Counting systems and the First Hilbert problem
By Yaroslav D. Sergeyev. 2010
54 citations recorded by the source corpus.
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different accuracies. The traditional and the new approaches are compared and discussed.
Subfields: Mathematical Physics, Statistics and Probability, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/48d893e75d16d5d03edcec9ec15bdff21fc0f716
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In Mathematical Physics
In Statistics and Probability
In Theoretical Computer Science
Citations in the corpus
- Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems (2017, methodology): “Themethodology described here has been successfully applied in several areas ofMathematics andComputer Science: single andmultiple criteria optimization (see [20,32–34,43,116]), cellular automata (see [29–31]), Euclidean and hyperbolic geometry (see [68,69]), percolation (see [56,57,110]), fractals ”