Complex sentence: The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound.
Split into simpler sentences: The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis. The axiom says that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound.