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October 7 Colloquium

by Mauro Di Nasso, University of Pisa, Italy

Numerosities: a possible way of refining Cantor's cardinality

It is a well-known phenomenon that every infinite set has proper subsets with the same cardinality. The theory of numerosity is a refinement of Cantor's cardinality that maintains the classical Euclid's principle stating that "the whole is larger than the part".

In this talk, I will present the basic features of numerosities. In particular, I will show how numerosities generalize the finite natural numbers by accommodating also "infinite" numbers. Its logical foundations as a sound mathematical theory will also be briefly discussed. All arguments will be presented in the basic language of mathematics, and no technical notions from logic will be assumed.

 


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