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