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Examples of the the word, inf , in a Sentence Context

The word ( inf ), is the 15387 most frequently used in English word vocabulary

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  1. Of points OK and a subsequence of such that OK ∈ Ink and OK → x as k → ∞. * LIM, inf ,In, which is also called the inner limit, consists of those elements which are
  2. M and a subset X. The ball measure of non-compactness is defined as: α (X) =, inf ,and the Murkowski measure of non-compactness is defined as: β (X) = inf
  3. For all but finitely many n (i.e., for cofinitely many n). That is, x ∈ LIM, inf ,In if and only if there exists some m>0 such that x ∈ In for all n>m. The limit
  4. Of real-valued functions mirrors that of the relation between the LIM sup, lim, inf , and the limit of a real sequence. Take metric spaces X and Y, a subspace E
  5. If and only if LIM inf X and LIM sup X agree, in which case LIM X LIM sup X LIM, inf ,X. This definition of the inf erior and superior limits is relatively strong
  6. That OK ∈ OK and OK → x as k → ∞. The limit LIM In exists if and only if LIM, inf ,In and LIM sup In agree, in which case LIM In LIM sup In LIM inf In. Special
  7. Operations. Besides the more obvious results,IEEE754 defines that - inf - inf , inf , inf and x ≠ Nan for any x (including Nan). Recommended functions and
  8. Then the outer limit will always contain the inner limit (i.e., lim, inf ,In ⊆ LIM sup In). The difference between the two definitions involves the
  9. Equivalently, this can be expressed as: \liming_ f (x)\GE f (x_0) where LIM, inf ,is the limit inf erior (of the function f at point x0). The function f is
  10. S. If no such number exists (because S is not bounded below),then we define, inf ,(S) −∞. If S is empty, we define inf (S) ∞ (see extended real number line
  11. M>0 such that x ∈ In for all n>m. The limit LIM X exists if and only if LIM, inf ,X and LIM sup X agree, in which case LIM X LIM sup X LIM inf X. This definition
  12. Inf. (That is, every element of K is the sup of some set of rationals, and the, inf ,of some other set of rationals. ) Thus an Archimedes field is any dense
  13. I am the natural numbers \math N. Here, we use the standard convention that, inf ,Ø =∞. ) The Hausdorff dimension of X is defined by: \operator name_ (X):
  14. Besides the more obvious results,IEEE754 defines that - inf - inf , inf , inf , and x ≠ Nan for any x (including Nan). Recommended functions and predicates *
  15. Has prevailed over that of Lucernarium (cf. Duane," Glossaries med. Et, inf , Lat. ", s. v. Desperate). The Gallic an Liturgy, the Arabic Liturgy, and, too
  16. Is primarily interested in cases where the limit does not exist. Whenever LIM, inf ,in and LIM sup in both exist, we have: \liming_x_n\LEQ\lineup_x_n. Limits
  17. Commentary of Mixed Type: The Glosses in MSS Harley 4946 and Ambrosia nus G111, inf , (Pontifical Institute of Medieval Studies,1996),pp. 24,31–32. Other
  18. Ε-δ definition by a simple re-arrangement, and by using a limit (LIM sup, lim, inf ,) to define oscillation: if (at a given point) for a given ε0 there is no δ
  19. Of the empty set is negative inf inity, while the greatest lower bound (, inf ,or minimum) is positive inf inity. By analogy with the above, in the domain of
  20. Formula can still apply by generalizing the definition of x (F):: x (F1) =, inf ,For an example of a Lorenz curve, see Pareto distribution. Properties A Lorenz
  21. In exists if and only if LIM sup In LIM inf In, and in that case, lim In LIM, inf ,In=LIM sup In. In this sense, the sequence has a limit so long as all but
  22. From metric spaces to metric spaces There is a notion of LIM sup and LIM, inf ,for functions defined on a metric space whose relationship to limits of
  23. Or Minkowski content, of a measurable subset A of X is defined as the LIM, inf ,: \mud+ (A) = \liming_ \franc, where: A_\var epsilon = \ is the extension of
  24. S is not bounded below),then we define inf (S) −∞. If S is empty, we define, inf ,(S) ∞ (see extended real number line). An important property of the real
