{"id":1821,"date":"2017-11-02T09:49:55","date_gmt":"2017-11-02T09:49:55","guid":{"rendered":"http:\/\/www.wolof-online.com\/?p=1821"},"modified":"2017-12-08T11:47:36","modified_gmt":"2017-12-08T11:47:36","slug":"seex-anta-joob-xayma-ci-wolof-la-heorie-des-ensembles","status":"publish","type":"post","link":"https:\/\/www.wolof-online.com\/?p=1821","title":{"rendered":"Seex Anta J\u00f3ob: Xayma ci Wolof – La h\u00e9orie des Ensembles"},"content":{"rendered":"

\"\"<\/a>Ensembles \u00e9quivalents<\/p>\n

Deux ensembles M et N sont \u00e9quivalents si \u00e0 un \u00e9l\u00e9ment de M correspond un \u00e9l\u00e9ment et un seul de N, et r\u00e9ciproquement. Le caract\u00e8re commun \u00e0 tous les ensembles \u00e9quivalents est leur nombre cardinal (leur cardinal), leur puissance, c\u2019est-\u00e0-dire le nombre de leurs \u00e9l\u00e9ments.<\/p>\n

Faramf\u00e0cce Mboole yi<\/em><\/strong>
\nMboole weccikoo<\/em><\/strong><\/p>\n

\u00d1aari mboole M ak N weccikoo na\u00f1u, su fekkee ne doom boo j\u00ebl ci M m\u00ebn koo m\u00e9ngale ak benn doom kott ci N, te boo tukkee ci doomi N wuti yoy M, ba tey muy noonu. M\u00e0ndarga mi mboole yu weccikoo bokk mooy seen limub dayo (seenub dayo), seen k\u00e0ttan, maanaam seen doom yi, menn mu nekk ci \u00f1oom.<\/em><\/strong><\/p>\n

ENSEMBLES INFINIS ; NOMBRES CARDINAUX TRANSFINIS<\/p>\n

Soit : N = { 1, 2, 3, \u2026 } l\u2019ensemble des nombres naturels et soit G { 2, 4, 6, \u2026 } l\u2019ensemble des nombres positifs pairs. Si x d\u00e9signe un \u00e9l\u00e9ment de N et y l\u2019\u00e9l\u00e9ment de G qui lui correspond, la fonction qui r\u00e9alise l\u2019application de N sur G est y = 2 x ; cette fonction fait correspondre \u00e0 tout nombre naturel d\u2019une mani\u00e8re biunivoque un nombre positif pair. Les ensembles N et G sont \u00e9quivalents, ont m\u00eame puissance, m\u00eame nombre cardinal. Il e\u00fbt \u00e9t\u00e9 impossible de tenter d\u2019\u00e9tablir ce th\u00e9or\u00e8me en comptant les \u00e9l\u00e9ments respectifs des deux ensembles infinis, d\u2019o\u00f9 l\u2019int\u00e9r\u00eat de la notion d\u2019ensemble \u00e9quivalent qui permet d\u2019\u00e9tablir l\u2019\u00e9galit\u00e9 de deux infiniment grands.<\/p>\n

MBOOLE YU G\u00c0PPUWUL ; LIMI DAYO YU J\u00c9GGIB G\u00c0PP<\/em><\/strong><\/p>\n

Nanu tudde N = { 1, 2, 3, \u2026 } mbooleem limi \u00ab judduwaale \u00bb yi ; na G = { 2, 4, 6. \u2026 } nekk mbooleem \u00ab lim yi \u00ebpp tus \u00bb te t\u00f3olu\u00f1u. Su X dee doomub N, y di doomub G bi m\u00e9ngook X, \u00ab aju \u00bb giy joxe d\u00ebppug N ci G mooy y = 2 x ; aju googu day m\u00e9ngale limub judduwaale bu nekk ak benn lim bu \u00ebpp tus te t\u00f3olul, m\u00e9ngaleliin wu bennante. \u00d1aari mboole yi di N ak G weccikoo na\u00f1u seen k\u00e0ttan, niki seen limub dayo tolloo. \u00ab D\u00ebgguy matematig \u00bb googu, ku b\u00ebggoon a tukkee ci, w\u00e0\u00f1\u00f1 doomi N ak G yi di mboole yu g\u00e0ppoodiku doo ko m\u00ebn a wone. Xalaatul mboole weccikoo yi, li tax m\u00ebneef a wone yemug \u00f1aari lim yu g\u00e0ppoodiku, kon am na njari\u00f1.<\/em><\/strong><\/p>\n

ENSEMBLES FINIS ET INFINIS : d\u00e9finition de DEDEKIND<\/p>\n

L\u2019\u00e9quivalence des ensembles N et G fait appara\u00eetre une propri\u00e9t\u00e9 surprenante des ensembles infinis. G est un sous-ensemble v\u00e9ritable de N et pourtant G est \u00e9quivalent \u00e0 N, ce que nous traduisons par les relations :
\nG \u00cc N\u00a0\u00a0 ;\u00a0\u00a0 G ~ N<\/p>\n

MBOOLE YU G\u00c0PPU, AK YU G\u00c0PPOODIKU : D\u00c9EGIINU DEDEKIND<\/strong><\/em><\/p>\n

