{"id":613,"date":"2017-05-30T07:30:38","date_gmt":"2017-05-30T05:30:38","guid":{"rendered":"http:\/\/theory-of-science.com\/de\/?page_id=613"},"modified":"2021-02-04T16:38:44","modified_gmt":"2021-02-04T15:38:44","slug":"uebung-14-03","status":"publish","type":"page","link":"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-14\/uebung-14-03\/","title":{"rendered":"\u00dc14-3: Mengenvergleich"},"content":{"rendered":"\n<p>Seien <em>X<\/em> und <em>Y<\/em> endliche Mengen und <em>X<\/em>&nbsp;\u2286 <em>Y<\/em>. Wir bilden die Gr\u00f6\u00dfen \u2135 ( <em>X<\/em> ) und \u2135 ( <em>Y<\/em> ) und dividieren \u2135 ( <em>Y<\/em> ) durch \u2135 ( <em>X<\/em> ).<\/p>\n\n\n\n<p><strong>a)<\/strong> Wenn <em>X<\/em> genau 100 Elemente hat und <em>Y<\/em> 95 Elemente, formulieren Sie die Gr\u00f6\u00dfenverh\u00e4ltnisse von <em>X<\/em> und <em>Y<\/em> zahlenm\u00e4\u00dfig.<\/p>\n\n\n\n<p><strong>b)<\/strong> Zeichnen Sie beide Mengen und bilden Sie die Mengen <em>X<\/em>&nbsp;\u2229 <em>Y<\/em> und <em>X<\/em> \\ ( <em>X<\/em>&nbsp;\u2229 <em>Y<\/em> ) und stellen Sie das Verh\u00e4ltnis von <em>X<\/em> und <em>Y<\/em> zahlenm\u00e4\u00dfig dar. Analysieren Sie den Bruch \u2135 ( <em>X<\/em> \\ ( <em>X<\/em>&nbsp;\u2229 <em>Y<\/em> ) ) \/ \u2135 ( <em>X<\/em> ).<\/p>\n\n\n\n<p><strong>c)<\/strong> Wenn <em>X<\/em> 1000534 Elemente und <em>Y<\/em> 1000500 Elemente hat, bilden Sie die Ungleichung | \u2135 ( <em>X<\/em> ) &#8211; \u2135 ( <em>Y<\/em> ) | &lt; \u03b5. Wie gro\u00df muss die Zahl&nbsp;\u03b5 sein, um diese Ungleichung zu erf\u00fcllen?<br><\/p>\n\n\n<ul class=\"nav nav-pills nav-justified\">\n<li><a href=\"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-14\/uebung-14-02\/\">&lt;&lt;&lt;<\/a><\/li>\n<li><a href=\"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-14\/uebung-14-04\/\">&gt;&gt;&gt;<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Seien X und Y endliche Mengen und X&nbsp;\u2286 Y. Wir bilden die Gr\u00f6\u00dfen \u2135 ( X ) und \u2135 ( Y ) und dividieren \u2135 ( Y ) durch \u2135 ( X ). a) Wenn X genau 100 Elemente hat und Y 95 Elemente, formulieren Sie die Gr\u00f6\u00dfenverh\u00e4ltnisse von X und Y zahlenm\u00e4\u00dfig. b) Zeichnen [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":73,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"page-fullwidth.php","meta":{"footnotes":""},"class_list":["post-613","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/613","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/comments?post=613"}],"version-history":[{"count":7,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/613\/revisions"}],"predecessor-version":[{"id":4473,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/613\/revisions\/4473"}],"up":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/73"}],"wp:attachment":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/media?parent=613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}