e-Pedagogium 2009, 9(1):97-102

Axiom of Choice's consequences for methodological material in mathematics teaching

Tomáš Zdráhal
Tomáš Zdráhal, Departments of Mathematics of Faculties of Education, Palacky University in Olomouc and J. E. Purkyne University in Usti n. L., Czech Republic, tomas.zdrahal@upol.cz

The article deals with one effect of the Axiom of Choice's bearing on understanding how to get better insight into traditional mathematical notions and concepts. It is shown that the investigation of a special function brings didactic and methodological mathematical material for the demonstration of the modern concept of teaching mathematics at universities.

Keywords: Homomorphism, functional equation, Cauchy equation, Axiom of Choice, Hamel basis, discontinuous additive function

Published: February 1, 2009  Show citation

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Zdráhal, T. (2009). Axiom of Choice's consequences for methodological material in mathematics teaching. e-Pedagogium, 9(1), 97-102
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    References

    1. J. Aczél: Lectures on functional equations and their applications, Academic press, New York - San Francisko - London, 1966
    2. M. Kuczma: An introduction to the theory of functional equations and inequalities, Cauchy's equation and Jensen's inequality, PWN, Warszawa - Kraków - Katowice, 1985
    3. F. Neuman: Fukcionální rovnice, Matematický seminář SNTL, Praha, 1986
    4. J. Smítal: O funkciách a funkcionálnych rovniciach, Knižnica Epsilon, Alfa, Bratislava, 1984
    5. T. Zdráhal: Generalizations of some theorems of Steinhaus, Aequationes Math 56/3 1998, 298
    6. T. Zdráhal: On some consequences of universal sets,Matematyka 6, Prace naukowe WSP Czestochowa 1999, 153-157
    7. T. Zdráhal: Zobecněné elementární funkce, Acta Universitatis Purkynianae 125, Studia Mathematica, Ustí nad Labem, 2006
    8. T. Zdráhal: Některé vlastnosti aditivní funkce, Matematika v škole dnes a zajtra, KU Ružomberok 2007, 333-338

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