Science and Mathematics Education Commons^™

Walking Diagonally: A Simple Proof Of Countability Of The Set Of All Finite Subsets Of Naturals, Miroslav Kures

BAU Journal - Science and Technology

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 …