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Guida Alla Teoria Degli Insiemi
Paperback
Series: Convergenze
FictionGeneral MathematicsTeaching Instruction
ISBN13: 9788847007680
Publisher: Springer
Published: Feb 13 2008
Pages: 148
Weight: 0.53
Height: 0.35 Width: 6.14 Depth: 9.21
Language: Italian
Il libro vuole aiutare a studiare la teoria degli insiemi indicando l'articolazione della teoria, a partire dal concetto di infinito per arrivare alla definizione dei numeri, sia finiti sia infiniti, con la diramazione tra ordinali e cardinali; insiste sulle proprietà degli insiemi numerabili, e sul continuo. Non sostituisce un manuale, perché non ci sono tutte le dimostrazioni ma solo alcune, considerate importanti, che danno il gusto dello stile di questa materia.
Ricorda come la teoria sia nata dalle esigenze dell'analisi matematica e come sia legata al problema dei fondamenti; discute il riduzionismo e presenta anche la teoria alternativa rivale delle categorie.
Distingue la teoria propria dell'infinito dal linguaggio insiemistico che pervade la matematica.
Nelle applicazioni si insiste sul principio di induzione e sulle definizioni induttive, e sulla derivazione delle proprietà degli insiemi finiti, con tutte le definizioni equivalenti di finito, e si indica lo studio delle versioni effettive dei risultati teorici, in particolare la definizione esplicita di funzioni ed enumerazioni, fino gettare un ponte con la teoria della calcolabilità , in vista dell'insegnamento.
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