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Background: In the previous authorsВ’ publications it was shown that modeling of fundamental properties of mathematics within the teaching process is very efficient. A group of fundamental properties consists of several so-called dualistic properties, which are inherent in all the branches of mathematics in all periods of its history. The purpose of this article is to bring to light some up-to-date factors, which generate a new appearance of the dualistic properties as well as their gradual modification. Methods: ...