Answer to Question #148126 in Discrete Mathematics for Promise Omiponle

Question #148126
(a) Show that a subset of a countable set is countable.
1
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\\to \\mathbb N". Since the restriction "f|_B:B\\to\\mathbb 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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