Well-ordering is a principle in mathematics that states every non-empty set of positive integers has a least element. This means that if you have a collection of whole numbers, you can always find the smallest number in that group. This concept is fundamental in number theory and helps in understanding the structure of the integers. The well-ordering principle is closely related to the natural numbers and is often used in proofs and algorithms. It ensures that any process that involves counting or ordering can be systematically approached, making it a crucial concept in areas like set theory and mathematical induction.