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English Title

A SIMPLE PROOF OF COUNTABILITY OF THE SET OF ALL FINITE SUBSETS OF NATURALS

Keywords

set theory, diagonalization method, countability, teaching methods, university basic mathematics

Disciplines

Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

The countability of the set of finite subsets of natural numbers is derived. In addition to the derivation itself, the use of diagonal method is illustratively presented; thinking about infinite sets relate to the name of Georg Ferdinand Ludwig Philipp Cantor, the creator of set theory, which has become a fundamental theory in mathematics. The proof of the claim is original, although the theorem is an analogy with the famous theorem about the countability of rational numbers. A certain insight into the subsets of natural numbers is given. Anyway, the technique could be considered already at high school level as it is essential for mathematical thinking.

ISSN

2706-784X

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