Weccikoo mbooley N ak G fee\u00f1al na ne mboole yu g\u00e0ppoodiku yi am na\u00f1u moomeel gu doy waar ndax G mboole \u00ebmbu d\u00ebgg ci N la te terewul mu weccikoo ak N, ba tax m\u00ebneef a bind :<\/strong><\/em>
\nG \u00cc N\u00a0\u00a0\u00a0 ;\u00a0\u00a0\u00a0 G ~ N<\/strong><\/em><\/p>\n

alors que pour les ensembles finis la relation d\u2019inclusion A \u00cc B est incompatible avec la relation d\u2019\u00e9quivalence A ~ B d\u2019o\u00f9 les d\u00e9finitions de DEDEKIND : \u00ab S\u2019il n\u2019existe aucun sous-ensemble v\u00e9ritable de M qui soit \u00e9quivalent \u00e0 M, M est un ensemble fini. S\u2019il existe un sous-ensemble v\u00e9ritable de M \u00e9quivalent \u00e0 M, M est un ensemble infini. \u00bb
\nTe su doon mboole yu g\u00e0ppu joteb \u00ebmbe bii, A\u00cc B, du m\u00ebn a nekkandoo d\u00ebgg ak joteb weccikoo bii A~B : lii tax Dedekind joxe d\u00e9egiin yii : \u00ab Bu amul menn mboole mu ndaw mu \u00ebmbu ci M mom d\u00ebgg mu weccikoo ak M, M mboole mu g\u00e0ppu la. Su amee am mboole mu ndaw mu \u00ebmbu ci M mom d\u00ebgg mu weccikoo ak M, M mboole mu g\u00e0ppoodiku la \u00bb.<\/strong><\/em><\/p>\n

Th\u00e9or\u00e8me.<\/p>\n

L\u2019ensemble des nombres naturels :<\/p>\n

N = { 1, 2, 3, \u2026 }<\/p>\n

et l\u2019ensemble des nombres positifs impairs :<\/p>\n

U = { 1, 3, 5, \u2026 }<\/p>\n

sont \u00e9quivalents en vertu de l\u2019application :<\/p>\n

u = 2 n _ 1<\/p>\n

qui, \u00e0 tout \u00e9l\u00e9ment n de N, fait correspondre un \u00e9l\u00e9ment u de U.<\/p>\n

D\u00ebggug matematig<\/em><\/strong><\/p>\n

Mbooleem limi judduwaale yi :<\/em><\/strong><\/p>\n

N = \u00d1 { 1, 2, 3, \u2026 }<\/em><\/strong><\/p>\n

ak mbooleem lim yi \u00ebpp tus te t\u00f3ol :<\/em><\/strong><\/p>\n

U = { 1, 3, 5, \u2026 }<\/em><\/strong><\/p>\n

weccikoo na\u00f1u ndax d\u00ebppaleyiin wii :<\/em><\/strong>
\nU = 2 n _ 1<\/em><\/strong><\/p>\n

biral na ne doomub N bu ne di (n) m\u00e9ngaloo na ak doomub U di (u).<\/em><\/strong><\/p>\n

Des ensembles finis \u00e9quivalents sont caract\u00e9ris\u00e9s par le m\u00eame nombre cardinal. Ces nombres cardinaux (finis) sont les nombres naturels qu\u2019on discerne en comptant les \u00e9l\u00e9ments de l\u2019ensemble. Des ensembles infinis \u00e9quivalents (de m\u00eame puissance) sont caract\u00e9ris\u00e9s \u00e9galement par des nombres cardinaux \u00e9gaux appel\u00e9s transfinis. Ces nombres cardinaux transfinis constituent une extension des nombres naturels.<\/p>\n

Mboole yu g\u00e0ppu te weccikoo m\u00e0ndargawoo na\u00f1u seen limub dayo yem di benn : limi dayo yu g\u00e0ppu yooyu \u00f1ooy limi judduwaale yees di nemmiku bees di wa\u00f1\u00f1 doomi mboole yi. Mboole yu g\u00e0ppoodiku te weccikoo (maanaam yem k\u00e0ttan) m\u00e0ndargawoo na\u00f1u \u00f1oom it limi dayo yu yem, yu nu tudde lim yu g\u00e0ppoodiku ; limi dayo yu g\u00e0ppoodiku yooyu yaatal na\u00f1u limi\u00a0 judduwaale yi.<\/p>\n

Jukk bi: http:\/\/osad.sn<\/p>\n","protected":false},"excerpt":{"rendered":"

Ensembles \u00e9quivalents Deux ensembles M et N sont \u00e9quivalents si \u00e0 un \u00e9l\u00e9ment de M correspond un \u00e9l\u00e9ment et un seul de N, et r\u00e9ciproquement. Le caract\u00e8re commun \u00e0 tous les ensembles \u00e9quivalents est leur nombre cardinal (leur cardinal), leur puissance, c\u2019est-\u00e0-dire le nombre de leurs \u00e9l\u00e9ments. Faramf\u00e0cce Mboole yi Mboole weccikoo \u00d1aari mboole M…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1,16],"tags":[],"_links":{"self":[{"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/posts\/1821"}],"collection":[{"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1821"}],"version-history":[{"count":6,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/posts\/1821\/revisions"}],"predecessor-version":[{"id":1851,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=\/wp\/v2\/posts\/1821\/revisions\/1851"}],"wp:attachment":[{"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wolof-online.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}