Well-Ordering Theorem

The Well-Ordering Theorem states that every non-empty set of positive integers has a smallest element. In simpler terms, if you have a group of whole numbers that are greater than zero, you can always find the smallest number among them. This concept is fundamental in mathematics, particularly in proofs and arguments related to ordering and comparing numbers. It ensures that when dealing with infinite sets, like all whole numbers, there’s a reliable way to identify the smallest member, which is crucial for various mathematical principles and theories.