The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty set of real numbers has an upper bound, then it has a least upper bound.
The least upper bound axiom is an axiom of real analysis. A nonempty set of real numbers has an upper bound. This is what this real analysis is stating. It has a least upper bound. The least upper bound axiom is also abbreviated as the LUB axiom.