{"id":24616,"date":"2020-08-22T15:35:08","date_gmt":"2020-08-22T19:35:08","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=24616"},"modified":"2020-08-22T15:39:27","modified_gmt":"2020-08-22T19:39:27","slug":"reordering-alternating-series","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=24616","title":{"rendered":"Reordering alternating series"},"content":{"rendered":"\n<p><a href=\"https:\/\/cindyjs.org\/gallery\/main\/AlternatingSeries\/\">Reordering alternating series<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed-twitter wp-block-embed is-type-rich is-provider-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">The alternating harmonic series 1 &#8211; 1\/2 + 1\/3 &#8211; 1\/4 + 1\/5 &#8211; 1\/6 + &#8230; can be rearranged to approach any limit you want! This amazing fact (a special case of the Riemann rearrangement theorem) is elegantly illustrated by this applet <a href=\"https:\/\/t.co\/d06ntY8xBP\">https:\/\/t.co\/d06ntY8xBP<\/a> (ht <a href=\"https:\/\/twitter.com\/paultpearson?ref_src=twsrc%5Etfw\">@paultpearson<\/a>). <a href=\"https:\/\/t.co\/Ve3pNRCFPp\">pic.twitter.com\/Ve3pNRCFPp<\/a><\/p>&mdash; Steven Strogatz (@stevenstrogatz) <a href=\"https:\/\/twitter.com\/stevenstrogatz\/status\/1296045068609105920?ref_src=twsrc%5Etfw\">August 19, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed-twitter wp-block-embed is-type-rich is-provider-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">There&#39;s a terrific write-up of Riemann&#39;s Rearrangement Theorem here, <a href=\"https:\/\/t.co\/np3UEVTtcs\">https:\/\/t.co\/np3UEVTtcs<\/a>, from an old issue of <a href=\"https:\/\/twitter.com\/NCTM?ref_src=twsrc%5Etfw\">@NCTM<\/a>&#39;s Mathematics Teacher.<\/p>&mdash; Patrick Honner (@MrHonner) <a href=\"https:\/\/twitter.com\/MrHonner\/status\/1296049951529668608?ref_src=twsrc%5Etfw\">August 19, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Reordering alternating series<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-24616","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/24616","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24616"}],"version-history":[{"count":2,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/24616\/revisions"}],"predecessor-version":[{"id":24622,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/24616\/revisions\/24622"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}