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This article is devoted to the different representations of real numbers. In particular, the following types are distinguished and discussed: (1)representations based on theorems referring to the axiomatic characterization of the field of real numbers, (2) genetic representations – related to the construction of real numbers, (3) visual representations – mainly related to the geometrical way of presenting...
In this paper we survey, also in historical perspective, the results connected with the notion of the commutativity degree of a finite group, i.e., the probability that two randomly selected elements of the group commute.
It is well known that there exist many metrics on a non-emptyset. In the case of $(X, \varrho)$ − a finite metric set, it can be easily shown that all the metrics on X are equivalent. This paper examines the number of non-equivalent metrics on uncountably infinite sets.
In the training process of students – future teachers of mathematics, an important role is played by, among others, participation in the diploma seminar, during which the student (being at the final stage of studies)is tasked with preparing a bachelor’s or master’s thesis. This dissertation may be purely mathematical in nature or refer to problems in didactics of mathematics. The article aims to develop...
We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second...
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