Advertise on Northwest Firearms
Defensive Arts
Gun Deals
DSG Arms
Sporting Systems
Buster Beaver Cerakote
HighLine Firearms
Low Price Guns
Oregon Rifleworks
Southwest Firearms
Simply Triggers
J&B Firearm Sales
In mathematics, the least-upper-bound property (sometimes the completeness or supremum property) is a fundamental property of the real numbers and certain other ordered sets. A set X has the least-upper-bound property if and only if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X.
The least-upper-bound property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness. It can be used to prove many of the fundamental results of real analysis, such as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as an axiom in synthetic constructions of the real numbers (see least upper bound axiom), and it is also intimately related to the construction of the real numbers using Dedekind cuts.
In order theory, this property can be generalized to a notion of completeness for any partially ordered set. A linearly ordered set that is dense and has the least upper bound property is called a linear continuum.

View More On Wikipedia.org
DSG Arms
Cerberus Training Group
Advertise on Northwest Firearms
Project Appleseed
Copeland Custom Gunworks
Southwest Firearms Forum
NW Custom Firearms
Sporting Systems
Top