{"id":169,"date":"2001-07-10T14:10:00","date_gmt":"2001-07-10T22:10:00","guid":{"rendered":"http:\/\/www.netjeff.com\/wp\/?p=169"},"modified":"2012-05-17T20:45:03","modified_gmt":"2012-05-18T03:45:03","slug":"a-classic-algebra-paradox","status":"publish","type":"post","link":"https:\/\/www.netjeff.com\/wp\/?p=169","title":{"rendered":"A classic algebra \"paradox\""},"content":{"rendered":"<p>Think about this one:<\/p>\n<table border=\"0\" cellspacing=\"2\" cellpadding=\"2\">\n<tbody>\n<tr>\n<td align=\"right\">a<\/td>\n<td align=\"center\">=<\/td>\n<td>b<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">a<sup>2<\/sup><\/td>\n<td align=\"center\" valign=\"bottom\">=<\/td>\n<td valign=\"bottom\">ab<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">a<sup>2<\/sup>-b<sup>2<\/sup><\/td>\n<td align=\"center\" valign=\"bottom\">=<\/td>\n<td>ab-b<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td align=\"right\">(a+b)(a-b)<\/td>\n<td align=\"center\">=<\/td>\n<td>b(a-b)<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">(a+b)<\/td>\n<td align=\"center\">=<\/td>\n<td>b<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">a+a<\/td>\n<td align=\"center\">=<\/td>\n<td>a<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">2a<\/td>\n<td align=\"center\">=<\/td>\n<td>a<\/td>\n<\/tr>\n<tr>\n<td align=\"right\">2<\/td>\n<td align=\"center\">=<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Once you understand the trick, you can \"prove\" anything you want, like 0=1 or 3=5.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Think about this one: a = b a2 = ab a2-b2 = ab-b2 (a+b)(a-b) = b(a-b) (a+b) = b a+a = a 2a = a 2 = 1 Once you understand the trick, you can \"prove\" anything you want, like 0=1 or 3=5.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-169","post","type-post","status-publish","format-standard","hentry","category-science"],"_links":{"self":[{"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/posts\/169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=169"}],"version-history":[{"count":1,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/posts\/169\/revisions"}],"predecessor-version":[{"id":935,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=\/wp\/v2\/posts\/169\/revisions\/935"}],"wp:attachment":[{"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.netjeff.com\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}