The Well-Ordering Theorem states that every non-empty set of positive integers has a least element. This means that if you take any collection of positive whole numbers, you can always find the smallest number in that collection. This theorem is fundamental in mathematics, particularly in number theory and proofs by induction. This theorem is closely related to the concept of ordinal numbers and is often used in proofs involving the principle of mathematical induction. It is also a key component in the foundations of set theory, influencing how mathematicians understand and work with infinite sets.