greatest lower bound การใช้

• Greatest lower bounds in turn are given by the greatest common divisor.
• Bolzano was the first to recognize the greatest lower bound property of the real numbers.
• The Lebesgue outer measure emerges as the greatest lower bound ( infimum ) of the lengths from among all possible such sets.
• A set may have many lower bounds, or none at all, but can have at most one greatest lower bound.
• It is known that \ mathcal { D } is not a lattice, as there are pairs of degrees with no greatest lower bound.
• The symbols  " and  " denote the least upper bound and greatest lower bound operations, respectively, in the complete Boolean algebra " B ".
• That is, the least upper bound ( sup or supremum ) of the empty set is negative infinity, while the greatest lower bound ( inf or infimum ) is positive infinity.
• If it is over the whole of the real numbers then it may just have an infimum ( greatest lower bound ), but it may never attain it ( it could asymptotically approach it ).
• The extreme value theorem enriches the boundedness theorem by saying that not only is the function bounded, but it also attains its least upper bound as its maximum and its greatest lower bound as its minimum.
• The notion of a complete lattice means that every subset of elements of has a unique least upper bound and a unique greatest lower bound; this generalizes the analogous upper bound and lower bound properties of the real numbers.
• Replacing " greatest lower bound " with " induction argument shows that the existence of all possible pairwise suprema ( infima ), as per the definition, implies the existence of all non-empty finite suprema ( infima ).
• Once again ignoring complications involved with a continuous spectrum of " "'H " "', suppose it is bounded from below and that its greatest lower bound is " E " 0.
• Conversely, if L is a matroid lattice, one may define a rank function on sets of its atoms, by defining the rank of a set of atoms to be the lattice rank of the greatest lower bound of the set.
• A semilattice ( or more precisely a meet-semilattice ) ( L, \ le ) is a partially ordered set where every pair of elements a, b \ in L has a greatest lower bound, denoted a \ wedge b.
• Since exact energy eigenstates are infinitely spread out and are therefore usually excluded from a formal mathematical description, a stronger definition is that the mass gap is the greatest lower bound of the energy of any state which is orthogonal to the vacuum.
• Mathematically, the security level access may also be expressed in terms of the lattice ( a partial order set ) where each object and subject have a greatest lower bound ( meet ) and least upper bound ( join ) of access rights.
• The intersection of two flats is again a flat, defining a greatest lower bound operation on pairs of flats; one can also define a least upper bound of a pair of flats to be the ( unique ) maximal superset of their union that has the same rank as their union.
• Semilattices can also be defined idempotent binary operations, and any such operation induces a partial order ( and the respective inverse order ) such that the result of the operation for any two elements is the least upper bound ( or greatest lower bound ) of the elements with respect to this partial order.
• If the lattice is defined in terms of the order instead, i . e . ( A, d " ) is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, and the meet and join operations so defined satisfy the distributive law, then the complementation can also be defined as an involutive anti-automorphism, that is, a structure " A " = ( A, d ", ?) such that: