Cardinal Number - Cardinal Arithmetic

Cardinal Arithmetic

We can define arithmetic operations on cardinal numbers that generalize the ordinary operations for natural numbers. It can be shown that for finite cardinals these operations coincide with the usual operations for natural numbers. Furthermore, these operations share many properties with ordinary arithmetic.

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Famous quotes containing the words cardinal and/or arithmetic:

    One must not make oneself cheap here—that is a cardinal point—or else one is done. Whoever is most impertinent has the best chance.
    Wolfgang Amadeus Mozart (1756–1791)

    I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
    Gottlob Frege (1848–1925)