METHODOLOGICAL FEATURES OF INVESTIGATING SETS HAVING THE CARDINALITY OF A CONTINUUM

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 approach establishes that the Cantor set has the cardinality 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 functional analysis with numeral systems covered in algebra and programming courses. It significantly increases the number of practical tasks for students' independent work on Cantor sets, deepens their understanding of the techniques for constructing such sets, and enhances their mastery of methods 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 advanced focus on mathematics in general secondary education institutions.