The least-upper-bound property states that every nonempty set of real numbers that has an upper bound has a supremum in the real numbers. It is an order-theoretic formulation of the completeness of the real numbers.
Articles by others on the same topic
The completeness of the real numbers is a fundamental property that distinguishes the real numbers \(\mathbb{R}\) from the rational numbers \(\mathbb{Q}\). Completeness refers to the idea that every non-empty set of real numbers that is bounded above has a least upper bound (also known as the supremum).