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d’un nombre est le résultat de la multiplication de ce nombre, par son prédecesseur, lui même multiplié par son prédécesseur et ainsi jusqu’a multiplier par 1. La factorielle est définie, ou calculable seulement pour les nombres entiers positifs (plus grands viagra super active plus review ou égaux à kamagra vs viagra 0). La factorielle d’un nombre n s’écrit en raccourci n!
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Et bien les mathématiciens nous disent et même nous démontrent (mais ce n’est pas l’objet ici) que ce n’était pas la peine de ce fatiguer pour 3 couleurs il y a FACTORIELLE 3 combinaisons !
Sur cet exemple simple on s’en sortait assez bien sans connaitre factorielle, mais en exercice amusez vous à faire la liste de toutes les combinaisons possible des 4 couleurs viagra from canada reviews R,V,B et J (Jaune). Vous savez maintenant, qu’il y en a 4! = 24 c’est déjà pas mal…

Factorielle une fonction (vraiment) récursive


Si on regarde de près on s’aperçoit que pour calculer le 6! précédent on aurait pu moins se fatiguer (il est de notoriété publique que les plus canada pharmacy online feinéants sont les plus intelligents). 5! c’est par définition 5 x 4 x 3 x 2 x 1 mais on a vu que 4! = 4 x 3 x 2 x 1 donc 5! n’est pas autre chose que 5 x 4! c’est tout de même plus facile à écrire. C’est aussi plus facile à calculer quand on connait 4!
En résumé la factorielle peut toujours se définir cialis en fonction de la factorielle précédente. Et si factorielle se définit grace…à factorielle c’est bien une fonction auto référente : 10! = 10 x 9! 45! = 45 x 44! 1230! = 1230 x 1229! etc.

Définition générale de factorielle

nous ne nous intéressons plus ici à des over the counter products like viagra exemples de résultat de facoriellel pour un nombre précis, mais à factorielle pour un nombre pulmonary hypertension treatment viagra quel qu’il soit que nous appelleront ‘n’ .

Définition complète ou cialis exhaustive ( »en extension » disent les matheux)
D’après les quelques xexmples des paragraphes précédents on peutrapidement déduire que :

n! = n x (n-1) x (n-2) x (n-3) x …………………………..x 3 x 2 x1


Définition compacte ou récursive ( »en compréhension » disent les matheux)

n! = n x (n -1)! et 0! = 1

C’est la définition que nous retiendrons. Mais est elle vraiment

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essayons de (re) calculer 4! avec cette simple définition :

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Cette définition récursive très courte à donc suffi à calculer de manière mécanique 4! , mais pour cela il a fallu conserver toutes les étapes intermédiaires du calcul pour pouvoir « remonter le calcul à l’envers ». En d’autres termes (plus utilisés en informatique) à chaque fois, factorielle s’appelle elle même genericviagra-toprxstore.com mais avec des valeurs différentes, dans un contexte différent.
Il est très important de noter ici encore que :

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  • si nous n’avions pas connu au moins une valeur de factorielle, en l’occurence 0! =1 , ce processus d’auto appel de factorielle se serait sans doute arrété mais n’aurait pas
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Bach, les canons et les fugues…AUtoréférence et récursion musicale

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Il fut un musicien complet qui maîtrisait la facture des instruments tout autant que la technique instrumentale, la composition comme l’improvisation, la pédagogie comme la gestion d’une institution musicale.

d’apres Wikipedia online viagra : http://fr.wikipedia.org/wiki/Bach


Un canon est une forme musicale polyphonique ainsi qu’un procédé compositionel basé sur l’imitation, dans lequel une idée musicale — le thème cialis online — s’énonce et se développe d’une voix à une

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  • Les différentes parties d’un canon peuvent se succéder à l’unisson — cas le plus répandu —, mais également à d’autres intervalles — octave ou quinte, principalement.
  • Exemple de la chanson enfantine Frère Jacques ; début du canon :


d’apres Wikipedia : http://fr.wikipedia.org/wiki/Canon_(musique)

/wiki/Fugue#Un_pas_de_plus_vers_la_fugue_:_le_canon )

La fugue

La http://cialisonline-online4rx.com/ fugue dans sa forme conventionnelle actuelle, c’est-à-dire telle que l’a léguée Bach, est en soi la résolution d’un problème de structure et de cohérence non résolu par les formes préexistantes. Le ricercare, le motet et autres formes anciennes souffraient d’un manque d’unité

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On a effectivement ici un cercle vicieux, dans la mesure où l’un des personnages de l’histoire trompe sa femme AKA ‘la sorcière’ de manière éhontée :

Un directeur de société, appelle sa secrétaire et lui dit :
- Vanessa, j’ai un séminaire à Rome pendant une semaine et je veux que vous m’accompagniez. Vous connaîtrez ainsi mieux notre société et nos associés… Veuillez préparer le voyage, s’il vous plaît.
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Aussitôt Philippe, le mari de Vanessa, appelle sa maîtresse et lui dit :
- Florence, mon trésor, la sorcière part à l’étranger pendant une semaine. Nous aurons une semaine tout à nous ma reine…
La maîtresse Florence, appelle aussitôt l’élève auquel elle donne des cours particuliers et lui dit :
- Manuel, j’ai beaucoup trop de travail la semaine prochaine, je ne pourrais pas assurer tes cours particuliers. Ne viens pas en cours
Manuel appelle son grand-père et lui dit :
- Grand-père, la semaine prochaine je n’ai pas cours. Mon professeur Florence a beaucoup de travail. Cela tombe bien, on va, enfin, pouvoir passer une semaine ensemble.
Le grand-père (qui n’est autre que le Directeur de cette histoire) rappelle sa secrétaire Vanessa et lui dit :
- Vanessa, suspendez la préparation du voyage à Rome, je vais passer la semaine prochaine en compagnie de mon petit-fils que je n’ai pas vu depuis bien longtemps. Nous n’irons pas au séminaire. Annulez toutes les réservations, hôtel, avion,etc.
La secrétaire rappelle son mari et lui dit :
- Philippe, ce clown de directeur a changé d’avis, il vient d’annuler le voyage. Rome c’est fichu.
Le mari rappelle aussitôt sa maîtresse, Florence, et  lui dit :
- Mon amour, excuse moi, nous ne passerons pas la semaine prochaine ensemble. Le voyage de ma « conne » de femme a été annulé !
Le professeur appelle aussitôt son élève Manuel et lui dit :
- Manuel, écoute bien, j’ai pu arranger mon emploi du temps. La semaine prochaine je pourrai assurer tes cours particuliers habituels.
Le garçon rappelle son grand-père (le directeur de société) et lui dit :
- Grand père, cette « lourdasse » de professeur vient de me dire que la semaine prochaine elle pourra me dispenser ses cours particuliers ! Excuse-moi, je ne pourrais pas passer la semaine prochaine en ta compagnie.
Le grand-père (directeur) rappelle sa secrétaire et lui dit :
- Mon petit-fils Manuel vient de me dire qu’il ne pourra pas être avec moi la semaine prochaine : Il reprend ses cours. Reprenez la préparation du voyage, les réservations pour le séminaire à Rome : Nous y allons !!!

Merci à Olivier qui m’a transmis cette histoire.

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