{"id":232642,"date":"2022-03-28T17:20:10","date_gmt":"2022-03-28T15:20:10","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=232642"},"modified":"2025-09-29T11:27:16","modified_gmt":"2025-09-29T09:27:16","slug":"cardinal-dun-ensemble-fini","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/cardinal-dun-ensemble-fini\/","title":{"rendered":"Comprendre le cardinal d’un ensemble fini"},"content":{"rendered":"\n

Voici un cours qui te permettra de comprendre le cardinal d’un ensemble fini<\/strong>. Tu trouveras toutes les d\u00e9finitions et les propositions indispensables pour assimiler parfaitement cette notion math\u00e9matiques.<\/p>\n\n\n\n

Poursuis ta d\u00e9couverte avec des cours particuliers de maths<\/a><\/strong>, te plongeant dans le monde fascinant du d\u00e9nombrement pour devenir un as du calcul du cardinal d’ensembles finis. \ud83c\udfb2<\/p>\n\n\n\n

G\u00e9n\u00e9ralit\u00e9s<\/h2>\n\n\n\n

D\u00e9finition d’un ensemble fini \/ infini<\/h3>\n\n\n\n\n
  • Un ensemble \"E\" est fini s’il est vide ou s’il existe \"n\in\mathbb{N}^{*}\". <\/li>\n
  • Un ensemble non fini est un ensemble infini.<\/li>\n\n\n\n

    Remarque<\/strong><\/p>\n\n\n\n\nQuitte \u00e0 consid\u00e9rer la bijection r\u00e9ciproque, la d\u00e9finition est \u00e9quivalente \u00e0 dire qu\u2019il existe une bijection de \"E\" sur \"[\![1;\"n\"]\!]\".\n\n\n\n

    Bien qu’intuitive, on admet la proposition suivante.<\/p>\n\n\n\n

    Proposition : Cardinal d’un ensemble fini<\/h3>\n\n\n\n\nSoit \"E\" un ensemble fini non vide. Il existe un unique entier naturel \"n\in\mathbb{N}^{*}\" tel que \"E\" puisse \u00eatre mis en bijection avec \"[\![1;\"n\"]\!]\".\nCet unique entier s’appelle le cardinal de \"E\" et est not\u00e9 \"|E|\", card(\"E\") ou encore #\"E\".\n\n\n\n

    Proposition <\/h3>\n\n\n\n\nSoient \"E\" et \"F\" deux ensembles finis.\n\"E\" et \"F\" ont le m\u00eame cardinal si, et seulement si, il existe une bijection de \"E\" sur \"F\".\n\n\n
    \n

    Conseils m\u00e9thodologiques \ud83d\udca1<\/p>\n<\/div>\n

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    Cette proposition r\u00e9sume \u00e0 elle seule tout l’art du d\u00e9nombrement. D\u00e9nombrer un ensemble, c’est trouver une bijection entre un autre ensemble plus facile \u00e0 d\u00e9nombrer.<\/p>\n\n <\/div>\n <\/section>\n\n\n\n

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    \"livre<\/figure>\n<\/div>\n\n\n\n
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    Cet article est extrait de l’ouvrage Maths MPSI-MP2I. Tout-en-un : cours, m\u00e9thodes, entra\u00eenement et corrig\u00e9s <\/em>(\u00e9ditions Vuibert, juin 2021) <\/em>\u00e9crit par E. Thomas, S. Bellec, G. Boutard. ISBN n\u00b09782311408720<\/em><\/p>\n<\/div>\n<\/div>\n\n\n

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    \n 3\/5 - (2 votes) <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

    Voici un cours qui te permettra de comprendre le cardinal d’un ensemble fini. Tu trouveras toutes les d\u00e9finitions (…)<\/p>\n","protected":false},"author":158,"featured_media":244282,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":""},"category":[803,810],"tag":[78,345],"class_list":["post-232642","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-prepa","tag-prepa-scientifique"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/232642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/158"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=232642"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/232642\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/244282"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=232642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=232642"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=232642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}