Counting systems and the First Hilbert problem

Details Counting systems and the First Hilbert problem Counting systems and the First Hilbert problem

2012-03-14

arxiv.org/abs/1203.4141v1

Nonlinear Analysis Series A: Theory, Methods & Applications, 2010, 72(3-4), 1701-1708

Mathematics

General Mathematics

16 pages, no figures

Scientific paper

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.

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