Insieme infinito

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Un insieme infinito è intuitivamente un insieme per il quale non sia possibile elencare i suoi elementi.

Definizioni matematicamente rigorose si possono dare nella teoria degli insiemi. In particolare esistono tre tipi di caratterizzazione o possibili definizioni degli insiemi infiniti:

Le tre definizioni si possono dimostrare[1] equivalenti assumendo l'assioma della scelta. Tale assioma si rivela in effetti indispensabile per mostrare che un insieme non-finito è infinito secondo Cantor o Dedekind: si può dimostrare che gli altri assiomi di Zermelo-Fraenkel da soli non possono provare l'equivalenza delle caratterizzazioni poiché ammettono un modello in cui ci sono insiemi che sono infiniti ma finiti rispetto all'accezione di Dedekind.

Note

  1. ^ Luca Barbieri Viale, Che cos'è un numero? : Una introduzione all'algebra, Cortina, 2013, ISBN 978-88-6030-604-3, OCLC 898699172. URL consultato il 17 dicembre 2022.

Bibliografia

  • Luca Barbieri Viale, Teorema 2.26, Che cos'è un numero?, Milano, Raffaello Cortina, 2013, ISBN 9788860306043.

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