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| Submission declined on 25 March 2025 by AgerJoy (talk). Neologisms are not considered suitable for Wikipedia unless they receive substantial use and press coverage; this requires strong evidence in independent, reliable, published sources. Links to sites specifically intended to promote the neologism itself do not establish its notability.
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| Submission declined on 18 January 2025 by Chaotic Enby (talk). This draft's references do not show that the subject qualifies for a Wikipedia article. In summary, the draft needs multiple published sources that are: Declined by Chaotic Enby 4 months ago.
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The numerosity of an infinite set, as introduced by the Italian mathematician Vieri Benci and some of his collaborators, is a concept that develops Cantor’s notion of cardinality. While Cantor’s classical cardinality classifies sets based on the existence of a one-to-one correspondence with other sets (defining, for example, for countable sets, and so on for larger infinities), the idea of numerosity aims to provide an alternative viewpoint, linking to the common Euclidean notion that "the whole is greater than the part". All of this naturally leads to the hypernatural numbers.[1]
In short, Benci and his collaborators propose associating with an infinite set a numerical value that more directly reflects its “number of elements”, without resorting solely to one-to-one correspondences[2][3][4][5][6][7]. This approach uses tools from logic and analysis, seeking to give an operational meaning to the notion of “counting” even when dealing with infinite sets. Numerosity thus proves useful for the study of certain problems in discrete mathematics and is the subject of research within alternative (or complementary) theories to traditional Cantorian cardinality.
- ^ "Theories of Numerosities (Stanford Encyclopedia of Philosophy)". plato.stanford.edu. Retrieved 2025-01-15.
- ^ Benci, V. (1995). "I Numeri e gli Insiemi Etichettati", Laterza, Bari, Italia. Conferenze del seminario di matematica dell' Università di Bari, vol. 261, pp. 29
- ^ Benci, V.; Di Nasso, M. (2003). "Numerosities of labelled sets: a new way of counting". Advances in Mathematics 173: 50–67
- ^ Benci, V.; Di Nasso, M.; Forti, M. (2006). "An Aristotelian notion of size". Annals of Pure and Applied Logic 143:1–3, 43–53
- ^ Benci, V.; Di Nasso, M.; Forti, M. (2007). "An Euclidean Measure of Size for Mathematical Universes". Logique & Analyse 197: 43–62
- ^ Di Nasso, M; Forti, M. (2010). "Numerosities of point sets over the real line". Transactions of the American Mathematical Society 362:10, 5355–5371
- ^ Benci, V.; Di Nasso, M. (2019). "How to measure the infinite", World Scientific, Hackensack, NJ (in particular, Part 5 of the book is entirely devoted to numerosity)
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