR OPERATOR→ CX77 two intersecting logical or
L N-ARY TIMES OPERATOR
L MODULO TWO SUM
L SUMMATION WITH INTEGRALL QUADRUPLE INTEGRAL OPERATOR[composed: U+222B + U+222B + U+222B + U+222B]
L FINITE PART INTEGRALL INTEGRAL WITH DOUBLE STROKEL INTEGRAL AVERAGE WITH SLASHL CIRCULATION FUNCTION
L ANTICLOCKWISE INTEGRATION
L LINE INTEGRATION WITH RECTANGULAR PATH AROUND POLE
L LINE INTEGRATION WITH SEMICIRCULAR PATH AROUND POLE
L LINE INTEGRATION NOT INCLUDING THE POLE
L INTEGRAL AROUND A POINT OPERATORL QUATERNION INTEGRAL OPERATORL INTEGRAL OVERPRINTED WITH LEFTWARDS ARROW WITH HOOK
L INTEGRAL OVERPRINTED WITH TIMES SIGNL INTEGRAL OVERPRINTED WITH CAPL INTEGRAL OVERPRINTED WITH CUP
L UPPER INTEGRAL WITH OVERBAR
L LOWER INTEGRAL WITH UNDERBAR
L JOIN= large bowtie (relational database theory)→ 22C8 BOWTIEL LARGE LEFT TRIANGLE OPERATOR. relational database theory

7

Math Symbols

CX37
CX38
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

2000-03-14

L Z NOTATION SCHEMA COMPOSITION→ CX5A Z notation relational composition
L Z NOTATION SCHEMA PIPING→ 226B much greater-thanL Z NOTATION SCHEMA PROJECTION→ 21BE upwards harpoon with barb rightwards
B PLUS SIGN WITH SMALL CIRCLE ABOVEB PLUS SIGN WITH CIRCUMFLEX ACCENT ABOVEB PLUS SIGN WITH TILDE ABOVEB PLUS SIGN WITH DOT BELOWB PLUS SIGN WITH TILDE BELOWB PLUS SIGN WITH SUBSCRIPT TWO= nim-addition
B FILLED TRIANGLE WITH PLUS
B MINUS SIGN WITH COMMA ABOVEB MINUS SIGN WITH DOT BELOWB FALLING DOTS MINUS
B RISING DOTS MINUS
B PLUS SIGN IN LEFT HALF CIRCLEB PLUS SIGN IN RIGHT HALF CIRCLEB VECTOR OR CROSS PRODUCT→ 00D7 multiplication sign
B MULTIPLICATION SIGN WITH DOT ABOVEB MULTIPLICATION SIGN WITH UNDERBARB SEMIDIRECT PRODUCT MULTIPLICATION SIGN WITH BOTTOM CLOSEDB SMASH PRODUCTB MULTIPLICATION SIGN IN LEFT HALF CIRCLEB MULTIPLICATION SIGN IN RIGHT HALF CIRCLEB CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENTB MULTIPLICATION SIGN IN DOUBLE CIRCLEB CIRCLED DIVISION SIGNB PLUS IN TRIANGLEB MINUS IN TRIANGLE
B MULTIPLICATION SIGN IN TRIANGLEB INTERIOR PRODUCTB RIGHTHAND INTERIOR PRODUCT→ 2319 turned not signB Z NOTATION RELATIONAL COMPOSITION→ CX37 Z notation schema composition[removed: 2040]
B AMALGAMATION OR COPRODUCT→ 2210 n-ary coproduct
B INTERSECTION WITH DOTB UNION WITH MINUS= Z NOTATION BAG SUBTRACTION
B UNION WITH OVERBARB INTERSECTION WITH OVERBARB INTERSECTION WITH LOGICAL AND
B UNION WITH LOGICAL OR
B UNION ABOVE INTERSECTIONB INTERSECTION ABOVE UNIONB UNION ABOVE BAR ABOVE INTERSECTIONB INTERSECTION ABOVE BAR ABOVE UNIONB UNION BESIDE AND JOINED WITH UNION

