Show that the sed of odd natural numbers is countable.
To begin, the set of odd natural numbers is intuitively infinite. In order for this set to be countably infinite, there must exist some function that maps the set of natural numbers onto it. Defining such a function is fairly trivial:
\[f(x) = 2x + 1\]This function is a bijection from \(\mathbb{N}\) to the set of odd natural numbers therefore they are countable.