{"id":217594,"date":"2025-07-11T02:04:37","date_gmt":"2025-07-11T07:04:37","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/07\/cauchy-sequence"},"modified":"2025-07-11T02:04:37","modified_gmt":"2025-07-11T07:04:37","slug":"cauchy-sequence","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/07\/cauchy-sequence","title":{"rendered":"Cauchy sequence"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/cauchy-sequence2.jpg\"><\/a><\/p>\n<p>In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses.<sup id= cite_ref-FOOTNOTELang1992_1-0 class= reference> [ 1 ] <\/sup> More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other. Cauchy sequences are named after Augustin-Louis Cauchy; they may occasionally be known as fundamental sequences.<sup id= cite_ref-2 class= reference> [ 2 ]<\/sup>.<\/p>\n<p><!-- Link: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cauchy_sequence#:~:text=In\">https:\/\/en.wikipedia.org\/wiki\/Cauchy_sequence#:~:text=In<\/a> mathematics, a Cauchy sequence,given target= --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. [ 1 ] More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other. Cauchy sequences are named after Augustin-Louis [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229],"tags":[],"class_list":["post-217594","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/217594","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=217594"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/217594\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=217594"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=217594"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=217594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}