It is assumed that individuals must have a preference relationship between any two sets of goods; either we must be able to say that they weakly prefer A to B, or that they weakly prefer B to A, or both (indifference). Used of a flower. \[q=\sup A(p=\inf A) . (2) The set $$N$$ of all naturals is bounded below (e.g., by $$1,0, \frac{1}{2},-1, \ldots$$) and $$1=\min N;$$ N has no maximum, for each $$q \in N$$ is exceeded by some $$n \in N$$ (e.g. ( plural completeness axioms) (mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset). If $$A$$ has one lower bound $$p,$$ it has many (e.g., take any \(p^{\prime}