8

Math Symbols

2000-03-14

CX68
B INTERSECTION BESIDE AND JOINED WITH INTERSECTION
CX6B
B CLOSED UNION WITH SERIFS
CX6C
B CLOSED INTERSECTION WITH SERIFSCX6D
B DOUBLE SQUARE INTERSECTION
CX6E
B DOUBLE SQUARE UNION
CX71
B CLOSED UNION WITH SERIFS AND SMASH PRODUCTCX72B LOGICAL AND WITH DOT ABOVE
CX73
B LOGICAL OR WITH DOT ABOVE
CX74
B DOUBLE LOGICAL AND
CX75
B DOUBLE LOGICAL OR
CX76 * B TWO INTERSECTING LOGICAL AND→ CX1F two logical and operator
CX77 * B TWO INTERSECTING LOGICAL OR→ CX20 two logical or operator
CX78
B SLOPING LARGE OR
CX79
B SLOPING LARGE AND
CX7A
R LOGICAL OR OVERLAPPING LOGICAL AND
CX7B
B LOGICAL AND WITH MIDDLE STEMCX7C
B LOGICAL OR WITH MIDDLE STEMCX7D
B LOGICAL AND WITH HORIZONTAL DASH
CX7E
B LOGICAL OR WITH HORIZONTAL DASH
CX7F
B LOGICAL AND WITH DOUBLE OVERBAR→ 2306 perspective
CX80
B LOGICAL AND WITH UNDERBAR
CX81
B LOGICAL AND WITH DOUBLE UNDERBAR→ 2259 estimates
CX82
B SMALL VEE WITH UNDERBAR
CX83
B LOGICAL OR WITH DOUBLE OVERBARCX84
B LOGICAL OR WITH DOUBLE UNDERBAR→ 225A equiangular to
CX85
B Z NOTATION DOMAIN ANTIRESTRICTIONCX86
B Z NOTATION RANGE ANTIRESTRICTION
CX87
R EQUAL SIGN WITH DOT BELOW
CX8B
R IDENTICAL WITH DOT ABOVECX8D
R TRIPLE HORIZONTAL BAR WITH DOUBLE VERTICAL STROKE= identical and parallel to
CX8E
R TRIPLE HORIZONTAL BAR WITH TRIPLE VERTICAL STROKECX92
R TILDE OPERATOR WITH DOT
CX94
R TILDE OPERATOR WITH RISING DOTS
→ 223B homothetic
CX97
R SIMILAR MINUS SIMILAR
CX9E
R CONGRUENT WITH OVERDOTCXA0R REVERSED CONGRUENTCXA1R DOUBLE TILDE OPERATOR WITH CIRCUMFLEX ACCENTCXA2R APPROXIMATELY EQUAL OR EQUAL TOCXA6B EQUAL ABOVE PLUS
CXA7
B PLUS ABOVE EQUALCXA8R EQUAL ABOVE TILDE OPERATORCXA9R DOUBLE COLON EQUALCXAAR TWO CONSECUTIVE EQUAL SIGNSCXABR THREE CONSECUTIVE EQUAL SIGNSCXACR EQUAL SIGN WITH TWO DOTS ABOVE AND TWO DOTS BELOWCXADR EQUIVALENT WITH FOUR DOTS ABOVECXAER LESS-THAN WITH CIRCLE INSIDE

