#### Article Title

WALKING DIAGONALLY: A SIMPLE PROOF OF COUNTABILITY OF THE SET OF ALL FINITE SUBSETS OF NATURALS

#### 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.

#### Recommended Citation

Kures, Miroslav
(2021)
"WALKING DIAGONALLY: A SIMPLE PROOF OF COUNTABILITY OF THE SET OF ALL FINITE SUBSETS OF NATURALS,"
*BAU Journal - Science and Technology*: Vol. 3
:
Iss.
1
, Article 7.

Available at:
https://digitalcommons.bau.edu.lb/stjournal/vol3/iss1/7

#### ISSN

2706-784X