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   <body>
      
      <h1><a name="chars" id="chars"></a>6 Characters, Entities and Fonts
      </h1>
      <!-- TOP NAVIGATION BAR -->
      <div class="minitoc">
         
           Overview: <a href="overview-d.html">Mathematical Markup Language (MathML) Version 2.0 (Second Edition)</a><br>
           Previous: 5 <a href="chapter5-d.html">Combining Presentation and Content Markup</a><br>
           Next: 7 <a href="chapter7-d.html">The MathML Interface</a><br><br>6 <a href="chapter6-d.html">Characters, Entities and Fonts</a><br>&nbsp;&nbsp;&nbsp;&nbsp;6.1 <a href="chapter6-d.html#chars.intro">Introduction</a><br>&nbsp;&nbsp;&nbsp;&nbsp;6.2 <a href="chapter6-d.html#chars.mathmlchars">MathML Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.2.1 <a href="chapter6-d.html#chars.unicodechars">Unicode Character Data</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.2.2 <a href="chapter6-d.html#chars.mglyph">Special Characters Not in Unicode</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.2.3 <a href="chapter6-d.html#chars.BMP-SMP">Mathematical Alphanumeric Symbols
            Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.2.4 <a href="chapter6-d.html#chars.nonmark">Non-Marking Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;6.3 <a href="chapter6-d.html#id.6.3">Character Symbol Listings</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.1 <a href="chapter6-d.html#chars.special">Special Constants</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.2 <a href="chapter6-d.html#chars.byxxx">Character Tables (ASCII format)</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.3 <a href="chapter6-d.html#chars.16x16-tables">Tables arranged by Unicode block</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.4 <a href="chapter6-d.html#chars.math-negated-tables">Negated
            Mathematical Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.5 <a href="chapter6-d.html#chars.math-variant-tables">Variant
            Mathematical Characters</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.6 <a href="chapter6-d.html#chars.letter-like-tables">Mathematical Alphanumeric Symbols</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.7 <a href="chapter6-d.html#chars.entity.tables">MathML Character Names</a><br>&nbsp;&nbsp;&nbsp;&nbsp;6.4 <a href="chapter6-d.html#id.6.4">Differences from Characters in MathML 1</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.4.1 <a href="chapter6-d.html#id.6.4.1">Coverage</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.4.2 <a href="chapter6-d.html#id.6.4.2">Fewer Non-marking Characters </a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.4.3 <a href="chapter6-d.html#id.6.4.3">ISO Tables</a><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.4.4 <a href="chapter6-d.html#chars.char-status">Status of Character Encodings</a><br></div>
      <div class="div1">
         <div class="div2">
            
            <h2><a name="chars.intro" id="chars.intro"></a>6.1 Introduction
            </h2>
            <p>
               Notation and symbols have proved very important for
               mathematics. Mathematics has grown in part because <span class="diff-del"> of the
                  succinctness and suggestiveness of its evolving notation<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
               <span class="diff-add">its notation continually changes toward being succinct and 
                  suggestive<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>. There
               have been many new signs <span class="diff-chg">developed<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> for use in mathematical
               notation, and mathematicians have not held back from making use
               of many symbols originally <span class="diff-chg">introduced<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> elsewhere. The result is
               that mathematics makes use of a very large collection of
               symbols.  It is difficult to write mathematics fluently if these
               characters are not available for use<span class="diff-del"> in coding<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>. It is difficult
               to read mathematics if corresponding glyphs are not available
               for presentation on specific display devices.
               
            </p>
            <div class="diff-del">
               <p>
                  This situation posed a problem for the first W3C Math Working Group
                  when it was brought into existence.  It did not fall naturally within
                  the purview of developing a specification enabling mathematics to be
                  used with HTML and producing a DTD for <span class="diff-chg">the Working
                     Group<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> to worry about more than
                  the entities allowed in the DTD. However, as experience has shown, a
                  long list of entities with no means to display them is of little use,
                  and a cause of frequent frustrations in trying to use a standard. On
                  the other hand, a large collection of glyphs and fonts representing
                  characters without a standard way to refer to them is not of much use
                  either.
                  
               </p><a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></div>
            <p>
               The W3C Math Working Group therefore took on directly the task of
               specifying part of the full mechanism needed to proceed from
               notation to final presentation, and started collaboration with
               organizations undertaking specification of the rest.
               
            </p>
            <p>
               This chapter of the MathML specification contains a listing of character names for
               use <span class="diff-chg">with<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> MathML, recommendations for their use, and
               warnings to pay attention to the correct form of the corresponding code points
               given in the UCS (Universal Character Set) as codified in Unicode and ISO 10646
               [see <a href="appendixk-d.html#Unicode">[Unicode]</a> and the <a href="http://www.unicode.org/">Unicode
                  Web site</a>].  For simplicity we shall refer to this character set by the short
               name Unicode.  Though Unicode changes from time to time so that it is specified
               exactly by using version numbers, unless this brings clarity on some point we
               shall not use them.  <span class="diff-chg">The specification of MathML 2.0
                  <span class="diff-add"><a href="appendixk-d.html#MathML2">[MathML2]</a><a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> used to make use of some characters that were
                  not part of Unicode 3.0 but which had been proposed to the Unicode Technical
                  Committee (UTC), and thus for inclusion in ISO 10646.  They have been included in
                  the revisions Unicode 3.1 and 3.2.  As of the publication of the MathML 2.0 (Second Edition) the current version is Unicode
                  4.0.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> (For more detail about this see
               <a href="chapter6-d.html#chars.char-status">Section&nbsp;6.4.4 Status of Character Encodings</a>.)
            </p>
            <p>
               <span class="diff-chg">
                  While a long process of review and adoption by UTC and ISO/IEC of the
                  characters of special interest to mathematics and MathML is now<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
               complete <span class="diff-del">(<a href="http://www.unicode.org/unicode/alloc/Pipeline.html">Unicode Work
                     in Progress</a>)<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> there remains the possibility of some further
               modification of the lists of characters accepted<span class="diff-del">, of the code
                  assignments for those adopted, or of the names given them by Unicode<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
               To make sure any possible corrections to relevant standards are taken
               into account, and for the latest character tables and font information,
               see the <a href="http://www.w3.org/Math/">W3C Math Working Group
                  home page</a> and the <a href="http://www.unicode.org/">Unicode
                  site</a> <span class="diff-add">(see, for instance, <a href="http://www.unicode.org/unicode/alloc/Pipeline.html">Unicode Work
                     in Progress</a>)<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
               
