<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><blockquote type="cite" class=""><div class="">On Aug 19, 2018, at 05:53, Themis Matsoukas <<a href="mailto:tmatsoukas@icloud.com" class="">tmatsoukas@icloud.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><blockquote type="cite" style="font-family: AgmenaPro-Regular; font-size: 14px; 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="Apple-interchange-newline">BTW, the last time I used \equiv for defining something (something like $E_{d,\gamma}f\equiv f$, a referee swatted it down. :=)<br class=""><br class=""></blockquote><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; 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: AgmenaPro-Regular; font-size: 14px; 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="">…and good to know that \equiv is unacceptable :)</span></div></blockquote></div><br class=""><div class="">I tend to not use \equiv, but rather favor := (or even = with ‘def’ on top) for an “equal by definition,” where in effect the term on the left is introduced for the first time. The \equiv lends itself better to express an identity between two terms. In other words, and extending a bit, \equiv expresses the idea of a “canonical isomorphism,” and therefore \cong (or some such) just is an isomorphism.</div><div class=""><br class=""></div><div class="">My two math cents.</div><div class=""><br class=""></div><div class="">—Ettore</div><div class=""><br class=""></div><div class=""><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; widows: 2; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><font face="Lantinghei TC" class=""><span style="font-size: 11px;" class="">Ettore Aldrovandi</span></font></div><div class=""><font face="Lantinghei TC" class=""><span style="font-size: 11px;" class="">Department of Mathematics, Florida State University</span></font></div><div class=""><font face="Lantinghei TC" class=""><span style="font-size: 11px;" class="">1017 Academic Way * <a href="http://www.math.fsu.edu/~ealdrov" class="">http://www.math.fsu.edu/~ealdrov</a></span></font></div><div class=""><font face="Lantinghei TC" class=""><span style="font-size: 11px;" class="">Tallahassee, FL 32306-4510, USA * * aldrovandi at math dot fsu dot edu</span></font></div></div></div></div></div></div></div></div></div></div><div><br class=""><blockquote type="cite" class=""></blockquote></div></div></body></html>