{"id":739,"date":"2007-08-17T08:10:12","date_gmt":"2007-08-17T08:10:12","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=739"},"modified":"2014-02-16T20:02:31","modified_gmt":"2014-02-16T12:02:31","slug":"my-infinitys-bigger-than-yours","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/my-infinitys-bigger-than-yours-739","title":{"rendered":"My infinity&#8217;s bigger than yours"},"content":{"rendered":"<p>An article from Scientific American (no longer available) explains how Infinity Comes in Different Sizes.<\/p>\n<p>According to the article, the 19th century German mathematician Georg Cantor showed ...<\/p>\n<blockquote>\n<p>... there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals.<\/p>\n<\/blockquote>\n<p>I remember being blown away by the concepts of \"countably infinite\" (for example, the whole numbers 0, 1, 2, 3, ... is a countably infinite set) and \"uncountably infinite\" (for example, the number of <b>all<\/b> numbers - that's all the rationals, irrationals, complex numbers, etc.)<\/p>\n<p>Cantor created <b>Set Theory<\/b>, a topic that was used and abused in secondary schools for many years. According to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Georg_Cantor\">this Wikipedia article<\/a>, after developing the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Transfinite_number\">concept of transfinite numbers<\/a>, Cantor took himself a little too seriously and died a seriously depressed man.<\/p>\n<p>I can't resist concluding with Einstein's profound quote:<\/p>\n<blockquote>\n<p>Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.<\/p>\n<\/blockquote>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/my-infinitys-bigger-than-yours-739#comments\" id=\"comms\">3 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is there a number bigger than infinity?<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/739"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=739"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/739\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}