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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.

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