{"id":12,"date":"2004-02-29T12:48:51","date_gmt":"2004-02-29T12:48:51","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=12"},"modified":"2007-03-22T17:08:44","modified_gmt":"2007-03-22T17:08:44","slug":"zero","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=12","title":{"rendered":"Zero"},"content":{"rendered":"<ol>\n<li>Why is <img src='\/maths\/latexrender\/pictures\/281b03a4f07dbc12ef3bc5263369ffcd.gif' title='0! = 1' alt='0! = 1' align=absmiddle> ?<\/li>\n<li>By looking at <img src='\/maths\/latexrender\/pictures\/08c75be5cdf8c2b9fffdff748da30455.gif' title='\\displaystyle\\lim_{x\\to 0}0^x' alt='\\displaystyle\\lim_{x\\to 0}0^x' align=absmiddle> and at <img src='\/maths\/latexrender\/pictures\/7b6d7d2de50af5de4a955436a135c064.gif' title='\\displaystyle\\lim_{x\\to 0}x^0' alt='\\displaystyle\\lim_{x\\to 0}x^0' align=absmiddle> what can you say about <img src='\/maths\/latexrender\/pictures\/601341530f30ffce8390632db2aa2e4f.gif' title='0^0' alt='0^0' align=absmiddle> ?<\/li>\n<li>Can <img src='\/maths\/latexrender\/pictures\/952fb7f45b1f8cce3431cc164ac8a41d.gif' title='\\sqrt[0]{x}' alt='\\sqrt[0]{x}' align=absmiddle> (<em>the zero<sup>th<\/sup> root of x<\/em>) be defined? If so, how; if not, why?<\/li>\n<li>Criticise the following &#8216;proof&#8217;: If <img src='\/maths\/latexrender\/pictures\/3a887b53f7ea2eb580eb21c51bbea577.gif' title='n\\in\\mathbb{Z}' alt='n\\in\\mathbb{Z}' align=absmiddle> then <img src='\/maths\/latexrender\/pictures\/a72fed8c7feac97270ca6bc98d1a0dc0.gif' title='\\displaystyle\\lim_{n\\to 0}\\frac{n}{n}=\\frac{\\displaystyle\\lim_{n\\to 0}n}{\\displaystyle\\lim_{n\\to 0}n}=\\frac{0}{0}=1' alt='\\displaystyle\\lim_{n\\to 0}\\frac{n}{n}=\\frac{\\displaystyle\\lim_{n\\to 0}n}{\\displaystyle\\lim_{n\\to 0}n}=\\frac{0}{0}=1' align=absmiddle><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Why is ? By looking at and at what can you say about ? Can (the zeroth root of x) be defined? If so, how; if not, why? Criticise the following &#8216;proof&#8217;: If then<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-12","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/12","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/12\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}