In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.
The first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdös-Rado theorem (1956). On the other hand in 60’s of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdös-Rado theorem....
Nowadays using graphic display calculators (GDCs) is becoming more and more popular in learning and teaching mathematics. One of the main usages of this device is to obtain a graph of almost all functions with one variable. If we have a graph of a function we can observe some special properties of the function. Graphic display calculators (even without computer algebra system (CAS)) can do even more - calculate derivative at any point and draw graphs of derivatives of the first and the second degree,...
The necessity of teaching such an activity as generalization was considered by Z. Krygowska in the ‘70s (Krygowska, 1977). The formation of this ability requires an adequate selection of non-stereotypical tasks, for which the algorithm is unknown to the person solving the task, ones in which a student is forced to search for their own method of solving the task on the basis of their knowledge. In literature, there are known studies concerning the process of generalization of students of different...
Limits are one of the most fundamental and important concepts of calculus, because having a proper understanding of this concept is a prerequisite for understanding such concepts as continuity, differentiation, and integration. Thus, researchers and teachers seem to outdo one another in looking for the best methods of introducing limits. One of the methods is using IT and graphic software to illustrate the idea of limits. It Seems that such a method, while useful, is overflowing with the risk of...
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