            </p>
         </div>
         <div class="div2">
            
            <h2><a name="chars.mathmlchars" id="chars.mathmlchars"></a>6.2 MathML Characters
            </h2>
            <p>
               A MathML token element <a href="chapter3-d.html#presm.tokel">Section&nbsp;3.2 Token Elements</a>, and <a href="chapter4-d.html#contm.tokenel">Section&nbsp;4.4.1 Token Elements</a> takes as content a sequence of <em>MathML
                  Characters</em>.  MathML Characters are defined to be either
               Unicode characters legal in XML documents or <code>mglyph</code> elements. 
               The latter are used to represent
               characters that do not have a Unicode encoding, as described in
               <a href="chapter3-d.html#presm.mglyph">Section&nbsp;3.2.9 Accessing glyphs for
                  characters from MathML 
                    (mglyph)</a>. 
               <span class="diff-chg"> Because the Unicode UCS provided
                  approximately one thousand special alphabetic characters for the use
                  of mathematics with Unicode 3.1, and  over 900 further
                  special symbols in Unicode 3.2, the need for 
                  <code>mglyph</code> should be rare. <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
               
            </p>
            <div class="div3">
               
               <h3><a name="chars.unicodechars" id="chars.unicodechars"></a>6.2.1 Unicode Character Data
               </h3>
               <p>
                  As always in XML, any character allowed by XML may be used in MathML
                  in an XML document.  The legal characters have the hexadecimal code
                  numbers 09 (tab = U+0009), 0A (line feed = U+000A), 0D (carriage
                  return = U+000D), 20-D7FF (U+0020..U+D7FF), E000-FFFD
                  (U+E000..U+FFFD), and 10000-10FFFF (U+010000..U+10FFFF). The
                  <span class="diff-chg">notation, just introduced in parentheses,<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> 
                  beginning with U+ is <span class="diff-chg">that<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> recommended by Unicode
                  for referring to Unicode characters [see <a href="appendixk-d.html#Unicode">[Unicode]</a>, page
                  xxviii]. The exclusions above code number D7FF are of the blocks used
                  in surrogate pairs, and the two characters guaranteed not to be
                  Unicode characters at all.  U+FFFE is excluded to allow determination
                  of byte order in certain encodings.
                  
               </p>
               <p>
                  There are essentially three different ways of encoding character data.
                  
                  
               </p>
               <ul>
                  <li>
                     <p>
                          Using characters directly: For example, an A may be entered as 'A'
                          from a keyboard (character <span class="diff-chg">U+0041<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>).  This option is only available
                          if the character encoding specified for the XML document includes
                          the character.  Most commonly used encodings will have 'A' in the
                          ASCII position.  In many encodings, characters may need more than
                          one byte.  Note that if the document is, for example, encoded in
                          Latin-1 (ISO-8859-1) then <em>only</em> the characters in that
                          encoding are available directly.  <span class="diff-del">Unfortunately, most mathematical
                             symbols may not be encoded as character data in this way.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                        <span class="diff-add">Using UTF-8 or UTF-16, the only two encodings that 
                           all XML processors are required to accept, mathematical symbols can 
                           be encoded as character data.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                          
                     </p>
                  </li>
                  <li>
                     <p>
                        Using numeric XML character references: Using this notation, 'A' may be
                        represented as &amp;<span class="diff-chg">#65;<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> (decimal) or  &amp;#x41; (hex).
                        Note that the numbers always refer to the Unicode encoding (and not to
                        the character encoding used in the XML file). By using <span class="diff-chg">character<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                        references it is always possible to access the entire Unicode range.
                        For a general XML vocabulary, there is a disadvantage to this approach:
                        character references may not be used in XML element or attribute
                        names.  However, this is not an issue for MathML, as all element names in
                        MathML are restricted to ASCII characters.
                        
                     </p>
                  </li>
                  <li>
                     <p>
                        Using entity references: The MathML DTD defines internal entities that
                        expand to character data. Thus for example the entity reference
                        &amp;eacute; may be used rather than the character reference
                        "&amp;#xE9; or, if, for example, the document is encoded in
                        ISO-8859-1, the character &eacute;. An XML fragment that uses an entity
                        reference which is not defined in a DTD is not well-formed; therefore
                        it will be rejected by an XML parser. For this reason
                        <em>every</em> fragment using entity references <em>must</em>
                        use a DOCTYPE declaration which specifies the MathML DTD, or a DTD
                        that at least declares any entity reference used in the MathML
                        instance.  The need to use a DOCTYPE complicates inclusion of MathML in
                        some documents. However, entity references are very useful for small
                        illustrative examples, and are used in most examples in this document.
                        
                     </p>
                     <div class="diff-del">
                        <p>
                           For this reason entity references are perhaps not optimal for use in
                           generated MathML, however they are very useful for small illustrative
                           examples, as used in this document.
                           
                        </p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
                  </li>
               </ul>
            </div>
            <div class="div3">
               
               <h3><a name="chars.mglyph" id="chars.mglyph"></a>6.2.2 Special Characters Not in Unicode
               </h3>
               <p>
                  For special purposes, one may need to use a character which is not in
                  Unicode<span class="diff-del">, even with the expected additions<a href="appendixj-d.html#d0e55670"><sub class="diff-link">J</sub></a></span>. 
                  In these cases
                  one may use the <a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
                  element for direct access to a glyph from some font and creation of
                  a MathML <span class="diff-chg">substitute for the corresponding character<a href="appendixj-d.html#d0e55670"><sub class="diff-link">J</sub></a></span>.
                  All MathML token elements that accept character data also accept an
                  <code>mglyph</code> in their content.
                  
