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Uncountable sets and an infinite real number game

Matthew Baker
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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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Matthew Baker. 2006-06-11. Uncountable sets and an infinite real number game. https://arxiv.org/abs/math/0606253

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