Numerosities of labelled sets: a new way of counting

By Vieri Benci, Mauro Di Nasso. 2003

99 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1370f90f6f979c497f7d14e5c21efa8f2c8e33d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yaroslav D. Sergeyev
2. Marco Forti
3. Vieri Benci
4. Mauro Di Nasso
5. Leon Horsten
6. Sylvia Wenmackers

In Mathematical Physics

1. Yaroslav D. Sergeyev
2. Marco Forti
3. Vieri Benci
4. Mauro Di Nasso
5. Leon Horsten
6. Sylvia Wenmackers

Citations in the corpus

• The eightfold path to Nonstandard Analysis (2004, methodology): “More important, can the sum and product operations (defined by means of disjoint unions and Cartesian products) satisfy the usual algebraic properties of natural numbers?(50) And still more demanding, can this extension of the natural numbers be taken as a basis for producing hyperrational and hyper”
• Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains (2009, unknown): “Numerous trials have been done during the centuries in order to evolve existing numeral systems 2 in such a way that infinite and infinitesimal numbers could be included in them (see [1–7]).”
• Alpha-theory: An elementary axiomatics for nonstandard analysis (2003, background): “By adopting the notion of numerosity introduced in [6], an interpretation of the ideal number a can be given as the numerosity of the set of natural numbers (see [7]).”
• Non-Archimedean Probability (2011, background): “For fair lotteries, the probability assigned to an event by NAP-theory is directly proportional to the ‘numerosity’ of the subset representing that event [3].”
• Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems (2017, background): “Even though there exist codes allowing one to work symbolically with 1 and other symbols related to the concepts of infinity and infinitesimals, traditional computers work numerically only with finite numbers and situations where the usage of infinite or infinitesimal quantities is required are stud”