Download PDF by Louis Frécon: Eléments de mathématiques discrètes


By Louis Frécon

ISBN-10: 2880744792

ISBN-13: 9782880744793

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Tableau 1 . 1 Union, définition logique. aeX aeY ae XvY non non non non oui oui oui non oui oui oui oui y / \. - - - ....... _ _ _ Fig. 4 Diagramme d'une union XvY. PROPOSITIONS 1 . 1 4 - Quels que soient les ensembles E, F, G, on a : E v (F v G) = (E v F) v G = v {E, F, G} = E v F v G EvF=FvE EvE=E Ev0=0vE=E /associativité1 /conunutativité /idempotence /0 élément neutre 1 . 1 5 - Si les ensembles E et F sont finis : max( I E I , I F I ) � I E v F I :::; IE I + I F I . 1 . 1 6 - Si on a un référentiel R : E v F ç R, et si R est fini : I E v F I � IR I .


2 représente E par une tache plus ou moins régulière interne à celle représentant l'ensemble U dont E est une restriction. 2 E = { x E U 1 p(x) } => I EI � IU I 1 . 1 . 7 - L'e11semble vide ou ensemble à 0 élément, est noté 0 . 3 - 0 = { } et 1 0 1 = Fig. 1 . 1 Ensemble en compréhension. 0. En termes d'abstraction / compréhension, 0 est l'ensemble des objets réalisant un prédicat toujours faux. Ensembles & éléments 23 Nom. Logique et théorie des ensembles classiques reposent sur un principe de non­ contradiction.

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Eléments de mathématiques discrètes by Louis Frécon

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