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Logique Et Raisonnements Mathématiques
Paperback
Series: Mathematiques, Book 185
Publisher: Mathema
Published: Dec 21 2025
Pages: 188
Weight: 0.99
Height: 0.40 Width: 8.50 Depth: 11.00
Language: French
LOGIQUE ET RAISONNEMENTS MATHÉMATIQUES
Cet ouvrage, entièrement révisé dans cette seconde édition, présente la théorie de la démonstration en tant que discipline et en tant qu'outil. Les premiers chapitres présentent les bases du raisonnement mathématique et la syntaxe associée au calcul des énoncés. La deuxième partie traite plus particulièrement de la théorie de la démonstration, discipline à part entière des mathématiques. Des énoncés d'exercices avec leurs corrigés sont proposés en fin de chapitres.
Ce cours ne sera pas non plus un apprentissage de l'art de raisonner en mathématique. La logique des mathématiques repose sur le présupposé d'une aptitude commune à raisonner qui nous permet de communiquer et de convaincre qu'un raisonnement est correct. S'il existe bien un raisonnement mathématique, il s'élabore sur une spécialisation du raisonnement commun dans le contexte des mathématiques. Ses spécificités s'acquièrent d'abord ... par la pratique des mathématiques (y compris bien-sûr la pratique de la logique mathématique), même si nous espérons que la formalisation de la logique que nous allons donner permettra de clarifier et de préciser cette pratique.
- LOGIQUE MATHÉMATIQUES
- PROPOSITIONS - FONCTIONS PROPOSITIONNELLES
- QUANTIFICATEURS - PROPOSITIONS QUANTIFIÉES
- OPÉRATIONS LOGIQUES
- NÉGATION LOGIQUE
- DISJONCTION LOGIQUE
- CONJONCTION LOGIQUE
- IMPLICATION LOGIQUE
- ÉQUIVALENCE LOGIQUE
- RAISONNEMENTS MATHÉMATIQUES
- CONTRA-POSÉE
- DISJONCTION DES CAS
- IMPLICATION
- ÉQUIVALENCE
- ABSURDE
- RÉCURRENCE
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