{"id":26883,"date":"2020-11-21T22:36:08","date_gmt":"2020-11-22T03:36:08","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=26883"},"modified":"2020-11-21T22:36:11","modified_gmt":"2020-11-22T03:36:11","slug":"pathological-function-volterras-function","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=26883","title":{"rendered":"Pathological function: Volterra&#8217;s function"},"content":{"rendered":"\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\">Pathological function: Volterra&#39;s function. This function V is differentiable but V&#39; is not integrable! It seems like this is a counterexample to the Fundamental Theorem of Calculus, but it isn&#39;t. In calc textbooks, the FTC requires the function to be continuous, which V&#39; isn&#39;t. <a href=\"https:\/\/t.co\/oyCTNDi1pA\">pic.twitter.com\/oyCTNDi1pA<\/a><\/p>&mdash; Dave Richeson (@divbyzero) <a href=\"https:\/\/twitter.com\/divbyzero\/status\/1329880124456640512?ref_src=twsrc%5Etfw\">November 20, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"","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-26883","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/26883","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=26883"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/26883\/revisions"}],"predecessor-version":[{"id":26884,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/26883\/revisions\/26884"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}