{"id":152435,"date":"2022-12-10T17:25:20","date_gmt":"2022-12-10T23:25:20","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2022\/12\/infinite-patterns-appear-in-numbers-described-as-moving-systems"},"modified":"2022-12-10T17:25:20","modified_gmt":"2022-12-10T23:25:20","slug":"infinite-patterns-appear-in-numbers-described-as-moving-systems","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2022\/12\/infinite-patterns-appear-in-numbers-described-as-moving-systems","title":{"rendered":"Infinite Patterns Appear In Numbers Described as Moving Systems"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/infinite-patterns-appear-in-numbers-described-as-moving-systems2.jpg\"><\/a><\/p>\n<p><b><strong>Furstenberg\u2019s Proof<\/strong><\/b><\/p>\n<p>Szemer\u00e9di had been examining sets that contain a \u201cpositive fraction\u201d of all the integers. Take, for example, the set containing all multiples of 5. As you look at bigger and bigger swaths of the number line, multiples of 5 continue to appear regularly. Mathematicians say that the set containing all multiples of 5 has the fraction of a fifth of all the integers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Furstenberg\u2019s Proof Szemer\u00e9di had been examining sets that contain a \u201cpositive fraction\u201d of all the integers. Take, for example, the set containing all multiples of 5. As you look at bigger and bigger swaths of the number line, multiples of 5 continue to appear regularly. Mathematicians say that the set containing all multiples of 5 [\u2026]<\/p>\n","protected":false},"author":661,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229],"tags":[],"class_list":["post-152435","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/152435","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\/661"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=152435"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/152435\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=152435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=152435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=152435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}