What's a countably infinite set? A. A finite set. B. A subset of the natural numbers. C. A set that has the the same size as the set of natural numbers. D. A set that has the same size as the set of real numbers.

Sol135:

A countably infinite set is a set that has the same cardinality (size) as the set of natural numbers. In other words, it is a set that can be put into one-to-one correspondence with the set of natural numbers. This means that the elements of the set can be listed out in a sequence, such that each element appears exactly once in the list, and the list continues indefinitely. Examples of countably infinite sets include the set of integers, the set of even integers, and the set of all rational numbers.