Numerosity theory was introduced to formalize the idea that counting the size of infinite sets is possible while maintaining the ancient principle that "the whole is greater than the part." In fact, contrary to Cantorian cardinality, the numerosity of a proper subset is always strictly smaller. The construction of models for numerosity has revealed some interesting foundational issues, as well as strong connections with nonstandard analysis and Ramsey theory. We will briefly discuss these issues, and also make some remarks on the relationships between numerosity and the notion of measure considered in mathematical analysis.
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