A well-order is a specific type of ordering for a set, where every non-empty subset has a least element. This means that if you take any group of elements from the set, you can always find the smallest one according to the order defined. Well-orders are important in mathematics, particularly in set theory and number theory. An example of a well-ordered set is the set of natural numbers 0, 1, 2, 3, .... In this set, any subset, like 2, 3, 5, has a least element, which is 2. This property helps in proving various mathematical concepts, such as the principle of induction and the existence of certain types of sequences.