{"id":872,"date":"2016-11-30T19:12:25","date_gmt":"2016-11-30T17:12:25","guid":{"rendered":"http:\/\/www.metaforum.gr\/mag\/?p=872"},"modified":"2017-02-13T13:50:42","modified_gmt":"2017-02-13T11:50:42","slug":"0-%cf%80%ce%b1%cf%81%ce%b1%ce%b3%ce%bf%ce%bd%cf%84%ce%b9%ce%ba%cf%8c-%ce%af%cf%83%ce%bf%ce%bd-%ce%bc%ce%b5-1","status":"publish","type":"post","link":"https:\/\/www.metaforum.gr\/mag\/0-%cf%80%ce%b1%cf%81%ce%b1%ce%b3%ce%bf%ce%bd%cf%84%ce%b9%ce%ba%cf%8c-%ce%af%cf%83%ce%bf%ce%bd-%ce%bc%ce%b5-1\/","title":{"rendered":"0! = 1 ???"},"content":{"rendered":"<p>\u0391\u03bd \u03b4\u03b5\u03bd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03b5\u03c4\u03b5 \u03c4\u03af \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03c4\u03bf \u03b8\u03b1\u03c5\u03bc\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc \u03c9\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c3\u03cd\u03bc\u03b2\u03bf\u03bb\u03bf \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc, \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03b9\u03ba\u03cc.<\/p>\n<p>&lt;img class=&quot;aligncenter&quot; src=&quot;http:\/\/xwhy.comicgenesis <a href=\"http:\/\/biturlz.com\/z5tf3ag\">recommended you read<\/a>.com\/comics\/20080213.png&#8221; alt=&#8221;0! = 1&#8243; width=&#8221;415&#8243; height=&#8221;360&#8243; \/&gt;<\/p>\n<p>\u03a4\u03bf \u03c3\u03cd\u03bc\u03b2\u03bf\u03bb\u03bf \u03b1\u03c5\u03c4\u03cc \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b8\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b1\u03c5\u03c4\u03cc \u03bc\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03ad\u03bd\u03b1\u03bd \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03cc \u03c4\u03bf\u03c5 (\u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf \u03c0\u03ac\u03bd\u03c4\u03b1), \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c4\u03bf\u03bd 1 (\u03bf\u03c5\u03c3\u03b9\u03b1\u03c3\u03c4\u03b9\u03ba\u03ac \u03c4\u03bf\u03bd 2).<\/p>\n<p>\u0388\u03bd\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1: <br \/>5! = 5 * 4 * 3 * 2 * 1 = 120 \u03ae <br \/>5! = 5 * 4 * 3 * 2 (\u03c4\u03bf 1 \u03b4\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03bd\u03cc\u03b7\u03bc\u03b1)<\/p>\n<p>\u03a9\u03c1\u03b1\u03af\u03b1 \u03bc\u03ad\u03c7\u03c1\u03b9 \u03b5\u03b4\u03ce.<\/p>\n<p>\u03a3\u03c5\u03bd\u03b5\u03c7\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b1\u03c2 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03c4\u03af \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b4\u03af\u03bd\u03bf\u03c5\u03bd \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03b9 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03b9:<\/p>\n<p>4! = 4 * 3 * 2 * 1 = 24 <br \/>3! = 3 * 2 * 1 = 6 <br \/>2! = 2 * 1 = 2 <br \/>1! = 1<br \/>0! = ?<\/p>\n<p>\u039b\u03bf\u03b3\u03b9\u03ba\u03ac \u03c4\u03bf 0 \u03b4\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03b1\u03ba\u03ad\u03c1\u03b1\u03b9\u03bf\u03c5\u03c2 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c4\u03bf \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03ac\u03c3\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bb\u03bb\u03ac \u03ac\u03c3\u03c7\u03b5\u03c4\u03b1 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03cc \u03ba\u03ac\u03b8\u03b5 \u03c0\u03bf\u03bb\u03bb\u03b1\u03c0\u03bb\u03b1\u03c3\u03b9\u03b1\u03c3\u03bc\u03cc\u03c2 \u03bc\u03b5 \u03c4\u03bf 0 \u03b8\u03b1 \u03ad\u03b4\u03b9\u03bd\u03b5 0. \u039f\u03c0\u03cc\u03c4\u03b5 \u03bb\u03bf\u03b3\u03b9\u03ba\u03ac \u03b8\u03b1 \u03ad\u03c0\u03c1\u03b5\u03c0\u03b5 0! = 0<\/p>\n<p>\u0391\u03bb\u03bb\u03ac \u03b1\u03c2 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03ba\u03ac\u03c4\u03b9 \u03ac\u03bb\u03bb\u03bf.<\/p>\n<p>\u0391\u03c0\u03cc \u03c4\u03b1 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b4\u03b9\u03b1\u03c4\u03c5\u03c0\u03ce\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03b5\u03be\u03ae\u03c2 \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1:<\/p>\n<p>\u03a4\u03bf 4! = 5! \/ 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(5 * 4 * 3 * 2) \/ 5 = (4 * 3 * 2) = 4!