               </p>
               <p>
                  Beware, however, that the font chosen may not be available to all
                  MathML processors.
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="chars.BMP-SMP" id="chars.BMP-SMP"></a>6.2.3 Mathematical Alphanumeric Symbols
                  Characters
               </h3>
               <p>
                  A noticeable feature of mathematical and scientific writing is the use
                  of single letters to denote variables and constants in a given
                  context.  The increasing complexity of science has led to the use of
                  certain common alphabet and font variations to provide enough special
                  symbols of this letter-like type.  These denotations are in fact
                  <em>not</em> letters that may be used to make up words with
                  recognized meanings, but individual carriers of semantics themselves.
                  Writing a string of such symbols is usually interpreted in terms of
                  some composition law, for instance, multiplication.  Many letter-like
                  symbols may be quickly interpreted by specialists in a given area as
                  of a certain mathematical type: for instance, bold symbols, whether
                  based on Latin or Greek letters, as vectors in physics or engineering,
                  or fraktur symbols as Lie algebras in part of pure mathematics.  Again,
                  in given areas of science, some constants are recognizable letter
                  forms.  When you look carefully at the range of letter-like
                  mathematical symbols in common use today, as the STIX project
                  supported by major scientific and technical publishers did, you come
                  up with perhaps surprisingly many.  A proposal to facilitate
                  mathematical publishing by inclusion of mathematical alphabetic
                  symbols in the UCS was made, and has been favorably handled.
                  
               </p>
               <p>
                  The <span class="diff-chg">additional<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> Mathematical Alphanumeric Symbols 
                  <span class="diff-chg">provided<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> in Unicode 3.1 have
                  <span class="diff-del">provisional <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>code points in <em>Plane 1</em>, that is, in the first
                  plane with Unicode values higher than 2<sup>16</sup>.  This plane of
                  characters is also known as the Secondary Multilingual Plane (SMP),
                  in contrast to the Basic Multilingual Plane (BMP) which <span class="diff-chg">
                     was originally the entire extent of Unicode<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.  Support for Plane 1 characters in currently
                  deployed software is not always reliable, and in particular support
                  for these Mathematical Alphanumeric Symbol characters is not likely to be
                  widespread until after <span class="diff-chg">public fonts covering the characters
                     adopted for mathematics are available<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
                  
               </p>
               <p>
                  As discussed in <a href="chapter3-d.html#presm.commatt">Section&nbsp;3.2.2 Mathematics style attributes common to token
                     elements</a>, MathML offers an
                  alternative mechanism to specify mathematical alphabetic 
                  characters<span class="diff-chg">.  This alternative spans the gap between the
                     specification of Unicode 3.1 and its associated deployment in software and
                     fonts.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                  Namely, one uses the <code>mathvariant</code>
                  attribute on the surrounding token element, which will most commonly
                  be <code>mi</code>.  In this section we detail the
                  correspondence that a MathML processor should apply between certain
                  characters in <em>Plane 0</em> (BMP) of Unicode, modified by the
                  <code>mathvariant</code> attribute, and the Plane 1
                  Mathematical Alphanumeric Symbol characters.
                  
               </p>
               <p>The basic idea of the correspondence is fairly simple.
                  For example, a Mathematical Fraktur alphabet is <span class="diff-chg">
                     in Plane 1<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>, and
                  the code point for Mathematical Fraktur A is 
                  <span class="diff-chg">U+1D504<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
                  Thus using these <span class="diff-del">proposed<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> characters, a typical example might be
                  
               </p><pre>
&lt;mi&gt;&amp;#x1D504;&lt;/mi&gt;
</pre><p>
                  However, an alternative, equivalent markup would be to use
                  the standard A and modify the identifier using the
                  <code>mathvariant</code> attribute, as follows:
                  
               </p><pre>
&lt;mi mathvariant="fraktur"&gt;A&lt;/mi&gt;
</pre><p>
                  The exact correspondence between a mathematical alphabetic character
                  and an unstyled character is complicated by the fact that certain
                  characters that were already present in Unicode are not in the
                  'expected' sequence.
                  
               </p>
               <p>
                  The detailed correspondence is shown in the tables given in
                  <a href="chapter6-d.html#chars.letter-like-tables">Section&nbsp;6.3.6 Mathematical Alphanumeric Symbols</a>.
                  
