<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Oct 2, 2021, at 2:41 PM, Jim Thomas <<a href="mailto:jaswthomas@sbcglobal.net" class="">jaswthomas@sbcglobal.net</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><blockquote type="cite" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">On Oct 1, 2021, at 6:09 AM, Fred J. Tydeman <<a href="mailto:tydeman@tybor.com" class="">tydeman@tybor.com</a>> wrote:<br class=""><br class="">On Thu, 30 Sep 2021 15:46:56 -0700 Jim Thomas wrote:<br class=""><blockquote type="cite" class=""><br class="">b) The results are not equivalent because they have different quantum exponents.<br class=""><br class=""></blockquote><br class="">How about:<br class=""><br class="">The results are equal, but have different quantum exponents, hence are not equivalent.<br class=""></blockquote><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">The statement suggests that if the results were equal (meaning compare equal) and had the same quantum exponent, then they would be equivalent, which is not true for signed zeros. The two result 12.34 and 12.340, on the preceding two lines, are obviously equal. So saying the results are equal doesn’t seem needed.<span class="Apple-converted-space"> </span></span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""></div></blockquote><div><br class=""></div><div>Sorry. These last two sentences can only have confused the situation. The referenced preceding two lines </div><div><br class=""></div></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;" class=""><div><div>1. × 12.34 = (+1, 1, 0) × (+1, 1234, −2) = (+1, 1234, −2) = 12.34 </div></div><div><div><br class=""></div></div><div><div>1.0 × 12.34 = (+1, 10, −1) × (+1, 1234, −2) = (+1, 12340, −3) = 12.340</div></div></blockquote><div><div><br class=""></div><div>exemplify two different transformations, the first valid, the second not valid.</div><div><br class=""></div><div>The current text and the suggested changes start with “The results” which would seem to refer to the two preceding lines, which is misleading. I believe WG14 was concerned about the use of “equal” here and not this second problem.</div><div><br class=""></div><div>Here's another suggestion for the new words (to follow the two lines above):</div><div><br class=""></div></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;" class=""><div><div>c) In the second case, the factor 12.34 and the result 12.340 have different quantum exponents, demonstrating that 1.0 * x and x are not equivalent expressions. </div><div><br class=""></div></div></blockquote>- Jim Thomas<br class=""><div><div><br class=""></div><blockquote type="cite" class=""><div class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">(I believe the original idea behind the term "numerically equal” was to exclude different signed zeros and hence imply more than just equal or compare equal.)</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">- Jim Thomas</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><blockquote type="cite" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br class="">---<br class="">Fred J. 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