Transfinite Arithmetic

In mathematics, transfinite arithmetic is the generalization of elementary arithmetic to infinite quantities like infinite sets. It was originally discovered by the Russian-born German mathematician Georg Cantor.

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    “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.”
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