               </p>
               <p>
                  Mathematical Alphanumeric Symbol characters should not be used for styled text.
                  For example, Mathematical Fraktur A must not be used to just select
                  a blackletter font for an uppercase A. Doing this sort of thing
                  would create problems for searching, restyling (e.g. for accessibility), 
                  and many other kinds of processing.
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="chars.nonmark" id="chars.nonmark"></a>6.2.4 Non-Marking Characters
               </h3>
               <p>
                  Some characters, although important for the quality of print or
                  alternative rendering, do not have glyph marks that correspond
                  directly <span class="diff-add">to them<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>.  They are called here non-marking characters.<span class="diff-del">Below we have
                     a table of those adopted for the purposes of MathML.<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>
                  Their roles are
                  discussed in <a href="chapter3-d.html">Chapter&nbsp;3 Presentation Markup</a> and <a href="chapter4-d.html">Chapter&nbsp;4 Content Markup</a><span class="diff-del">,
                     respectively.  The values of the spaces given are
                     recommendations. Some of these characters are among those with new
                     Unicode values, and some are given as combinations of Unicode
                     characters employing the new special mathematics modifier character
                     (U0FE00). The correspondence between the spacing amounts mentioned
                     below and those in the Unicode descriptions is not exact, but the
                     matches are good<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>.
               </p>
               <p>In MathML 2 control of page composition, such as line-breaking, is
                  effected by the use of the proper attributes on the <code>mspace</code> element.
               </p>
               <div class="diff-chg">
                  <p>The characters below are not simple spacers.  They are
                     especially important new additions to the UCS because they provide
                     textual clues which can increase the quality of print rendering,
                     permit correct audio rendering, and allow the unique recovery of
                     mathematical semantics from text which is visually ambiguous.
                  </p><a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></div>
               <table id="chars.table-white">
                  <thead>
                     <tr>
                        <th rowspan="1" colspan="1">Character name</th>
                        <th rowspan="1" colspan="1">Unicode</th>
                        <th rowspan="1" colspan="1">Description</th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;Tab;</code></td>
                        <td rowspan="1" colspan="1">00009</td>
                        <td rowspan="1" colspan="1">tabulator stop; horizontal tabulation</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NewLine;</code></td>
                        <td rowspan="1" colspan="1">0000A</td>
                        <td rowspan="1" colspan="1">force a line break; line feed</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;Space;</code></td>
                        <td rowspan="1" colspan="1">00020</td>
                        <td rowspan="1" colspan="1">one em of space in the current font</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NonBreakingSpace;</code></td>
                        <td rowspan="1" colspan="1">000A0</td>
                        <td rowspan="1" colspan="1">space that is not a legal breakpoint</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;ZeroWidthSpace;</code></td>
                        <td rowspan="1" colspan="1">0200B</td>
                        <td rowspan="1" colspan="1">space of no width at all</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;VeryThinSpace;</code></td>
                        <td rowspan="1" colspan="1">0200A</td>
                        <td rowspan="1" colspan="1">space of width 1/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;ThinSpace;</code></td>
                        <td rowspan="1" colspan="1">02009</td>
                        <td rowspan="1" colspan="1">space of width 3/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;MediumSpace;</code></td>
                        <td rowspan="1" colspan="1">02005</td>
                        <td rowspan="1" colspan="1">space of width 4/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;ThickSpace;</code></td>
                        <td rowspan="1" colspan="1">02009-0200A-0200A</td>
                        <td rowspan="1" colspan="1">space of width 5/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NegativeVeryThinSpace;</code></td>
                        <td rowspan="1" colspan="1">0200A-0FE00</td>
                        <td rowspan="1" colspan="1">space of width -1/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NegativeThinSpace;</code></td>
                        <td rowspan="1" colspan="1">02009-0FE00</td>
                        <td rowspan="1" colspan="1">space of width -3/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NegativeMediumSpace;</code></td>
                        <td rowspan="1" colspan="1">0205F-0FE00</td>
                        <td rowspan="1" colspan="1">space of width -4/18 em</td>
                     </tr>
                     <tr class="diff-del">
                        <td rowspan="1" colspan="1"><code>&amp;NegativeThickSpace;</code></td>
                        <td rowspan="1" colspan="1">02005-0FE00</td>
                        <td rowspan="1" colspan="1">space of width -5/18 em</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;InvisibleTimes;</code></td>
                        <td rowspan="1" colspan="1">02062</td>
                        <td rowspan="1" colspan="1">marks multiplication when it is understood without a mark
                           (<a href="chapter3-d.html#presm.mo">Section&nbsp;3.2.5 Operator, Fence, Separator or Accent
                                (mo)</a></td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;InvisibleComma;</code></td>
                        <td rowspan="1" colspan="1">02063</td>
                        <td rowspan="1" colspan="1">used as a separator, e.g., in indices (<a href="chapter3-d.html#presm.mo">Section&nbsp;3.2.5 Operator, Fence, Separator or Accent
                                (mo)</a></td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;ApplyFunction;</code></td>
                        <td rowspan="1" colspan="1">02061</td>
                        <td rowspan="1" colspan="1">character showing function application in presentation tagging
                           (<a href="chapter3-d.html#presm.mo">Section&nbsp;3.2.5 Operator, Fence, Separator or Accent
                                (mo)</a></td>
                     </tr>
                  </tbody>
               </table>
            </div>
         </div>
         <div class="div2">
            
            <h2><a name="id.6.3" id="id.6.3"></a>6.3 Character Symbol Listings
            </h2>
            <p>The Universal Character Set (UCS) of Unicode and ISO 10646
               continues to evolve, see <a href="chapter6-d.html#chars.char-status">Section&nbsp;6.4.4 Status of Character Encodings</a>.  
               <span class="diff-add">At the time of writing the standard is Unicode 4.0.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
               <span class="diff-del">A small
                  number of the changes recently introduced, relative to those resulting
                  from the needs of Asian languages, are those designed exactly to
                  facilitate the use of Unicode by the 'equation-writing' community.
                  This specification is written on the assumption that the code
                  assignments suggested to ISO/IEC JTC1/SC2/WG2 by the UTC will be
                  confirmed as they are in public draft forms of Unicode 3.1 and 3.2.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
               <span class="diff-chg">As before, we can only reiterate that for latest developments on
                  details of character standards as far as they influence mathematical
                  formalism the  <a href="http://www.w3.org/Math/">home page of the
                     W3C Math Activity</a> should be consulted.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span></p>
            <p>The characters are given with entity names as well as Unicode
               numbers.  To facilitate comprehension of a fairly large list of names,
               which totals over 2000 in this case, we offer more than one way to find
               to a given character.  A corresponding full set of entity declarations
               is in the DTD in <a href="appendixa-d.html">Appendix&nbsp;A Parsing MathML</a>. For discussion of entity
               declarations see that appendix.
               
