**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.

Read more about this topic: Cardinal Number

### 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)