Abstract
Dedekind had ushered in the idea that mathematical concepts might profitably be defined in terms of a naive conception of sets. His friend Cantor extended this to a theory of sets of various sizes, and came to a number of paradoxical conclusions, such as the existence of a one-to-one correspondence between a line and a square, which threatened the fundamental idea of the dimension of these and other domains.
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© 2015 Springer International Publishing Switzerland
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Gray, J. (2015). Cantor, Set Theory, and Foundations. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_28
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DOI: https://doi.org/10.1007/978-3-319-23715-2_28
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