9Math Symbols

CXAF
CXB0
CXB1
CXB2
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

2000-03-14

R GREATER-THAN WITH CIRCLE INSIDER LESS-THAN WITH QUESTION MARK ABOVER GREATER-THAN WITH QUESTION MARK ABOVER LESS-THAN OR SLANTED EQUAL TO
R GREATER-THAN OR SLANTED EQUAL TO
R LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDER GREATER-THAN OR SLANTED EQUAL TO WITH DOT INSIDER LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVER GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVER LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHTR GREATER-THAN OR SLANTED EQUAL TO WITH DOT ABOVE LEFTR LESS-THAN OR APPROXIMATER GREATER-THAN OR APPROXIMATER LESS-THAN AND NOT ONE-LINE EQUAL TO
R GREATER-THAN AND NOT ONE-LINE EQUAL TO
R LESS-THAN AND NOT APPROXIMATER GREATER-THAN AND NOT APPROXIMATER LESS-THAN ABOVE TWO-LINE EQUAL ABOVE GREATER-THAN
R GREATER-THAN ABOVE TWO-LINE EQUAL ABOVE LESS-THAN
R LESS-THAN ABOVE SIMILAR OR EQUALR GREATER-THAN ABOVE SIMILAR OR EQUALR LESS-THAN ABOVE SIMILAR ABOVE GREATER-THAN
R GREATER-THAN ABOVE SIMILAR ABOVE LESS-THAN
R LESS-THAN ABOVE GREATER-THAN ABOVE TWO-LINE EQUALR GREATER-THAN ABOVE LESS-THAN ABOVE TWO-LINE EQUALR LESS-THAN ABOVE SLANTED EQUAL ABOVE GREATER-THAN ABOVE SLANTED EQUALR GREATER-THAN ABOVE SLANTED EQUAL ABOVE LESS-THAN ABOVE SLANTED EQUALR SLANTED EQUAL TO OR LESS-THAN
R SLANTED EQUAL TO OR GREATER-THAN
R SLANTED EQUAL TO OR LESS-THAN WITH DOT INSIDER SLANTED EQUAL TO OR GREATER-THAN WITH DOT INSIDER TWO-LINE EQUAL TO OR LESS-THAN
R TWO-LINE EQUAL TO OR GREATER-THAN
R TWO-LINE SLANTED EQUAL TO OR LESS-THAN
R TWO-LINE SLANTED EQUAL TO OR GREATER-THAN
R SIMILAR OR LESS-THAN
R SIMILAR OR GREATER-THAN
R SIMILAR ABOVE LESS-THAN ABOVE EQUALR SIMILAR ABOVE GREATER-THAN ABOVE EQUALR DOUBLE NESTED LESS-THAN SIGN
= absolute continuity
R DOUBLE NESTED GREATER-THAN SIGNR DOUBLE LESS-THAN WITH UNDERBAR

10

Math Symbols

2000-03-14

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 asize-graded sequence with the present Unicode squares 25A0, 25A1, 25AA and 25AB. Ideally, thelargest should be just a bit larger than 25A0 (but not as large as 2588), and the smallest, justa 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 aparticular notion. (Several different geometric shapes are used in this manner, the most common
being squares and circles.)11Math Symbols

2000-03-14

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
DX4F

R GREATER-THAN OVERLAPPING LESS-THAN
R GREATER-THAN BESIDE LESS-THAN
R LESS-THAN CLOSED BY CURVER GREATER-THAN CLOSED BY CURVER LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUALR GREATER-THAN CLOSED BY CURVE ABOVE SLANTED EQUALR SMALLER THAN
R LARGER THAN
R SMALLER THAN OR EQUALR LARGER THAN OR EQUAL
R BUMPY ABOVE TWO-LINE EQUAL
R PRECEDES ABOVE ONE-LINE EQUAL
R SUCCEEDS ABOVE ONE-LINE EQUAL
R PRECEDES ABOVE NOT ONE-LINE EQUAL
R SUCCEEDS ABOVE NOT ONE-LINE EQUAL
R PRECEDES ABOVE TWO-LINE EQUAL
R SUCCEEDS ABOVE TWO-LINE EQUAL
R PRECEDES ABOVE NOT TWO-LINE EQUAL
R SUCCEEDS ABOVE NOT TWO-LINE EQUAL
R PRECEDES ABOVE DOUBLE TILDE OPERATORR SUCCEEDS ABOVE DOUBLE TILDE OPERATOR
R PRECEDES ABOVE NOT DOUBLE TILDE OPERATORR SUCCEEDS ABOVE NOT DOUBLE TILDE OPERATOR
R DOUBLE PRECEDESR DOUBLE SUCCEEDSR SUBSET WITH DOTR SUPERSET WITH DOTR SUBSET WITH PLUS BELOWR SUPERSET WITH PLUS BELOWR SUBSET WITH MULTIPLICATION SIGN BELOWR SUPERSET WITH MULTIPLICATION SIGN BELOWR SUBSET OF OR EQUAL TO WITH DOT ABOVER SUPERSET OF OR EQUAL TO WITH DOT ABOVER SUBSET OF OR TWO-LINE EQUALR SUPERSET OF OR TWO-LINE EQUALR SUBSET OF ABOVE TILDE OPERATORR SUPERSET OF ABOVE TILDE OPERATORR SUBSET OF ABOVE DOUBLE TILDE OPERATORR SUPERSET OF ABOVE DOUBLE TILDE OPERATORR SUBSET OF OR NOT TWO-LINE EQUALR SUPERSET OF OR NOT TWO-LINE EQUALR SQUARE LEFT OPEN BOX OPERATORR SQUARE RIGHT OPEN BOX OPERATORR CLOSED SUBSETR CLOSED SUPERSETR CLOSED SUBSET OR EQUAL
R CLOSED SUPERSET OR EQUALR SUBSET ABOVE SUPERSETR SUPERSET ABOVE SUBSETR SUBSET ABOVE SUBSETR SUPERSET ABOVE SUPERSETR SUPERSET BESIDE SUBSET

