Sentence examples for greatest lower bound from inspiring English sources

Here, for a list L, sup(L ) and inf(L ) denote the lowest upper bound and greatest lower bound of L, respectively.

Obviously, a cone K is minihedral if and only if for any pair { x, y }, x, y ∈ X, bounded below in order there exists the greatest lower bound inf { x, y }.

Figure 5 Bolzano's diagram-free proof of the IVT is an argument from what later became known as the Dedekind completeness of the real numbers: every non-empty set of reals bounded above (below) has a least upper bound (greatest lower bound).

Since ψ is nondecreasing, then the sequence (K={p y_{n+1}, y_{n})}) of real numbers is decreasing and is bounded below by 0. Hence, K converges to (rgeq0), the greatest lower bound of K. We assert that (r=0).

And in any case how does one decide whether points on a line have a greatest lower bound?

We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders' values.

Recall that an upper (resp. lower) bound for M is an element p ∈ X with m ≺ p (resp. p ≺ m) for each m ∈ M; the least-upper (resp. greatest-lower) bound of M will be denoted sup M (resp. inf M).

In all the analyses presented here, we found a slope parameter that is statistically greater than zero (lower bound of CI is greater than zero).

The upper bound must be greater than the lower bound, which results in (14).

Their input/output behaviours are guaranteed to be greater than the lower bound of the reference model set and lower than the upper bound of this set.

Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set.