conclusion of countable set in real analysis
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The set of all finite subsets of the natural numbersis countable. The elements of any finite subset can be ordered into a finite sequence. There are only countably many finite sequences, so also there are only countably many finite subsets. ... (Basic)
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Theorem: The set of all finite subsets of the natural numbers is countable. The elements of any finite subset can be ordered into a finite sequence. There are only countably many finite sequences, so also there are only countably many finite subsets.
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