  25. Of Troyes, about the same period, composed a Breviaries Psalter ii (v., inf , V. HISTORY). In an ancient inventory occurs Breviaries Antiphonal, meaning
  26. Set. So, as in the previous example, ::: However, for and:: * LIM sup In LIM, inf ,In LIM In =: * LIM sup Zn LIM inf Zn LIM Zn =: In each of these four cases, the
  27. That is, the four elements that do not match the pattern do not affect the LIM, inf ,and LIM sup because there are only finitely many of them. In fact, these
  28. Limit is the empty set. That is, ::: However, for and:: * LIM sup In LIM, inf ,In LIM In =: * LIM sup Zn LIM inf Zn LIM Zn = * Consider the set X = and the
  29. Frac, where A (n) denotes the number of elements of A not exceeding n and, inf ,is minimum. The Schliemann density is well-defined even if the limit of A (
  30. The minimum or greatest lower bound of a subset S of real numbers is denoted by, inf ,(S) and is defined to be the biggest real number that is smaller than or
  31. Single rational. ) 6. The rationals are dense in K with respect to both sup and, inf , (That is, every element of K is the sup of some set of rationals, and the inf
  32. Of M and x is a point of M, we define the distance from x to S as: d (x, S ) =, inf ,Then d (x, S ) = 0 if and only if x belongs to the closure of S. Furthermore
  33. Eskichremen lend out (Gazelles Oracular 8 of Habaneros) (Attic as +, inf , Kichranai from chroma use) * Wades knowing (Doric) wades) (Clean
  34. S" Letitia Lit. Amber ". *The" Lodging Sacramental "; Bill. Amber., A. 24, inf , .,eleventh century. Del isle," ANC. Sack. ", LXXII. *The" Sacramental of San
  35. Contains a nonzero vector in Γ. The successive minimum OK is defined to be the, inf ,of the numbers λ such that OK contains k linearly independent vectors of Γ.
  36. The" Bianca Sacramental "; Bill. Am bros., A. 24,bis, inf ,., late ninth or early tenth century. Described by Del isle," ANC. Sack. ", LXXI
  37. However, for and:: * LIM sup In LIM inf In LIM In =: * LIM sup Zn LIM, inf ,Zn LIM Zn =: In each of these four cases, the elements of the limiting sets are
  38. In for all but finitely many n (i.e., cofinitely many n). That is, x ∈ LIM, inf ,In if and only if there exists a sequence of points such that OK ∈ OK and OK →
  39. Inf and the Murkowski measure of non-compactness is defined as: β (X) =, inf ,Since a ball of radius r has diameter at most 2r,we have α (X) ≤ β (X) ≤
  40. U (r) is contained in U (s). Once we have these sets, we define f (x) =, inf ,for every x ∈ X. Using the fact that the dyadic rationals are dense, it is then
  41. Which is more common in order theory, by \sees. Likewise, inf ima are denoted by, inf ,(S) or \wedges. In lattice theory it is common to use the minimum/meet and
  42. If and only if there exists a subsequence of such that x ∈ Ink for all k. * LIM, inf ,In consists of elements of X which belong to In for all but finitely many n (
  43. Distance d (x, y ) between the points x and y of M is defined as: d (x, y ) =, inf , Even though Riemannian manifolds are usually" curved," there is still a
  44. Finitely many elements. The limit LIM In exists if and only if LIM sup In LIM, inf ,In, and in that case, lim In LIM inf In=LIM sup In. In this sense, the sequence
  45. This is to say that x is a point of closure of S if the distance d (x, S ):, inf ,= 0. This definition generalizes to topological spaces by replacing" open ball
  46. Clearing Iraqi strong points which that division had bypassed. 3rd Battalion 187, inf , regt (3rd Brigade) was attached to 3rd Infantry Division and was the main
  47. Is, ::: However, for and:: * LIM sup In LIM inf In LIM In =: * LIM sup Zn LIM, inf ,Zn LIM Zn = * Consider the set X = and the sequence of subsets:: :\ = \.: As in
  48. Only if LIM inf In and LIM sup In agree, in which case LIM In LIM sup In LIM, inf ,In. Special case: discrete metric In this case, which is frequently used in
  49. Sets is the union AXN of sets in sequence. In this context, the inner limit LIM, inf ,In is the largest meeting of tails of the sequence, and the outer limit LIM sup
  50. Bernômetha Attic klêrôsômetha we will cast or obtain by lot (, inf , Berreai) (Cf. Attic Martha receive portion, Doric

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