{"id":217,"date":"2019-08-10T16:03:41","date_gmt":"2019-08-10T16:03:41","guid":{"rendered":"http:\/\/blog.atlant.is\/?p=217"},"modified":"2021-02-21T20:39:09","modified_gmt":"2021-02-21T18:39:09","slug":"theoreme-de-cantor-bernstein","status":"publish","type":"post","link":"https:\/\/blog.douzeb.is\/?p=217","title":{"rendered":"Th\u00e9or\u00e8me de Cantor Bernstein"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"683\" src=\"https:\/\/blog.atlant.is\/wp-content\/uploads\/2021\/02\/construction-of-a-bijection.jpg\" alt=\"\" class=\"wp-image-3530\" srcset=\"https:\/\/blog.douzeb.is\/wp-content\/uploads\/2021\/02\/construction-of-a-bijection.jpg 1024w, https:\/\/blog.douzeb.is\/wp-content\/uploads\/2021\/02\/construction-of-a-bijection-300x200.jpg 300w, https:\/\/blog.douzeb.is\/wp-content\/uploads\/2021\/02\/construction-of-a-bijection-768x512.jpg 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption><a href=\"http:\/\/budzynski.art\/projects\/84\/\">Construction of a bijection<\/a><\/figcaption><\/figure><\/div>\n\n\n\n<p>Soient <em>A<\/em> et <em>B<\/em> deux ensembles. Supposons l&rsquo;existence d&rsquo;une injection de <em>A<\/em> dans <em>B<\/em> et d&rsquo;une injection de <em>B<\/em> dans <em>A<\/em>. Alors <em>A<\/em> et <em>B<\/em> ont le m\u00eame cardinal.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p>Une d\u00e9monstration \u00e9l\u00e9mentaire est disponible <a href=\"https:\/\/en.wikipedia.org\/wiki\/Schr%C3%B6der%E2%80%93Bernstein_theorem#Proof\">ici<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Soient A et B deux ensembles. Supposons l&rsquo;existence d&rsquo;une injection de A dans B et d&rsquo;une injection de B dans A. Alors A et B ont le m\u00eame cardinal.<\/p>\n","protected":false},"author":1,"featured_media":3530,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[16],"tags":[],"ppma_author":[76],"authors":[{"term_id":76,"user_id":1,"is_guest":0,"slug":"fred","display_name":"Fred","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/ec0326d654fdf9f66e9eb42bb34a9bc4?s=96&d=mm&r=g","description":"","first_name":"","last_name":"","user_url":""}],"_links":{"self":[{"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/posts\/217"}],"collection":[{"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=217"}],"version-history":[{"count":3,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/posts\/217\/revisions"}],"predecessor-version":[{"id":3532,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/posts\/217\/revisions\/3532"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=\/wp\/v2\/media\/3530"}],"wp:attachment":[{"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=217"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/blog.douzeb.is\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}