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</o:shapelayout></xml><![endif]--></head><body lang=EN-GB link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='mso-fareast-language:EN-US'>I understand your concern. The term “limit” is not appropriate in all cases. How about something like the following?<o:p></o:p></span></p><p style='margin-left:36.0pt'><b>n-ary operator</b> — A<s><span style='color:red'>n</span></s> <u><span style='color:#3366FF'>mathematical</span></u> operator<s><span style='color:red'> that involves n terms when expanded </span></s><u><span style='color:#3366FF'>, typically a single operator character, optionally accompanied by superscript or subscript expressions, or both, representing the domain or limits of the mathematical operation</span></u>. For instance, the following example uses the Unicode (ISO 10646) summation sign (U+2211) which has the official name “N-ARY SUMMATION”.<o:p></o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'>However, this suggests that the description of the element limLoc (</span><span style='mso-fareast-language:EN-US'>§</span><span style='mso-fareast-language:EN-US'>22.1.2.53) needs to be adjusted in a similar way, e.g.<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-language:EN-US'>This element specifies the location of limits<u><span style='color:#3366FF'>, i.e. superscript or subscript expressions representing a domain or limits according to the mathematical operation, </span></u><span style='color:#3366FF'> </span>in n-ary operators. Limits can be either centered above and below the n-ary operator (shown in the first summation <u><span style='color:#3366FF'>example</span></u><span style='color:#3366FF'> </span>below), or positioned just to the right of the operator (shown in the second summation <u><span style='color:#3366FF'>example</span></u><span style='color:#3366FF'> </span>below).<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'>I think that the mathematical expression below the first paragraph of </span><span style='mso-fareast-language:EN-US'>§</span><span style='mso-fareast-language:EN-US'>22.1.2.53 is illustrative, not normative, so should be enclosed in an example.<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'>I hope that the above uses the term “domain” correctly, i.e. the set of values over which the operation is evaluated.<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'>Francis<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><b><span lang=EN-US>From:</span></b><span lang=EN-US> eb2mmrt@gmail.com <eb2mmrt@gmail.com> <b>On Behalf Of </b>MURATA Makoto<br><b>Sent:</b> 04 April 2018 15:50<br><b>To:</b> SC 34 WG4 <e-SC34-WG4@ecma-international.org><br><b>Subject:</b> Re: DR 17-0035<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>The proposed change looks strange but is consistent with OMath.<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:complexType</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> name=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"CT_Nary"</span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:sequence></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:element</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> name=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"naryPr"</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> type=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"CT_NaryPr"</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> minOccurs=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"0"</span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>/></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:element</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> name=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"sub"</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> type=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"CT_OMathArg"</span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>/></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:element</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> name=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"sup"</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> type=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"CT_OMathArg"</span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>/></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'><xsd:element</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> name=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"e"</span></span><span class=gmail-tan><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#F5844C'> type=</span></span><span class=gmail-tav><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#993300'>"CT_OMathArg"</span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>/></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'></xsd:sequence></span></span><span class=gmail-ti><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'> </span></span><span class=gmail-tel><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'></xsd:complexType></span></span><o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>However, I do not like the word "limit", since </span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>22.1.2.72 of Part 1 mentions Logical And and Logical OR.</span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>In these two cases, <sub> or <sup> do not represent </span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#000096'>limits.</span><o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><div><p class=MsoNormal>Regards,<o:p></o:p></p></div><div><p class=MsoNormal>Makoto<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>2018-03-09 5:25 GMT+09:00 Francis Cave <<a href="mailto:francis@franciscave.com" target="_blank">francis@franciscave.com</a>>:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm'><div><p>I think that the definition of "n-ary operator" in §15.1 is insufficient, because it fails to include the integral sign and other similar signs that operate on continuous (i.e. non-discrete) ranges of values. This is particularly unsatisfactory, given that the default n-ary operator character is the integral sign (see §22.1.2.20)! I therefore propose the following change to the definition of "n-ary operator":<o:p></o:p></p><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p><b>n-ary operator</b> — A<s><span style='color:red'>n</span></s> <u><span style='color:#3366FF'>mathematical</span></u> operator<s><span style='color:red'> that involves n terms when expanded</span></s><s><span style='font-size:13.5pt;font-family:"-webkit-standard",serif;color:red'> </span></s><u><span style='color:#3366FF'>, </span></u><u><span style='font-size:13.5pt;font-family:"-webkit-standard",serif;color:#3366FF'>typically a single operator character, optionally accompanied by expressions of a lower limit, an upper limit, or both</span></u>. For instance, the following example uses the Unicode (ISO 10646) summation sign (U+2211) which has the official name “N-ARY SUMMATION”.<o:p></o:p></p><p>[example expression here]<o:p></o:p></p></blockquote><p><span style='color:#888888'>Francis<o:p></o:p></span></p></div></blockquote></div><p class=MsoNormal><br><br clear=all><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><p class=MsoNormal>-- <o:p></o:p></p><div><p class=MsoNormal><br>Praying for the victims of the Japan Tohoku earthquake<br><br>Makoto<o:p></o:p></p></div></div></div></body></html>