FOM: Precursors and Cantor's originality
Richard E. Grandy
rgrandy at ruf.rice.edu
Thu Jun 13 20:18:30 EDT 2002
It seems to me that a number of Cantor's precursors noticed that some
infinite sets are "bigger" than others in the proper subset sense,
and a number noticed that sometimes a proper subset could be put in
one-one correspondence with the whole set. Those who noticed both
concluded that no sense could be made of sizes of infinity. Cantor's
originality was, after recognizing both, to reject the proper subset
criterion and make the existence of a 1-1 correspondence definitive
of equinumerosoity even when the proper set criterion indicated
otherwise. And of course to show that an enormously rich
mathemtical theory results!!
There are a number of instances in the history of science where two
notions were conflated for a long time and it was a major
breakthrough to separate them. In this case it is proper subset vs.
equinumerosity, others are velocity vs acceleration, heat vs.
temperature, and perhaps the fact that the earth is locally flat but
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