{"id":4517,"date":"2014-01-21T00:34:16","date_gmt":"2014-01-21T04:34:16","guid":{"rendered":"http:\/\/nycphantom.com\/journal\/?p=4517"},"modified":"2014-01-21T00:55:07","modified_gmt":"2014-01-21T04:55:07","slug":"grandis-series","status":"publish","type":"post","link":"http:\/\/nycphantom.com\/journal\/?p=4517","title":{"rendered":"Grandi's Series"},"content":{"rendered":"

David Tong posted a fun video <\/a>in Mathematics a few days ago:<\/p>\n

1+2+3+4+...= -1\/2<\/p>\n

This is called messing <\/a>around with the concept of infinity.<\/p>\n

After a long thought...(I must if I were to consider myself a math major)...my concluding response was:<\/p>\n

Ok. No more thinking about it I think I'd say nice trick, but to theologize it, I'd have to call it a heresy if not explained properly. I think it starts with Grandi's series: S1 = 1-1+1-1+...=1\/2. If we are to maintain \u221e (infinity) a concept instead of a number which would yield contradiction in this case, then we must also admit that 2(S1): 1+0+0+... is not simply 1+0, in the normal arithmetic sense. After that, we can discuss more about the wonders of \u221e.<\/em><\/p>\n

I must say, I admire greatly the enthusiasm of Brady Haran of the video. I have only seen one other mathematician with such enthusiasm and I do not remember his name (a Math PhD from Stony Brook years).<\/p>\n

This series is one of those \"I think something's wrong with it, but I just cannot figure it out right now\" kind of theories.<\/p>\n

It had me almost convinced (what a poor mathematician am I) and gone Willy Wonka for a little bit.<\/p>\n

I've briefly read on Cesaro's Sum<\/a>, quantum physics (renormalization)<\/a>,\u00a0 and other<\/a>\u00a0 clues<\/a>. I even discovered a renewed interest in number theory, such as that <\/a>which led to Andrew Wiles' proof of Fermat's Last Theorem.<\/p>\n

School's going to be fun. Nonetheless, too many things, too little time. Time management is crucial.<\/p>\n","protected":false},"excerpt":{"rendered":"

David Tong posted a fun video in Mathematics a few days ago: 1+2+3+4+...= -1\/2 This is called messing around with the concept of infinity. After a long thought...(I must if I were to consider myself a math major)...my concluding response … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,5],"tags":[],"class_list":["post-4517","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-news"],"_links":{"self":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4517","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4517"}],"version-history":[{"count":3,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4517\/revisions"}],"predecessor-version":[{"id":4520,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4517\/revisions\/4520"}],"wp:attachment":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4517"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4517"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}