Nonlinear Analysis Series A 72 (3-4):1701-1708 (2010)

Yaroslav Sergeyev
Università della Calabria
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.
Keywords The First Hilbert problem
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References found in this work BETA

Contributions to the Founding of the Theory of Transfinite Numbers.Cassius J. Keyser - 1916 - Journal of Philosophy, Psychology and Scientific Methods 13 (25):697-697.
Set Theory and the Continuum Hypothesis.Kenneth Kunen - 1966 - Journal of Symbolic Logic 35 (4):591-592.

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