(a) Show that a subset of a countable set is countable.
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Expert's answer
2020-12-17T08:26:28-0500
Let B be a subset of a countable set A. By defenition of a countable subset, there is an injection f:A→N. Since the restriction f∣B:B→N of an injection f to the subset B is an injection as well, we conclude that B is a countable set.
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