            </p>
            <p>
               The characters are listed by name, and sample glyphs provided for all
               of them.  Each character name is accompanied by a code for a character
               grouping chosen from a list given below, a short verbal description,
               and a Unicode hex code drawn from ISO 10646<span class="diff-del">, now extended in
                  accordance with the proposal forwarded by the UTC to ISO/IEC WG2 in
                  March 2000<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
               
            </p>
            <p>The character listings by alphabetical and Unicode order in
               <a href="chapter6-d.html#chars.entity.tables">Section&nbsp;6.3.7 MathML Character Names</a> are in harmony with the ISO
               character sets given, in that if some part of a set is included then
               the entire set is included.
               
            </p>
            <div class="div3">
               
               <h3><a name="chars.special" id="chars.special"></a>6.3.1 Special Constants
               </h3>
               <p> To begin we list separately a few of the special characters which
                  MathML has introduced.  These <span class="diff-chg">now have<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span>
                  Unicode values.  Rather like the non-marking <span class="diff-chg">characters<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span> above, they provide very useful
                  capabilities in the context of machinable mathematics.<span class="diff-del">  It might be
                     imagined there could also be entries below for <code>&amp;true;</code>, <code>&amp;false;</code> and <code>&amp;NotANumber;</code>, but these do not yet have Unicode
                     points assigned.  They can be introduced by the character extension
                     mechanisms provided by the <code>mglyph</code> and <code>csymbol</code> elements.<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span>
                  
                  
               </p>
               <table>
                  <thead>
                     <tr>
                        <th rowspan="1" colspan="1">Entity name</th>
                        <th rowspan="1" colspan="1">Unicode</th>
                        <th rowspan="1" colspan="1">Description</th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;CapitalDifferentialD;</code></td>
                        <td rowspan="1" colspan="1">02145</td>
                        <td rowspan="1" colspan="1">D for use in differentials, e.g. within integrals</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;DifferentialD;</code></td>
                        <td rowspan="1" colspan="1">02146</td>
                        <td rowspan="1" colspan="1">d for use in differentials, e.g. within integrals</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;ExponentialE;</code></td>
                        <td rowspan="1" colspan="1">02147</td>
                        <td rowspan="1" colspan="1">e for use for the exponential base of the natural logarithms</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><code>&amp;ImaginaryI;</code></td>
                        <td rowspan="1" colspan="1">02148</td>
                        <td rowspan="1" colspan="1">i for use as a square root of -1</td>
                     </tr>
                  </tbody>
               </table>
            </div>
            <div class="div3">
               
               <h3><a name="chars.byxxx" id="chars.byxxx"></a>6.3.2 Character Tables (ASCII format)
               </h3>
               <p>The first table offered is a very large ASCII listing of characters
                  considered particularly relevant to mathematics.  This is given in
                  <span class="diff-chg"><a href="bycodes-d.html">Unicode order</a><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
                  Most, but not all, of these characters have MathML names
                  defined via entity declarations in the DTD.  Those that do not are
                  usually symbols which seem mathematically peripheral, such as dingbats,
                  machine graphics or technical symbols.
                  
               </p>
               <p>
                  A second table lists those characters that do have MathML entity
                  names, <a href="byalpha-d.html">ordered alphabetically</a>, with
                  a lower-case letter preceding its upper-case counterpart.
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="chars.16x16-tables" id="chars.16x16-tables"></a>6.3.3 Tables arranged by Unicode block
               </h3>
               <p>
                  The tables in this section detail Unicode code points (displayed with
                  256 code points per table) that have mathematically significant
                  characters. The sample glyph images link to the <a href="bycodes-d.html">table of characters ordered by Unicode</a> given
                  in the previous section.<span class="diff-del"> As shown in the key for each table, the
                     status of each character (for example in Unicode 3.0 or in the
                     proposed additions) is indicated by a CSS class on the table cell
                     (which by default is indicated by varying the background color).<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>  The
                  names of the blocks are those of the Unicode blocks included in the
                  numerical range given; bracketing indicates <span class="diff-add">glyphs
                     for<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> characters of that type are not shown in these tables.
               </p>
               <table id="chars.table-unicode-block">
                  <thead>
                     <tr>
                        <th rowspan="1" colspan="1">Block Range</th>
                        <th rowspan="1" colspan="1">Description</th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="000-d.html">00000 - 000FF</a></td>
                        <td rowspan="1" colspan="1">Controls and Basic Latin, and Latin-1 Supplement</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="001-d.html">00100 - 001FF</a></td>
                        <td rowspan="1" colspan="1">Latin Extended-A, Latin Extended-B</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="002-d.html">00200 - 002FF</a></td>
                        <td rowspan="1" colspan="1">IPA Extensions, Spacing Modifier Letters</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="003-d.html">00300 - 003FF</a></td>
                        <td rowspan="1" colspan="1">Combining Diacritical Marks, Greek [and Coptic]
                           
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="004-d.html">00400 - 004FF</a></td>
                        <td rowspan="1" colspan="1">Cyrillic</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="020-d.html">02000 - 020FF</a></td>
                        <td rowspan="1" colspan="1">General Punctuation, Superscripts and Subscripts, Currency Symbols,
                           Combining Diacritical Marks for Symbols
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="021-d.html">02100 - 021FF</a></td>
                        <td rowspan="1" colspan="1">Letter-like Symbols, Number Forms, Arrows</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="022-d.html">02200 - 022FF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Operators</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="023-d.html">02300 - 023FF</a></td>
                        <td rowspan="1" colspan="1">Miscellaneous
                           Technical
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="024-d.html">02400 - 024FF</a></td>
                        <td rowspan="1" colspan="1">Control Pictures, Optical Character Recognition, Enclosed Alphanumerics</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="025-d.html">02500 - 025FF</a></td>
                        <td rowspan="1" colspan="1">Box Drawing, Block Elements, Geometric Shapes</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="026-d.html">02600 - 026FF</a></td>
                        <td rowspan="1" colspan="1">Miscellaneous Symbols  </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="027-d.html">02700 - 027FF</a></td>
                        <td rowspan="1" colspan="1">Dingbats</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="029-d.html">02900 - 029FF</a></td>
                        <td rowspan="1" colspan="1">Supplemental Arrows,  Miscellaneous Mathematical Symbols</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="02A-d.html">02A00 - 02AFF</a></td>
                        <td rowspan="1" colspan="1">Supplemental Mathematical Operators</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="030-d.html">03000 - 030FF</a></td>
                        <td rowspan="1" colspan="1">CJK Symbols and Punctuation, [Hiragana, Katakana]</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="0FB-d.html">0FB00 - 0FBFF</a></td>
                        <td rowspan="1" colspan="1">Alphabetic Presentation Forms </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="0FE-d.html">0FE00 - 0FEFF</a></td>
                        <td rowspan="1" colspan="1">[Combining Half Marks, CJK Compatibility Forms, Small Form Variants,
                           Arabic Presentation Forms-B]
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="1D4-d.html">1D400 - 1D4FF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Styled Latin (Bold, Italic, Bold Italic, Script,
                           Bold Script begins)
                           
