METHODOLOGICAL FEATURES OF INVESTIGATING SETS HAVING THE CARDINALITY OF A CONTINUUM.
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Students of mathematical specialties in higher education institutions encounter Cantor sets while studying the structure of closed sets in courses on function theory and functional analysis. In classical textbooks, the ternary numeral system is used to determine the cardinality of these sets. This ap- proach establishes that the Cantor set has the car- dinality of the continuum.
This paper presents a method for determining the cardinality of Cantor sets using alternative numeral systems. This approach integrates the study of Cantor sets in function theory and func- tional analysis with numeral systems covered in algebra and programming courses. It significantly increases the number of practical tasks for stu- dents' independent work on Cantor sets, deepens their understanding of the techniques for construct- ing such sets, and enhances their mastery of meth- ods for determining their cardinality.
Certain elements of this work can be utilized in extracurricular mathematics activities or for club- based projects in specialized classes with an ad- vanced focus on mathematics in general secondary education institutions.
Description
Savchenko O., Tsymbaliak K., Kuz’mich V. Methodological features of investigating sets having the cardinality of a continuum. Вісник Черкаського університету. Серія «Педагогічні науки»: зб. наукових праць. – Черкаси: вид-во Черкаського національного університету ім. Богдана Хмельницького, 2025. Вип. № 4. С. 37-42.
Keywords
methodological features, number system, set, cardinality of set, Cantor set, metric space, fractals, functional analysis.