# Uncountable Sets and an Infinite Real Number Game

by Matthew H. Baker (Georgia Institute of Technology)

This article originally appeared in:
Mathematics Magazine
December, 2007

Subject classification(s): Analysis | Real Analysis
Applicable Course(s): 4.11 Advanced Calc I, II, & Real Analysis

A short proof of the well-known fact that the unit interval $[0,1]$ is uncountable is presented by means of a simple infinite game. The author also used this game to show that a (non-empty) perfect subset of $[0,1]$ must be uncountable.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.