{"id":347,"date":"2022-09-23T13:02:45","date_gmt":"2022-09-23T13:02:45","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/pengkuan\/?p=347"},"modified":"2022-09-23T13:02:45","modified_gmt":"2022-09-23T13:02:45","slug":"examination-of-cantors-proofs-for-uncountability-and-axiom-for-counting-infinite-sets-2","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/pengkuan\/2022\/09\/23\/examination-of-cantors-proofs-for-uncountability-and-axiom-for-counting-infinite-sets-2\/","title":{"rendered":"Examination of Cantor\u2019s proofs for uncountability and axiom for counting infinite sets"},"content":{"rendered":"\n<p>An analysis of Cantor\u2019s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption assumes R belongs to L. This makes the claim \u201ca real number is constructed but is not in the list L\u201d questionable. We propose a solution to this problem, an axiom for counting infinite sets and a solution to continuum hypothesis.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>\u00ab<a href=\"https:\/\/www.academia.edu\/86410224\/Examination_of_Cantors_proofs_for_uncountability_and_axiom_for_counting_infinite_sets\">Examination of Cantor\u2019s proofs\nfor uncountability<\/a> and <a href=\"https:\/\/pengkuanonmaths.blogspot.com\/2022\/09\/examination-of-cantors-proofs-for.html\">axiom for counting infinite sets<\/a>\u00bb<\/p>\n\n\n\n<p><a href=\"https:\/\/www.academia.edu\/86410224\/Examination_of_Cantors_proofs_for_uncountability_and_axiom_for_counting_infinite_sets\">https:\/\/www.academia.edu\/86410224\/Examination_of_Cantors_proofs_for_uncountability_and_axiom_for_counting_infinite_sets<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>An analysis of Cantor\u2019s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/pengkuan\/2022\/09\/23\/examination-of-cantors-proofs-for-uncountability-and-axiom-for-counting-infinite-sets-2\/\">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-347","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/347","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=347"}],"version-history":[{"count":1,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/347\/revisions"}],"predecessor-version":[{"id":348,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/347\/revisions\/348"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/media?parent=347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/categories?post=347"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/tags?post=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}