# 9: Finite and Infinite Sets

- Page ID
- 7085

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- 9.3: Uncountable Sets
- We have seen examples of sets that are countably infinite, but we have not yet seen an example of an infinite set that is uncountable. We will do so in this section. The first example of an uncountable set will be the open interval of real numbers (0, 1). The proof that this interval is uncountable uses a method similar to the winning strategy for Player Two in the game of Dodge Ball from Preview Activity 1. Before considering the proof, we need to state an important results about decimal expres