nonempty set वाक्य
उदाहरण वाक्य
मोबाइल
- This property may be used to characterize realizers of finite partial orders : A nonempty set of linear extensions is a realizer if and only if it reverses every critical pair.
- Note that one formulation of AC is that the Cartesian product of a family of nonempty sets is nonempty; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward lines.
- Let \ mathcal { X } be a nonempty set and k a positive-definite real-valued kernel on \ mathcal { X } \ times \ mathcal { X } with corresponding reproducing kernel Hilbert space H _ k.
- Let A = \ cup _ i A _ i and B = \ cup _ j B _ j be partitions of disjoint nonempty sets A and B, where all A _ i and B _ j share a common size.
- Then TT is a topology on M . It is called the manifold topology induced by AA . A manifold is a nonempty set with an atlas so that the manifold topology is separated, i . e . distinct points have disjoint neighborhoods.
- It seems to me that if K = { " B " } where " B " has 2 elements, then PH ( K ) contains only sets whose sizes are powers of 2, whereas HP ( K ) contains all nonempty sets.
- If we had a black box that solved FIND-SUBSET-SUM in unit time, then it would be easy to solve SUBSET-SUM . Simply ask the black box to find the subset that sums to zero, then check whether it returned a nonempty set.
- They observed ( as did some other contemporary authors ) that the lattice of stable matchings was reminiscent of the conclusion of Tarski s fixed point theorem, which states that an increasing function from a complete lattice to itself has a nonempty set of fixed points that form a complete lattice.
- It states that for every indexed family ( S _ i ) _ { i \ in I } of nonempty sets there exists an indexed family ( x _ i ) _ { i \ in I } of elements such that x _ i \ in S _ i for every i \ in I.
- Let \ mathcal { X } be a nonempty set, k a positive-definite real-valued kernel on \ mathcal { X } \ times \ mathcal { X } with corresponding reproducing kernel Hilbert space H _ k, and let R \ colon H _ k \ to \ R be a differentiable regularization function.
- Another result analogous to Birkhoff's representation theorem, but applying to a broader class of lattices, is the theorem of that any finite join-distributive lattice may be represented as an antimatroid, a family of sets closed under unions but in which closure under intersections has been replaced by the property that each nonempty set has a removable element.
- In general we must select, for each element of the index set, an element of the nonempty set of limits of the projected ultrafilter base, and of course this uses AC . However, it also shows that the compactness of the product of compact Hausdorff spaces can be proved using ( BPI ), and in fact the converse also holds.
- More generally, if X is a nonempty set and \ lambda is a cardinal, then C \ subseteq [ X ] ^ \ lambda is " club " if every union of a subset of C is in C and every subset of X of cardinality less than \ lambda is contained in some element of C ( see stationary set ).
- In other words, a nonempty set equipped with the proximal relator \ mathcal { R } _ { \ delta _ { \ Phi, \ varepsilon } } has underlying structure provided by the proximal relator \ mathcal { R } _ { \ delta _ { \ Phi } } and provides a basis for the study of tolerance near sets in X that are near within some tolerance.
- If the method is applied to an infinite sequence ( " X " " i " : " i " " ? ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.
- Each choice function on a collection " X " of nonempty sets is an element of the family of sets, where a given set can occur more than once as a factor; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all " distinct " sets in the family.
- From this bit vector viewpoint, a concrete Boolean algebra can be defined equivalently as a nonempty set of bit vectors all of the same length ( more generally, indexed by the same set ) and closed under the bit vector operations of bitwise'", ( ", and ? as in 1010'" 0110 = 0010, 1010 ( " 0110 = 1110, and ?010 = 0101, the bit vector realizations of intersection, union, and complement respectively.
- The result is an explicit choice function : a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on . ( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number " k ", every family of " k " nonempty sets has a choice function . " ) This method cannot, however, be used to show that every countable family of nonempty sets has a choice function, as is asserted by the axiom of countable choice.
- The result is an explicit choice function : a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on . ( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number " k ", every family of " k " nonempty sets has a choice function . " ) This method cannot, however, be used to show that every countable family of nonempty sets has a choice function, as is asserted by the axiom of countable choice.
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