{"id":226,"date":"2016-02-05T21:41:47","date_gmt":"2016-02-05T20:41:47","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/pengkuan\/?p=226"},"modified":"2016-02-05T21:41:47","modified_gmt":"2016-02-05T20:41:47","slug":"on-the-uncountability-of-the-power-set-of-%e2%84%95","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/pengkuan\/2016\/02\/05\/on-the-uncountability-of-the-power-set-of-%e2%84%95\/","title":{"rendered":"On the uncountability of the power set of \u2115"},"content":{"rendered":"<p>This article discusses the uncountability of the power set of \u2115 proven by using the out-indexes subset contradiction. Cantor&#8217;s theorem proves that the power set of \u2115 is uncountable. This is a proof by contradiction. Suppose that the power set of \u2115 is countable. This allows us to put all subsets of \u2115 in a list. The contradiction will come from the indexes.<\/p>\n<p>Please read the article at <\/p>\n<p>PDF On the uncountability of the power set of \u2115<br \/>\n<a href=\"http:\/\/pengkuanonmaths.blogspot.com\/2016\/02\/on-uncountability-of-power-set-of.html\">http:\/\/pengkuanonmaths.blogspot.com\/2016\/02\/on-uncountability-of-power-set-of.html<\/a><br \/>\nor Word <a href=\"https:\/\/www.academia.edu\/21601620\/On_the_uncountability_of_the_power_set_of_N\">https:\/\/www.academia.edu\/21601620\/On_the_uncountability_of_the_power_set_of_N<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This article discusses the uncountability of the power set of \u2115 proven by using the out-indexes subset contradiction. Cantor&#8217;s theorem proves that the power set of \u2115 is uncountable. This is a proof by contradiction. Suppose that the power set &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/pengkuan\/2016\/02\/05\/on-the-uncountability-of-the-power-set-of-%e2%84%95\/\">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-226","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/226","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=226"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/226\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/media?parent=226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/categories?post=226"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/tags?post=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}