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Uncountable Sets and an Infinite Real Number Game

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.

Old Node ID: 
3677
MSC Codes: 
97Ixx
Author(s): 
Matthew H. Baker (Georgia Institute of Technology)
Publication Date: 
Saturday, May 14, 2011
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
December, 2007
Subject(s): 
Analysis
Real Analysis
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Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
91.00
Rating Sum: 
275.00
Rating Average: 
3.02
Applicable Course(s): 
4.11 Advanced Calc I, II, & Real Analysis
Modify Date: 
Saturday, May 14, 2011
Average: 3 (91 votes)

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