{"id":244,"date":"2016-11-24T14:43:47","date_gmt":"2016-11-24T14:43:47","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/pengkuan\/?p=244"},"modified":"2016-11-24T15:04:59","modified_gmt":"2016-11-24T15:04:59","slug":"lists-of-binary-sequences-and-uncountability","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/pengkuan\/2016\/11\/24\/lists-of-binary-sequences-and-uncountability\/","title":{"rendered":"Lists of binary sequences and uncountability"},"content":{"rendered":"<p>Creation of binary lists, discussion about the power set of \u2115, the diagonal argument, Cantor\u2019s first proof and uncountability. Binary system is kind of magic because it can express natural numbers, real numbers and subsets of natural numbers. Below, we will create lists of binary sequences to study the uncountability of the power set of \u2115 and real numbers.<\/p>\n<p>1.Infinite list of binary sequences<br \/>\n2.About the Power set of \u2115<br \/>\n3.Frame of Natural Infinity<br \/>\n4.List of numbers smaller than 1<br \/>\na.Creation of the numbers<br \/>\nb.Denseness of R..<br \/>\nc.Completeness of R..<br \/>\nd.Real numbers in [0,1[<br \/>\n5.About Cantor&#8217;s first proof<br \/>\n6.About the diagonal argument<br \/>\n7.Conclusion<\/p>\n<p>Please read the article at<\/p>\n<p>PDF Lists of binary sequences and uncountability<br \/>\n<a href=\"http:\/\/pengkuanonmaths.blogspot.com\/2016\/11\/lists-of-binary-sequences-and.html\">http:\/\/pengkuanonmaths.blogspot.com\/2016\/11\/lists-of-binary-sequences-and.html<\/a><br \/>\nor Word <a href=\"https:\/\/www.academia.edu\/30072323\/Lists_of_binary_sequences_and_uncountability\">https:\/\/www.academia.edu\/30072323\/Lists_of_binary_sequences_and_uncountability<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Creation of binary lists, discussion about the power set of \u2115, the diagonal argument, Cantor\u2019s first proof and uncountability. Binary system is kind of magic because it can express natural numbers, real numbers and subsets of natural numbers. Below, we &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/pengkuan\/2016\/11\/24\/lists-of-binary-sequences-and-uncountability\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-244","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/comments?post=244"}],"version-history":[{"count":3,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/244\/revisions"}],"predecessor-version":[{"id":248,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/244\/revisions\/248"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/categories?post=244"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/tags?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}