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="1D5-d.html">1D500 - 1D5FF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Styled Latin (Bold Script ends, Fraktur, Double-struck,
                           Bold Fraktur, Sans-serif, Sans-serif Bold begins)
                           
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="1D6-d.html">1D600 - 1D6FF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Styled Latin (Sans-serif Bold ends, Sans-serif Italic,
                           Sans-serif Bold Italic, Monospace, Bold), Mathematical Styled Greek (Bold, Italic begins)
                        </td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="1D7-d.html">1D700 - 1D7FF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Styled Greek (Italic continued, Bold Italic,
                           Sans-serif Bold), Mathematical Styled Digits 
                        </td>
                     </tr>
                  </tbody>
               </table>
            </div>
            <div class="div3">
               
               <h3><a name="chars.math-negated-tables" id="chars.math-negated-tables"></a>6.3.4 Negated
                  Mathematical Characters
               </h3>
               <p>
                  In addition to the Unicode Characters so far listed, one may use the
                  combining characters <span class="diff-chg">U+0338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (/), 
                  <span class="diff-chg">U+20D2<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (|) and <span class="diff-chg">U+20E5<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (\) to produce
                  negated or <span class="diff-chg">canceled<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> forms of characters. A combining character
                  should be placed immediately after its 'base' character, with no
                  intervening markup or space, just as is the case for combining accents.
                  
               </p>
               <p>
                  In principle, the negation characters may be applied to any Unicode
                  character, although fonts designed for mathematics typically have some
                  negated glyphs ready composed. A MathML renderer should be able to use
                  these pre-composed glyphs in these cases.  A compound character code
                  either represents a UCS character that is already available, as in the
                  case of <span class="diff-chg">U+003D+00338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> which amounts to 
                  <span class="diff-chg">U+2260<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>, or it does not as is the
                  case for <span class="diff-chg">U+2202+0338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>. The common cases of 
                  negations, <span class="diff-chg">of the latter  type<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>,
                  that have been identified are listed in the table
                  
               </p>
               <ul>
                  <li>
                     <p><a href="cancellations-d.html">cancellations</a></p>
                  </li>
               </ul>
               <p>
                  Note that it is the policy of the W3C and of Unicode that if a single
                  character is already defined for what can be achieved with a combining
                  character, that character must be used instead of the decomposed form.
                  It is also intended that no new single characters representing what
                  can be done by with existing compositions will be introduced. 
                  <span class="diff-add">For further information on these matters see
                     the Unicode Standard Annex 15, Unicode Normalization Forms 
                     <a href="appendixk-d.html#UAX15">[UAX15]</a>, especially
                     the discussion of Normalization Form C.<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="chars.math-variant-tables" id="chars.math-variant-tables"></a>6.3.5 Variant
                  Mathematical Characters
               </h3>
               <p>
                  Unicode attempts to avoid having several character codes for simple
                  font variants.  For a code point to be assigned there should be
                  more than a nuance in glyphs to be recorded.  To record 
                  variants worth noting there is a special character <span class="diff-chg">in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                  Unicode 3.2, U+FE00 (VARIATION SELECTOR-1), which
                  acts as a postfix modifier.  However the legally allowed
                  combinations with this variation selector are restricted to a
                  list recorded as part of Unicode. The  VARIATION SELECTOR-1
                  character may only be applied to the characters listed here.
                  The resulting combination is not regarded by Unicode as a separate
                  character, but a variation on the base character. Unicode aware systems
                  may render the combination as the base if the available fonts do not
                  support the variant glyph shape.
                  
               </p>
               <ul>
                  <li>
                     <p><a href="variants-d.html">variants</a></p>
                  </li>
               </ul>
            </div>
            <div class="div3">
               
               <h3><a name="chars.letter-like-tables" id="chars.letter-like-tables"></a>6.3.6 Mathematical Alphanumeric Symbols
               </h3>
               <p>
                  Here we list the special mathematical alphabets.  Note that the names
                  for these alphabetic runs should be regarded as conventions resulting
                  from recent tradition in the typesetting of mathematical formulas,
                  rather than as fixing exactly and forever the styles which are to be
                  used.  Of course, they do correspond to the styles presently most
                  common.  But, for instance, there may be font variations in the glyphs
                  from double-struck, open-face or blackboard bold fonts, all of which
                  would naturally be used for the characters in the range here labelled
                  Double-struck.  Similar considerations would apply to appellations
                  such as fraktur and gothic, or script and calligraphic.
                  
               </p>
               <p>
                  As discussed above, the use of these characters is formally equivalent
                  to the use of characters in Plane 0, together with a suitable value
                  for the <code>mathvariant</code> attribute.  The
                  correspondence is given in the character tables. Most of these
                  characters come from the <span class="diff-del">proposed<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> additions to Plane 1, however a few
                  characters (such as the double-struck letters N, P, Z, Q, R, C, H
                  representing common number sets) were already present in Unicode 3.0
                  and retain their original positions. These characters are highlighted
                  in the tables.
                  
