Sentence examples for a bottom element for from inspiring English sources
Also, we require that the correspondence has a bottom element for each member of its domain.
Theorem 6 Let T be a partially ordered set, and ( Γ t ) t ∈ T be a collection of games with extended weak general complementarities such that the joint best reply correspondence F ( ⋅, t ) is lower increasing in ( x, t ) on X × T and has a bottom element for every ( x, t ) ∈ X × T. Then the least Nash equilibrium is increasing in t.
( X, ≤ ) turns out to be a complete partially ordered set (CPO) if (i) X has a bottom element, ⊥; and (ii) for each directed subset D of X, the supremum exists.
Theorem 2 Let X be a CPO, and F : X → X be a correspondence such that for every x ∈ X, F ( x ) has a bottom element.
Thus, F h ( x ) has a bottom element by assumption.
Note that since F ⊥ coincides with F, it is true that F has a bottom element.
Noting that a bottom element exists in every F ( x, t ), define f t ( x ) = ⋀ F ( x, t ) for every ( x, t ) ∈ X × T. The function f t is order preserving since F ( ⋅, t ) is lower increasing.
It consists of a silicon substrate and two SAW gyroscopes using progressive waves, described in more detail in [16], in which the bottom element is used for y-axis detection and the top element is used for x-axis detection.
Since a ̲ is the bottom element, we also have a ̲ ≤ a i.
Consider the bottom element of F ( h ), say a ̲.
