Answer to Question #16743 in Real Analysis for Jay

Question

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

Answer 1

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.