1. The problem is to understand what a finite set is. 2. A set is a collection of distinct objects, called elements. 3. A finite set is a set that contains a countable number of elements. 4. More precisely, a set $S$ is finite if there exists a natural number $n$ such that the number of elements in $S$ is exactly $n$. 5. For example, the set $\{1, 2, 3\}$ is finite because it has exactly 3 elements. 6. In contrast, an infinite set has an uncountable or endless number of elements, like the set of all natural numbers $\mathbb{N} = \{1, 2, 3, \ldots\}$. 7. Therefore, a finite set is one where you can list all elements and count them to a final number.