               </p>
               <ul>
                  <li>
                     <p><a href="bold-d.html">Bold</a></p>
                  </li>
                  <li>
                     <p><a href="italic-d.html">Italic</a></p>
                  </li>
                  <li>
                     <p><a href="bold-italic-d.html">Bold Italic</a></p>
                  </li>
                  <li>
                     <p><a href="double-struck-d.html">Double-struck</a></p>
                  </li>
                  <li>
                     <p><a href="script-d.html">Script</a></p>
                  </li>
                  <li>
                     <p><a href="bold-script-d.html">Bold Script</a></p>
                  </li>
                  <li>
                     <p><a href="fraktur-d.html">Fraktur</a></p>
                  </li>
                  <li>
                     <p><a href="bold-fraktur-d.html">Bold Fraktur</a></p>
                  </li>
                  <li>
                     <p><a href="sans-serif-d.html">Sans-serif</a></p>
                  </li>
                  <li>
                     <p><a href="bold-sans-serif-d.html">Bold Sans-serif</a></p>
                  </li>
                  <li>
                     <p><a href="sans-serif-italic-d.html">Sans-serif Italic</a></p>
                  </li>
                  <li>
                     <p><a href="sans-serif-bold-italic-d.html">Sans-serif Bold Italic</a></p>
                  </li>
                  <li>
                     <p><a href="monospace-d.html">Monospace</a></p>
                  </li>
               </ul>
            </div>
            <div class="div3">
               
               <h3><a name="chars.entity.tables" id="chars.entity.tables"></a>6.3.7 MathML Character Names
               </h3>
               <p>
                  This section corresponds closely with the entity definitions in the DTD
                  described in <a href="appendixa-d.html">Appendix&nbsp;A Parsing MathML</a>. All of the entity sets except the
                  last correspond to entity sets defined by ISO 8879 or ISO 9573-13.
                  
               </p>
               <table>
                  <thead>
                     <tr>
                        <th rowspan="1" colspan="1">ISO Handle</th>
                        <th rowspan="1" colspan="1">Description</th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamsa-d.html">ISOAMSA</a></td>
                        <td rowspan="1" colspan="1"> Added Mathematical Symbols: Arrows</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamsb-d.html">ISOAMSB</a></td>
                        <td rowspan="1" colspan="1">Added Mathematical Symbols: Binary Operators</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamsc-d.html">ISOAMSC</a></td>
                        <td rowspan="1" colspan="1">Added Mathematical Symbols: Delimiters</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamsn-d.html">ISOAMSN</a></td>
                        <td rowspan="1" colspan="1">Added Mathematical Symbols: Negated Relations</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamso-d.html">ISOAMSO</a></td>
                        <td rowspan="1" colspan="1">Added Mathematical Symbols: Ordinary</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isoamsr-d.html">ISOAMSR</a></td>
                        <td rowspan="1" colspan="1">Added Mathematical Symbols: Relations</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isobox-d.html">ISOBOX</a></td>
                        <td rowspan="1" colspan="1">Box and Line Drawing</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isocyr1-d.html">ISOCYR1</a></td>
                        <td rowspan="1" colspan="1">Cyrillic-1</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isocyr2-d.html">ISOCYR2</a></td>
                        <td rowspan="1" colspan="1">Cyrillic-2</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isodia-d.html">ISODIA</a></td>
                        <td rowspan="1" colspan="1">Diacritical Marks</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isogrk3-d.html">ISOGRK3</a></td>
                        <td rowspan="1" colspan="1">Greek-3</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isolat1-d.html">ISOLAT1</a></td>
                        <td rowspan="1" colspan="1">Latin-1</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isolat2-d.html">ISOLAT2</a></td>
                        <td rowspan="1" colspan="1">Latin-2</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isomfrk-d.html">ISOMFRK</a></td>
                        <td rowspan="1" colspan="1">Mathematical Fraktur</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isomopf-d.html">ISOMOPF</a></td>
                        <td rowspan="1" colspan="1">Mathematical Openface (Double-struck)</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isomscr-d.html">ISOMSCR</a></td>
                        <td rowspan="1" colspan="1">Mathematical Script</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isonum-d.html">ISONUM</a></td>
                        <td rowspan="1" colspan="1">Numeric and Special Graphic</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isopub-d.html">ISOPUB</a></td>
                        <td rowspan="1" colspan="1">Publishing</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="isotech-d.html">ISOTECH</a></td>
                        <td rowspan="1" colspan="1">General Technical</td>
                     </tr>
                     <tr>
                        <td rowspan="1" colspan="1"><a href="mmlextra-d.html">MMLEXTRA</a></td>
                        <td rowspan="1" colspan="1">Extra Names added by MathML</td>
                     </tr>
                  </tbody>
               </table>
            </div>
         </div>
         <div class="div2">
            
            <h2><a name="id.6.4" id="id.6.4"></a>6.4 Differences from Characters in MathML 1
            </h2>
            <div class="div3">
               
