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:
“Honest towards ourselves and towards anyone else who is our friend; brave towards the enemy; magnanimous towards the defeated; polite—always: this is how the four cardinal virtues want us to act.”
—Friedrich Nietzsche (1844–1900)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)