{"id":5473,"date":"2010-05-11T03:00:09","date_gmt":"2010-05-11T08:00:09","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/swansont\/?p=5473"},"modified":"2010-05-11T03:00:09","modified_gmt":"2010-05-11T08:00:09","slug":"infinity-can-be-mind-boggling","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/swansont\/archives\/5473","title":{"rendered":"Infinity Can Be Mind-Boggling"},"content":{"rendered":"<p><a href=\"http:\/\/opinionator.blogs.nytimes.com\/2010\/05\/09\/the-hilbert-hotel\/\">The Hilbert Hotel<\/a><\/p>\n<blockquote><p>[T]he Hilbert Hotel doesn\u2019t merely have hundreds of rooms \u2014 it has an <em>infinite<\/em> number of them.  Whenever a new guest arrives, the manager shifts the occupant of room 1 to room 2, room 2 to room 3, and so on.  That frees up room 1 for the newcomer, and accommodates everyone else as well (though inconveniencing them by the move).<\/p>\n<p>Now suppose <em>infinitely<\/em> many new guests arrive, sweaty and short-tempered.  No problem.  The unflappable manager moves the occupant of room 1 to room 2, room 2 to room 4, room 3 to room 6, and so on.  This doubling trick opens up all the odd-numbered rooms \u2014 infinitely many of them \u2014 for the new guests.<\/p><\/blockquote>\n<p>It&#8217;s the end of the <a href=\"http:\/\/opinionator.blogs.nytimes.com\/2010\/01\/31\/from-fish-to-infinity\/\">From Fish to Infinity<\/a> series to which I had <a href=\"http:\/\/blogs.scienceforums.net\/swansont\/archives\/4726\">previously linked<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Hilbert Hotel [T]he Hilbert Hotel doesn\u2019t merely have hundreds of rooms \u2014 it has an infinite number of them. Whenever a new guest arrives, the manager shifts the occupant of room 1 to room 2, room 2 to room &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/swansont\/archives\/5473\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-5473","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/5473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/comments?post=5473"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/5473\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/media?parent=5473"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/categories?post=5473"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/tags?post=5473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}