12

Math Symbols

DX50
DX51
DX52
DX53
DX54
DX55
DX56
DX57
DX58
DX59
DX5A
DX5B
DX5C
DX5D
DX5E
DX61

DX62

DX63
DX64
DX65
DX66
DX67
DX68
DX69
DX6A
DX6B
DX6C
DX6D
DX6E
DX6F
DX70
DX71
DX72
DX73
DX74
DX75
DX76
DX77
DX78
DX79

2000-03-14

R SUPERSET BESIDE AND JOINED BY DASH WITH SUBSETR ELEMENT OF OPENING DOWNWARDSR PITCHFORK WITH TEE TOP
R TRANSVERSAL INTERSECTION→ 22D4 proper intersection
R FORKING. symbol is slashed although positive
R NONFORKING. negative symbol - has no slash
R SHORT LEFT TACKR SHORT DOWN TACKR SHORT UP TACKR PERPENDICULAR WITH S
R VERTICAL BAR TRIPLE RIGHT TURNSTILE= ordinarily satisfies
R DOUBLE VERTICAL BAR LEFT TURNSTILE
R VERTICAL BAR DOUBLE LEFT TURNSTILE
R DOUBLE VERTICAL BAR DOUBLE LEFT TURNSTILE
R LONG DASH FROM LEFT MEMBER OF DOUBLE VERTICAL→ 22A9 forces
R SHORT DOWN TACK WITH OVERBAR→ 22A4 down tack→ 2351 apl functional symbol up tack overbar
R SHORT UP TACK WITH UNDERBAR→ 22A5 up tack→ 234A apl functional symbol down tack underbar
R SHORT UP TACK ABOVE SHORT DOWN TACKR DOUBLE DOWN TACKR DOUBLE UP TACK= independence (probability theory)
R NOT WITH TWO HORIZONTAL STROKESR REVERSED NOT WITH TWO HORIZONTAL STROKESF TRIPLE VERTICAL BAR DELIMITER→ DX8B triple vertical bar binary relationF Z NOTATION SPOT
. medium-sized filled circle
F Z NOTATION TYPE COLONO LEFT WHITE BRACEC RIGHT WHITE BRACEO LEFT WHITE ANGULAR BRACKET→ 3108 left white tortoise shell bracket
C RIGHT WHITE ANGULAR BRACKET→ 3109 right white tortoise shell bracket
O Z NOTATION LEFT IMAGE BRACKETC Z NOTATION RIGHT IMAGE BRACKETO Z NOTATION LEFT BINDING BRACKETC Z NOTATION RIGHT BINDING BRACKETO LEFT BRACKET UNDERBARC RIGHT BRACKET UNDERBARO LEFT BRACKET WITH REVERSE SOLIDUS TOP CORNERC RIGHT BRACKET WITH REVERSE SOLIDUS BOTTOM CORNERO LEFT BRACKET WITH SOLIDUS BOTTOM CORNERC RIGHT BRACKET WITH SOLIDUS TOP CORNERO LEFT ANGLE BRACKET WITH DOT

