# Answer to Question #16743 in Real Analysis for Jay

Question #16743

Use the definition to prove that the set of all odd natural numbers is a countable set

Expert's answer

Let's enumerate the elements of the set of all odd natural numbers in a such way. Let the n-th member of the set be numbered by (n+1)/2. We've build the mapping from the set of all odd natural numbers to the set of natural numbers. So, the set of all odd natural numbers is a countable set.

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