What is a finite set?

A finite set is defined as a set that has a limited number of elements. This means that you can count the elements in the set and that the elements you can list will end at a certain point. For example, a set containing the numbers {1, 2, 3} has three elements and is considered finite.

In contrast, when we refer to sets with an unlimited number of elements, such as the set of all integers or the set of all real numbers, these are infinite sets. The concept of infinity is fundamentally different from finite sets, which are closed and countable. Therefore, the focus on the limitation in the number of elements is what distinctly classifies a set as finite. This understanding is crucial in many mathematical applications, particularly in combinatorics and set theory.