A well-ordered set is a type of set in which every non-empty subset has a least element. This means that for any group of elements you choose from the set, you can always find the smallest one according to the set's ordering. Well-ordered sets are often used in mathematics, particularly in set theory and ordinal numbers. An example of a well-ordered set is the set of natural numbers, ℕ, when arranged in their usual order. In this case, any subset of natural numbers will have a smallest number. Well-ordered sets are important for proving various mathematical concepts, including transfinite induction and Zermelo's well-ordering theorem.