Uncountable sets and an infinite real number game

2006/06/11 by Matthew Baker, Baker, Matthew
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #History and Overview (math.HO) #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms #math.GN #math.HO

paper · pdf · doi:10.48550/arxiv.math/0606253

7 pages

arxiv created 2006/06/11 · openalex publication_date 2006/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short proof of the well-known fact that the unit interval [0,1] is uncountable by means of a simple infinite game. We also show using this game that a (non-empty) perfect subset of [0,1] must be uncountable.

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