Problem 23.7. Prove that a set A is uncountable if there is an injective function

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Problem 23.7. Prove that a set A is uncountable if there is an injective function

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Since f is injective. There exists a subset S of A such that f is onto from (0,1) to S. (0,1) is uncountable set, so S is also uncountable, which implies A is uncountable as A is a superset of S.

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