13Math Symbols

DX7A
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

2000-03-14

C RIGHT ANGLE BRACKET WITH DOTO LEFT ARC LESS-THAN BRACKETC RIGHT ARC GREATER-THAN BRACKETDOUBLE LEFT ARC GREATER-THAN BRACKETDOUBLE RIGHT ARC LESS-THAN BRACKET
RIGHT MOUSTACHE
LEFT MOUSTACHE[removed: AX25][removed: AX26]
R DOES NOT DIVIDE WITH REVERSED NEGATION SLASHR CIRCLE WITH VERTICAL LINE BELOW
R VERTICAL LINE WITH CIRCLE BELOWN TOP WITH CIRCLE BELOW
B PARALLEL WITH HORIZONTAL STROKER 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 LEFTRIGHT ANGLE VARIANT WITH SQUAREMEASURED RIGHT ANGLE WITH DOTANGLE WITH S INSIDEACUTE ANGLESPHERICAL ANGLE OPENING LEFTSPHERICAL ANGLE OPENING UP
TURNED ANGLE
REVERSED ANGLE
ANGLE WITH UNDERBAR
REVERSED ANGLE WITH UNDERBAR[removed]
LARGE DOWNWARDS POINTING ANGLELARGE UPWARDS POINTING ANGLE
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE RIGHTMEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING UP AND TO THE LEFT
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE RIGHTMEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING DOWN AND TO THE LEFT
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND UP
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND UP
MEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING RIGHT AND DOWNMEASURED ANGLE WITH OPEN ARM ENDING IN ARROW POINTING LEFT AND DOWN
[removed: 2205]
N REVERSED EMPTY SET→ 2349 APL functional symbol circle backslash
N EMPTY SET OVERBAR

14

Math Symbols

DXAB
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

2000-03-14

N EMPTY SET WITH SMALL CIRCLE ABOVEN EMPTY SET RIGHT ARROW ABOVEN EMPTY SET LEFT ARROW ABOVECIRCLE WITH HORIZONTAL BAR
B CIRCLED VERTICAL BAR
B CIRCLED PARALLELB CIRCLED FALLING DIAGONALB CIRCLED PERPENDICULARCIRCLE DIVIDED BY HORIZONTAL BAR AND TOP HALF DIVIDED BY VERTICAL
CIRCLE WITH SUPERIMPOSED X
CIRCLED ANTICLOCKWISE-ROTATED DIVISION SIGNUP ARROW THROUGH CIRCLECIRCLED LARGE CIRCLE→ 233E APL functional symbol circle jot
CIRCLED FILLED CIRCLECIRCLED LESS-THAN
CIRCLED GREATER-THAN
CIRCLE WITH SMALL CIRCLE TO THE RIGHTCIRCLE WITH TWO HORIZONTAL STROKES TO THE RIGHTSQUARED RISING DIAGONAL SLASH→ 2341 APL functional symbol quad slash
SQUARED FALLING DIAGONAL SLASH→ 2342 APL functional symbol quad backslash
SQUARED ASTERISKSQUARED SMALL CIRCLE→ 233B APL functional symbol quad circle
B SQUARED SQUARETWO JOINED SQUARESTRIANGLE WITH DOT OVERTRIANGLE WITH UNDERBARS 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 BOWTIER RIGHT FILLED BOWTIER FILLED BOWTIER LEFT FILLED TIMES→ 22C9 left normal factor semidirect product
R RIGHT FILLED TIMES→ 22CA right normal factor semidirect product
WHITE HOURGLASS. vertical bowtie
FILLED HOURGLASSMOST POSITIVECONGRUENCE 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 OMITTEDN TIE OVER INFINITYN INFINITY NEGATED WITH VERTICAL BAR
R DOUBLE-ENDED MULTIMAP

