Теория бесконечности
и время

Theses Hypotheses of the Connection of Infinite Quantities and Countable Sets

Godarev-Lozovsky M.G.

We can confirm and clarify the following principle that we formulated earlier, which is the basis of mathematics. The countable set of signs of a decimal potentially infinite periodic fraction is complete, but contradictory, and the countable set of signs of a decimal actually infinite non-periodic fraction is incomplete, but consistent. As a result of the research, the hypothesis of the connection of infinite quantities and countable sets is proposed. The hypothesis is based on the statement that the difference between arbitrarily close rational numbers on the numerical axis is a potentially infinitesimal value, and the difference between a real and an infinitely close hyper – real number is an actual infinitesimal value.

Keywords. Number and quantity; Potential and actual infinity; Infinite fraction; Classical and non-standard analysis; Infinitesimal; Countable and uncountable sets; One-toone correspondence.