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Some aspects of teaching the concepts: arithmetic and weighted means at various levels of mathematical education

Bugajska-Jaszczołt B., Czajkowska M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

163-170

We refer to selected problems of formulating the definitions of arithmetic and weighted means in secondary school and at a higher level. The first problem discussed here are the results of theoretical research. We compare the manner of formulating the definitions, in particular, the level of formalization of mathematical language. We present the differences between various definitions, found in the analyzed textbooks, in such aspects as: generality, degree and kind of complication of logical structure, and intuitions provoked by them. We underline qualitatively different objects defined by them - arithmetic mean of numbers and arithmetic mean of scalable feature, emphasizing the consequences.

Axiomatization of the logic determined by some n-element relational systems with identity

Bugajska-Jaszczołt B.

Reports on Mathematical Logic

1998

No. 32

11-19

Let Nn = be the relational system of n - element set Nn = {1,2,..., n}, with identity and with fixed elements: 1,2,..., n. We show that logic L (Nn) determined by the system Nn is axiomatizable.