{"id":309,"date":"2013-08-14T10:59:46","date_gmt":"2013-08-14T08:59:46","guid":{"rendered":"http:\/\/pvdm.xs4all.nl\/blog\/?p=309"},"modified":"2013-09-16T11:05:12","modified_gmt":"2013-09-16T09:05:12","slug":"some-simple-math-proving-0999999999-equals-1","status":"publish","type":"post","link":"https:\/\/www.reeltoreel.nl\/blog\/?p=309","title":{"rendered":"Some simple math&#8230;..proving 0,999999999 equals 1"},"content":{"rendered":"<p>I am going to prove to you, using standard algebra, that<\/p>\n<p style=\"padding-left: 30px\"><strong>0,99999999999&#8230;.. equals 1.<\/strong><\/p>\n<p>Now I know that if you have even a basic understanding of maths you say: &#8216;I know for sure that&#8217;s not true&#8217;, but I will show you otherwise.<\/p>\n<p>So here is the breakdown:<\/p>\n<ol>\n<ol>\n<li>let&#8217;s start by substituting\u00a0<strong>0,99999999999&#8230;..\u00a0<\/strong>with the letter <strong>a<\/strong>, so<\/li>\n<\/ol>\n<\/ol>\n<p style=\"padding-left: 30px\"><strong>a =\u00a0<strong>0,99999999999&#8230;..\u00a0<\/strong><\/strong><\/p>\n<p style=\"padding-left: 30px\">That is easy huh?<\/p>\n<p>\u00a02. now say 10 times <strong>a<\/strong> would mean<\/p>\n<p style=\"padding-left: 30px\"><strong>10a = 9,99999999999&#8230;..<\/strong><\/p>\n<p style=\"padding-left: 30px\">that is still right, right? I don&#8217;t believe that there is any need for discussion here.<\/p>\n<p>3. if we substract <strong>a<\/strong> from that, of course you have to do that on <span style=\"text-decoration: underline\">both<\/span> sides of the equal sign, we get:<\/p>\n<p style=\"padding-left: 30px\"><strong>10a &#8211; a =\u00a0<strong>9,99999999999&#8230;.. \u00a0&#8211; a<\/strong><\/strong><\/p>\n<p style=\"padding-left: 30px\">still a correct formula.<\/p>\n<p>4. <span style=\"text-decoration: underline\">10a &#8211; a<\/span> is of course <span style=\"text-decoration: underline\">9a<\/span>, so:<\/p>\n<p style=\"padding-left: 30px\"><strong>9a =\u00a0<strong>9,99999999999&#8230;.. \u00a0&#8211; a<\/strong><\/strong><\/p>\n<p>\u00a05. but since<span style=\"text-decoration: underline\"> a = 0,99999999999<\/span> the right side of the formula could be written as <span style=\"text-decoration: underline\">9<\/span><\/p>\n<p style=\"padding-left: 30px\"><strong>9a = 9<\/strong><\/p>\n<p>6. and that means that\u00a0<span style=\"text-decoration: underline\">a<\/span> must be\u00a0<span style=\"text-decoration: underline\">1<\/span><\/p>\n<p style=\"padding-left: 30px\"><strong>a = 1<\/strong><\/p>\n<p>7. combining step 1 and step 6 I have proven to you that<\/p>\n<p style=\"padding-left: 30px\"><strong>0,9999999999&#8230;.. = 1<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I am going to prove to you, using standard algebra, that 0,99999999999&#8230;.. equals 1. Now I know that if you have even a basic understanding of maths you say: &#8216;I know for sure that&#8217;s not true&#8217;, but I will show you otherwise. So here is the breakdown: let&#8217;s start by substituting\u00a00,99999999999&#8230;..\u00a0with the letter a, so [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-309","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/posts\/309","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=309"}],"version-history":[{"count":1,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/posts\/309\/revisions"}],"predecessor-version":[{"id":310,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=\/wp\/v2\/posts\/309\/revisions\/310"}],"wp:attachment":[{"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reeltoreel.nl\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}