“The transfinite numbers are in a certain sense themselves new irrationalities”

— Georg Cantor

As quoted in Understanding the Infinite (1994) by Shaughan Lavine
Context: The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

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Georg Cantor 27

mathematician, inventor of set theory 1845–1918

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“The transfinite numbers are in a certain sense themselves new irrationalities”

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