               <h3><a name="id.6.4.1" id="id.6.4.1"></a>6.4.1 Coverage
               </h3>
               <p>
                  We have excluded a very few other characters that may have appeared in
                  the corresponding lists in MathML 1.  Those characters thus
                  <em>lost</em> will be found to be used very infrequently in the
                  experience of mathematical publishers, or simply to be completely
                  unacceptable for inclusion in Unicode.  However MathML 2 does provide
                  the <code>mglyph</code> element to accommodate new
                  characters that authors may wish to introduce.
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="id.6.4.2" id="id.6.4.2"></a>6.4.2 Fewer Non-marking Characters 
               </h3>
               <p>It used to be in MathML 1.0 that there were a number more
                  non-marking character entities listed.  These were concerned with
                  composition control, such as line-breaking. In MathML 2 such control
                  is effected by the use of the proper attributes on the <code>mspace</code> element. 
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="id.6.4.3" id="id.6.4.3"></a>6.4.3 ISO Tables
               </h3>
               <p>
                  The character listings by alphabetical and Unicode order in <a href="chapter6-d.html#chars.entity.tables">Section&nbsp;6.3.7 MathML Character Names</a> have now been brought more into line with
                  the corresponding ISO character sets than was the case in MathML 1.0,
                  in that if some part of a set is included then the entire set is
                  included. In addition, the group ISOCHEM has been dropped as more
                  properly the concern of chemists.  All the ISO mathematical alphabets
                  are listed, since there are now Unicode characters to point to,
                  in particular the bold Greek of ISOGRK3.  These changes have also been
                  reflected in the entity declarations in the DTD in <a href="appendixa-d.html">Appendix&nbsp;A Parsing MathML</a>.
                  
               </p>
            </div>
            <div class="div3">
               
               <h3><a name="chars.char-status" id="chars.char-status"></a>6.4.4 Status of Character Encodings
               </h3>
               <p>A significant change 
                  <span class="diff-chg">after MathML 1.0 occurred in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> the movement toward
                  adoption of more characters for mathematics in the UCS
                   and availability of public fonts for mathematics.  The
                  encoding of characters in the UCS is done
                  jointly by the Unicode Technical Committee and by ISO/IEC
                  JTC1/SC2/WG2.  The process of encoding takes quite some time from the
                  deliberation of first proposals to the final approval.
                  The characters mentioned in this chapter and listed in the associated
                  tables <span class="diff-chg">have been though the<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> various stages 
                  of this approval process.<span class="diff-del">  This section
                     gives detailed information about the stages relevant to this
                     specification and gives an overview of the characters affected.  The
                     lists, as well as other places that discuss characters, mention 
                     any cases when
                     characters are not fully approved or show this graphically.
                     Updates on the status of the characters will be provided by updates
                     to this specification, by errata to this
                     specification, and by notices on the 
                     <a href="http://www.w3.org/Math/">W3C Math home page</a>.
                     The final word on all Unicode matters is naturally to be found
                     at <a href="http://www.unicode.org/">the Unicode Consortium</a>.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span></p>
               <p>
                  <span class="diff-chg">At the time of the preparation of the MathML 2.0
                     specification <span class="diff-add"><a href="appendixk-d.html#MathML2">[MathML2]</a><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> the characters relevant to mathematics fell <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
                  into three categories:
                  <span class="diff-chg">fully<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> accepted characters, characters in final (JTC1) ISO/IEC ballot,
                  and characters before the final ISO/IEC ballot.
                  
               </p>
               <ul>
                  <li>
                     <p>
                        Fully accepted characters <span class="diff-chg">included <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>a large number of Latin, Greek, and
                        Cyrillic letters, a large number of Mathematical Operators and
                        symbols, including arrows, and so on.  Fully accepted characters
                        <span class="diff-chg">were<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> exactly those that are 
                        <span class="diff-chg">in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> both Unicode 3.0 <a href="appendixk-d.html#Unicode">[Unicode]</a> and ISO/IEC 10646-1:2000 <a href="appendixk-d.html#ISOIEC10646-1">[ISOIEC10646-1]</a>, which are identical code point by code point.  
                        <span class="diff-del">Fully
                           accepted characters are not specially marked or mentioned in this
                           specification; they do not pose any unusual implementation problems
                           other than possibly finding fonts to display them<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>  Those of obvious
                        special interest to mathematics <span class="diff-chg">numbered<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> over 
                        1,500, depending on how you count.
                        
                     </p>
                  </li>
                  <li>
                     <div class="diff-chg">
                        <p>
                           In April 2001, the Mathematical Alphanumeric Symbols came up for a final ballot
                           together with a large number of ideographs and other
                           characters not directly relevant for mathematics.  There were just
                           about 1,000 of these.   The additions were published as ISO/IEC 10646-2, 
                           and became part of Unicode 3.1.
                           
                        </p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
                     <div class="diff-del">
                        <p>
                           While acceptance of this ballot seems more likely than rejection,
                           implementers and users of MathML have to be aware that until the final
                           acceptance, they are using the code points of characters in final
                           ballot at their own risk. Entities (see <a href="chapter6-d.html#chars.entity.tables">Section&nbsp;6.3.7 MathML Character Names</a>) and the <code>mathvariant</code> attribute (see <a href="chapter3-d.html#presm.commatt">Section&nbsp;3.2.2 Mathematics style attributes common to token
                              elements</a>) can be used to avoid that risk.
                           
                        </p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
                  </li>
                  <li>
                     <div class="diff-chg">
                        <p>
                           Characters relevant to MathML that were before final ballot made up a long list
                           of operators and symbols, including some special constants and
                           non-marking characters (see <a href="chapter6-d.html#chars.nonmark">Section&nbsp;6.2.4 Non-Marking Characters</a> and
                           <a href="chapter6-d.html#chars.special">Section&nbsp;6.3.1 Special Constants</a>).  They numbered about 590 in all. 
                           With some small technical improvements and compromises the proposed additions
                           accepted were published as an amendment to [ISO/IEC
                           10646-1], and became part of Unicode 3.2.
                           
                        </p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
                     <div class="diff-chg">
                        <p>
                           Even with the good will shown to the mathematical community by the 
                           Unicode process a small number of characters of special interest
                           to some may not yet have been included.  The obvious solution of
                           avoiding their use may not satisfy all.  For these characters the
                           Unicode mechanism involving Private Use Area codes could be deployed,
                           in spite of all the dangers of confusion and collisions of conventions 
                           this brings with it. However, this is the situation for which 
                           <a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
                           was introduced. The use of <a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
                           is recommended to refer to symbols not included in Unicode.
                        </p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
                  </li>
               </ul>
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