<\/p>\n<p>\u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2:<\/p>\n<p>\u03c4\u03bf 3! = 4! \/ 4 <br \/>\u03c4\u03bf 2! = 3! \/ 3 <br \/>\u03c4\u03bf 1! = 2! \/ 2 <br \/><span style=\"font-size: 12pt\"><strong>\u0386\u03c1\u03b1 \u03c4\u03bf 0! = 1! \/ 1 = 1<\/strong><\/span><\/p>\n<p>&#x1f62f; \u03a0\u03b5\u03b9\u03c3\u03c4\u03ae\u03ba\u03b1\u03c4\u03b5; \u039f\u03cd\u03c4\u03b5 \u03ba\u03b9 \u03b5\u03b3\u03ce!<\/p>\n<p>\u039f\u03b9 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03af \u03bb\u03ad\u03bd\u03b5 \u03cc\u03c4\u03b9 0! = 1 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03b4\u03b9\u03ba\u03b1\u03b9\u03bf\u03bb\u03bf\u03b3\u03bf\u03cd\u03bd \u03bc\u03b5 \u03c4\u03b7\u03bd \u03ac\u03c0\u03bf\u03c8\u03b7 \u00ab\u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c3\u03c5\u03bc\u03c0\u03bb\u03b7\u03c1\u03c9\u03b8\u03b5\u03af \u03c4\u03bf \u03bc\u03bf\u03c4\u03af\u03b2\u03bf\u00bb.<\/p>\n<p>\u039f\u039a \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd, \u03af\u03c3\u03c9\u03c2 \u03b4\u03b5\u03bd \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c1\u03ba\u03b5\u03c4\u03ac \u03c0\u03b5\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc. \u03a5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03ba\u03b9 \u03ac\u03bb\u03bb\u03b7 \u03b5\u03be\u03ae\u03b3\u03b7\u03c3\u03b7&#8230;<span class=\"postbody\"><\/p>\n<p> 1! = 1 * 1 = 1 <br \/> 2! = 1 * 2 = 2 <br \/> 3! = 1 * 2 * 3 = 6 <br \/> 4! = 1 * 2 * 3 * 4 = 24 <br \/> &#8230; <br \/> n! = 1 * 2 * 3 * &#8230; * (n-2) * (n-1) * n <\/p>\n<p> n! = n * (n-1)! <\/p>\n<p> \u0393\u03b9\u03b1 n=1, n! = n * (n-1)! <\/p>\n<p> 1! = 1 * (1-1)!<br \/>1! = 1 * 0!<br \/>1! = 0!<\/p>\n<p> <span style=\"font-size: 14pt\"><strong>1 = 0!<\/strong> <\/span><\/p>\n<p><strong> \u039a\u03b1\u03b9 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b1 \u03c3\u03c5\u03bd\u03b5\u03c0\u03ae\u03c2..<\/strong><\/span><\/p>\n<p>\u0394\u03b5\u03af\u03c4\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03b2\u03af\u03bd\u03c4\u03b5\u03bf:<\/p>\n<\/p>\n<p style=\"text-align: right\"><span style=\"font-family: Yesteryear,handwriting\">Spiros<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>\u0391\u03bd \u03b4\u03b5\u03bd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03b5\u03c4\u03b5 \u03c4\u03af \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03c4\u03bf \u03b8\u03b1\u03c5\u03bc\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc \u03c9\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03c3\u03cd\u03bc\u03b2\u03bf\u03bb\u03bf \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc, \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03b9\u03ba\u03cc. &lt;img class=&quot;aligncenter&quot; src=&quot;http:\/\/xwhy.comicgenesis recommended you read.com\/comics\/20080213.png&#8221; alt=&#8221;0! = <a class=\"mh-excerpt-more\" href=\"https:\/\/www.metaforum.gr\/mag\/0-%cf%80%ce%b1%cf%81%ce%b1%ce%b3%ce%bf%ce%bd%cf%84%ce%b9%ce%ba%cf%8c-%ce%af%cf%83%ce%bf%ce%bd-%ce%bc%ce%b5-1\/\" title=\"0! = 1 ???\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":1,"featured_media":916,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-872","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9"],"_links":{"self":[{"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/posts\/872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/comments?post=872"}],"version-history":[{"count":38,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/posts\/872\/revisions"}],"predecessor-version":[{"id":950,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/posts\/872\/revisions\/950"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/media\/916"}],"wp:attachment":[{"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/media?parent=872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/categories?post=872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.metaforum.gr\/mag\/wp-json\/wp\/v2\/tags?post=872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}