15

Math Symbols

DXDF
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

2000-03-14

N SQUARE WITH CONTOURED OUTLINE= D’AlembertianR INCREASES AS
SHUFFLE PRODUCTR SLANTED PARALLEL SUPERIMPOSED ON EQUAL= homothetically congruent to
R TILDE ABOVE SLANTED PARALLEL SUPERIMPOSED ON EQUALR SLANTED PARALLEL SUPERIMPOSED ON THREE-LINE EQUAL= congruent and parallel
R TOP ARC ABOVE BOTTOM ARC
N THERMODYNAMIC. vertical bar crossed by two horizontals
N DOWN-POINTING TRIANGLE WITH LEFT HALF BLACKN DOWN-POINTING TRIANGLE WITH RIGHT HALF BLACKUPPER LEFT TRIANGLEUPPER RIGHT TRIANGLE
LOWER LEFT TRIANGLE
N WHITE MEDIUM SQUAREN BLACK MEDIUM SQUARE[removed][removed]
N WHITE VERY SMALL SQUAREN BLACK VERY SMALL SQUAREN WHITE DIAMOND WITH CENTERED DOT
N FILLED DIAMOND WITH DOWN ARROWFILLED LOZENGE[removed][removed: 2736]
N CIRCLE WITH DOWN ARROWN FILLED CIRCLE WITH DOWN ARROWN ERROR-BARRED WHITE SQUAREN ERROR-BARRED FILLED SQUAREN ERROR-BARRED WHITE DIAMONDN ERROR-BARRED FILLED DIAMONDN ERROR-BARRED WHITE CIRCLEN ERROR-BARRED FILLED CIRCLE

16

Symbol variants defined using a Variation Selector (VS)• 2268  + VS →less-than and not double equal - with vertical stroke• 2269+ VS →  greater-than and not double equal - with vertical stroke• 22DA Q + VS → _ less-than above slanted equal above greater-than• 22DB R + VS → ` greater-than above slanted equal above less-than• 2272 . + VS → ⱳ less-than or similar - following the slant of the lower leg• 2273 & + VS → ⱜ greater-than or similar - following the slant of the lower leg• 2A9D Ȿ + VS → ⱽ similar - following the slant of the upper leg - or less-than• 2A9E Ɀ + VS → ⱚ similar - following the slant of the upper leg - or greater-than• 2AAC o + VS → q smaller than or slanted equal• 2AAD p + VS → r larger than or slanted equal• 228A ( + VS →subset not equals - variant with stroke through bottom members• 228B ) + VS → ! superset not equals - variant with stroke through bottom members• 2ACB $ + VS → & subset not two-line equals - variant with stroke through bottom
members• 2ACC % + VS → ' superset not two-line equals - variant with stroke through bottom
members• 2A3B ´ + VS → ² interior product - tall variant with narrow foot• 2A3C µ + VS → ³ righthand interior product - tall variant with narrow footL
• 2295+ VS → 䊝 circled plus with white rim
N• 2297+ VS → 䊟 circled times with white rim• 229C 䊠 + VS →equal sign inside and touching a circle• 2225 k + VS → // slanted parallel•// + VS + 20E5 \ → /\/ slanted parallel with reverse slash** • 222A ∪** • 2229 ∩** • 2293 u** • 2294 t+ VS → ∪+ VS → ∩+ VS → u+ VS → tunion with serifs
intersection with serifs
square intersection with serifs
square union with serifs

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.

1

P.O. Box 6248, Providence, RI 02940-6248 USA
201 Charles Street, Providence, RI 02904-2294
Phone: 401-455-4000, Fax: 401-331-3842
www.ams.org
John Ewing, Executive Director
Phone: 401-455-4100, Email: jhe@ams.org

March 15, 2000

Mr. Mike Ksar
1501 Page Mill Road
MS: 5UL
Palo Alto, CA 94304
Dear Mr. Ksar:
The mathematically-oriented scientific community uses various styles of letters and symbols toconcisely represent functions, variables, operations and other mathematical objects that comprisethe language of mathematics. This presents an especially subtle problem because two different
styles of the same letter or symbol can have completely different meanings. Thus it is very
important to the community that there is a universally accepted standard encoding for the various
styles of letters and symbols it uses in its publications. If multiple versions of these were being
used in the literature, rather than a universally accepted version, it would significantly complicate
the communication between researchers, especially in the Web environment.
It is for this reason that the American Mathematical Society has devoted significant resources togathering the documentation for alpha/numeric and mathematical symbols and submitting it to theUnicode Technical Committee for its acceptance. Now that this has been accomplished we hopevery much that they will be accepted by WG2.
Sincerely yours,

John Ewing