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- W3023779196 abstract "ion, from a set M to its order type M and then to its cardinality M. Almost two decades after his [1874] result that the reals are uncountable, Cantor in a short note [1891] subsumed it via his celebrated diagonal argument. With it, he estab15After describing the similarity between ω and √ 2 as limits of sequences, Cantor [1887: 99] interestingly correlated the creation of the transfinite numbers to the creation of the irrational numbers, beyond merely breaking new ground in different number contexts: “The transfinite numbers are in a certain sense new irrationalities, and in my opinion the best method of defining the finite irrational numbers [via Cantor’s fundamental sequences] is wholly similar to, and I might even say in principle the same as, my method 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 [Wesen]; for the former like the latter are definite delimited forms or modifications of the actual infinite.” 16Ferreiros [1995] suggests how the formulation of the second number class as a completed totality with a succeeding transfinite number emerged directly from Cantor’s work on the operation P′, drawing Cantor’s transfinite numbers even closer to his earlier work on trigonometric series." @default.
- W3023779196 created "2020-05-13" @default.
- W3023779196 creator A5050426319 @default.
- W3023779196 date "2009-01-01" @default.
- W3023779196 modified "2023-09-25" @default.
- W3023779196 title "SET THEORY FROM CANTOR TO COHEN" @default.
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