{"id":100,"date":"2008-09-04T06:36:07","date_gmt":"2008-09-04T05:36:07","guid":{"rendered":"https:\/\/wpethzprd.ethz.ch\/kowalski\/2008\/09\/04\/encadrement\/"},"modified":"2024-02-20T13:40:58","modified_gmt":"2024-02-20T11:40:58","slug":"encadrement","status":"publish","type":"post","link":"https:\/\/blogs.ethz.ch\/kowalski\/2008\/09\/04\/encadrement\/","title":{"rendered":"Encadrement"},"content":{"rendered":"<p>Is there a particular word in English for a string of two inequalities which together give both a lower and an upper bound for a certain quantity?  French has <em>encadrement<\/em> for things like this, as in<\/p>\n<blockquote><p>Pour tout r\u00e9el <em>x<\/em>, on a l&#8217;encadrement<\/p>\n<p>$latex  x-\\frac{x^2}{2}\\leq \\cos(x)\\leq x-\\frac{x^2}{2}+\\frac{x^4}{24},$<\/p><\/blockquote>\n<p>This is often quite convenient &#8212; of course, one can say &#8220;we have the following inequalities&#8230;&#8221;, but the extra information is useful to have, and it helps avoiding too many repetitions.<\/p>\n<p><u><strong>Note<\/strong><\/u>: The <a href=\"http:\/\/dictionary.oed.com\">OED<\/a> only lists <em>encadr\u00e9 <\/em>as an English word, as a technical term in crystallography:<\/p>\n<blockquote><p>A crystal is named encadr\u00e9, when it has facets which form kinds of squares around the planes of a more simple form already existing in the same species, <em>R. Jameson, <\/em><strong>A treatise on the external characters of minerals<\/strong>, 1805.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Is there a particular word in English for a string of two inequalities which together give both a lower and an upper bound for a certain quantity? French has encadrement for things like this, as in Pour tout r\u00e9el x, on a l&#8217;encadrement $latex x-\\frac{x^2}{2}\\leq \\cos(x)\\leq x-\\frac{x^2}{2}+\\frac{x^4}{24},$ This is often quite convenient &#8212; of course, &hellip; <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2008\/09\/04\/encadrement\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Encadrement<\/span><\/a><\/p>\n","protected":false},"author":625,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[362,2],"tags":[],"class_list":["post-100","post","type-post","status-publish","format-standard","hentry","category-language","category-blogroll"],"_links":{"self":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/users\/625"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/comments?post=100"}],"version-history":[{"count":0,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/100\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/media?parent=100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/categories?post=100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/tags?post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}