Arithmétique élémentaire pour la formation des enseignants: Tome I: Les nombres naturels
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Pourquoi l'humanité a-t-elle développé des systèmes de numération? Quels en sont les avantages et quels en sont les inconvénients?
L'humanité a depuis longtemps trouvé divers moyens de représenter, par l'écriture (en utilisant des signes, par exemple), des quantités déterminées d'objets. Mais le développement de la société (la nécessité de compter les biens personnels, l'organisation fiscale des cités, le commerce, etc.) nécessite rapidement la réalisation de calculs, c'est-à-dire l'invention d'une arithmétique élémentaire (calculs impliquant des additions, soustractions, multiplications, etc.).
L'écriture des nombres a alors évolué, d'une part pour permettre la représentation simple de quantités et, d'autre part, pour faciliter les calculs.
Cette évolution aboutit à la constitution d'ensembles de signes et de règles permettant de représenter les nombres, ce qu'on appelle des systèmes de numération.
Dans ce livre, nous essaierons de montrer en quoi et pourquoi notre système de numération décimale est l'un des plus avantageux pour le développement de l'arithmétique. Nous proposerons aussi une étude détaillée des opérations élémentaires définies dans l'ensemble des nombres naturels, de leurs propriétés et de leur usage.
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