{"id":7253,"date":"2022-11-02T21:40:48","date_gmt":"2022-11-02T21:40:48","guid":{"rendered":"https:\/\/presswiki.allmath.gr\/wpwiki18\/?p=7253"},"modified":"2022-11-02T22:12:03","modified_gmt":"2022-11-02T22:12:03","slug":"%ce%b4%cf%85%ce%bd%ce%ac%ce%bc%ce%b5%ce%b9%cf%82-%ce%ac%cf%81%cf%81%ce%b7%cf%84%cf%89%ce%bd","status":"publish","type":"post","link":"https:\/\/presswiki.allmath.gr\/wpwiki18\/2022\/11\/02\/21\/40\/48\/7253\/","title":{"rendered":"\u0394\u03c5\u03bd\u03ac\u03bc\u03b5\u03b9\u03c2 \u03ac\u03c1\u03c1\u03b7\u03c4\u03c9\u03bd&#8230;"},"content":{"rendered":"\n<p>\u039d\u03b1 \u03b5\u03be\u03b5\u03c4\u03b1\u03c3\u03c4\u03b5\u03af \u03b1\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03ac\u03c1\u03c1\u03b7\u03c4\u03bf\u03b9 \\( a,b \\in  \\mathbb{R}-\\mathbb{Q} \\), \u03ce\u03c3\u03c4\u03b5 \\( a^b \\in \\mathbb{Q} \\)<\/p>\n\n\n\n<p><\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h2>\u03a3\u03ba\u03ad\u03c8\u03b7<\/h2>\n\n\n\n<p>\u0398\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \\(a=b=\\sqrt{2}\\) \u03ba\u03b1\u03b9  \\( \\sqrt{2}^{\\sqrt{2}}  \\in \\mathbb{Q} \\), \u03c4\u03cc\u03c4\u03b5 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b6\u03b7\u03c4\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2.<\/p>\n\n\n\n<p>\u0391\u03bd \\( \\sqrt{2}^{\\sqrt{2}}  \\not \\in \\mathbb{Q} \\) \u03b8\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc  <\/p>\n\n\n\n<p>\\(  \\left( \\sqrt{2}^{\\sqrt{2}} \\right)^{\\sqrt{2}} =   \\left( \\sqrt{2}^{\\sqrt{2}\\cdot \\sqrt{2}} \\right)  = \\sqrt{2} ^ 2 = 2\\)<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>\u039f\u03c0\u03cc\u03c4\u03b5 \u03c3&#8217;\u03b1\u03c5\u03c4\u03ae\u03bd \u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \\( a = \\sqrt{2}^{\\sqrt{2}} , b = \\sqrt{2} \\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u039d\u03b1 \u03b5\u03be\u03b5\u03c4\u03b1\u03c3\u03c4\u03b5\u03af \u03b1\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03ac\u03c1\u03c1\u03b7\u03c4\u03bf\u03b9 \\( a,b \\in \\mathbb{R}-\\mathbb{Q} \\), \u03ce\u03c3\u03c4\u03b5 \\( a^b \\in \\mathbb{Q} \\)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/7253"}],"collection":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/comments?post=7253"}],"version-history":[{"count":5,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/7253\/revisions"}],"predecessor-version":[{"id":7260,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/7253\/revisions\/7260"}],"wp:attachment":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/media?parent=7253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/categories?post=7253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/tags?post=7253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}