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

The word ( sup ), is the 16557 most frequently used in English word vocabulary

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  1. Of partially ordered sets) is continuous if for each subset A of X, we have, sup ,(f (A) ) = f ( sup (Y) ). Here sup is the sup reme with respect to the
  2. Distribution function F (x) is: D_n=\ sup _x | F_n (x)-F (x) | where, sup ,x is the sup reme of the set of distances. By the Given–Cantrell theorem, if
  3. To the 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
  4. Given a subset S of a totally or partially ordered set T, the sup reme (, sup ,) of S, if it exists, is the least element of T which is greater than or equal
  5. 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 of the inferior and sup erior limits is relatively
  6. The root test uses the number: C \lineup_\sort \lineup_\sort|z-a |" LIM, sup ," denotes the limit sup erior. The root test states that the series converges if
  7. For all but 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
  8. Everywhere differentiable function g: R → R is Lipschitz continuous (with K =, sup ,| g′ (x) |) if and only if it has bounded first derivative; one direction
  9. To a bounded scalar sequence. If we further consider both spaces with the, sup ,norm the extension map becomes an isometry. Indeed, if in the construction
  10. 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 case: discrete metric In this case, which is frequently
  11. Belong to In for (countably) infinitely many values of n. That is, x ∈ LIM, sup ,In if and only if there exists a subsequence of such that x ∈ Ink for all k. *
  12. F and g. If, in addition, we define sup (S) −∞ when S is empty and, sup ,(S) +∞ when S is not bounded above, then every set of real numbers has a
  13. To the general definition above. If is a sequence of subsets of X, then: * LIM, sup ,In consists of elements of X which belong to In for (countably) infinitely
  14. If for each subset A of X, we have sup ped (f (A) ) = f ( sup (Y) ). Here, sup ,is the sup reme with respect to the orderings in X and Y, respectively.
  15. Potato leaves, cassava leaves, Crancran, hot peppers, peanuts,beans, okra, sup , fish, beef,chicken, eggplant,onions, and tomatoes and chicken bones, which
  16. The sup reme or least upper bound of a set S of real numbers is denoted by, sup ,(S) and is defined to be the smallest real number that is greater than or
  17. 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 of the
  18. 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 case: discrete
  19. Metric space, this can be expressed as: \lineup_ f (x)\LE f (x_0) where LIM, sup ,is the limit sup erior (of the function f at point x0). (For non-metric
  20. Toast of the tetrarchy ", telling John the Baptist she will" drink pearls ..., sup ,on peacock's tongues. " Mary of Bethany (Neo-Aramaic מרים, Maryām, rendered
  21. D_\nifty (X, Y)=\math rm \ sup _\omega|X (\omega)-Y (\omega) |, where " ESS, sup ," represents the essential sup reme in the sense of measure theory. Equality
  22. 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 finitely many of
  23. Sets) is continuous if for each subset A of X, we have sup ped (f (A) ) = f (, sup ,(Y) ). Here sup is the sup reme with respect to the orderings in X and Y
  24. Max (\ \cup \math) +\nifty. That is, the least upper bound (, sup ,or sup reme) of the empty set is negative infinity, while the greatest lower
  25. Or inferior 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 =
  26. Is the empty 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
  27. Between pairs of points in the subset. So, if A is the subset, the diameter is:, sup , Some authors prefer to treat the empty set (A=\empty set) as a special case.
  28. To limits 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
  29. Of the sequence of events, and each event is a set of outcomes. That is, lim, sup ,En is the set of outcomes that occur infinitely many times within the infinite
  30. Is of Persian origin. Tenth tale (V,10) Pietro di Vincible goes from home to, sup ,: his wife brings a boy into the house to bear her company: Pietro returns, and
  31. 1: find n such that; then if, we are done. Otherwise, p in, and by setting k =, sup , one obtains. Generalizations of the pigeonhole principle A generalized version
  32. The limiting set. In particular, if is a sequence of subsets of X, then: * LIM, sup ,In, which is also called the outer limit, consists of those elements which are
  33. Soup, Suppe. (The Oxford English Dictionary, however,suggests that the root, sup , retains obscure origins. ) Other meanings In England, whereas " dinner ", when
  34. By b. Hence, by the completeness property of the real numbers, the sup reme c, sup ’S exists. That is, c is the lowest number that is greater than or equal to
  35. Sup \, \ + \ sup \, \ for any functional f and g. If, in addition, we define, sup ,(S) −∞ when S is empty and sup (S) +∞ when S is not bounded above, then
  36. Of points in In taken from (countably) infinitely many n. That is, x ∈ LIM, sup ,In if and only if there exists a sequence of points OK and a subsequence of
  37. 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 inferior/ sup erior
  38. 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 elements could be
  39. Structure is defined by a single pseudometric, namely the upper envelope, sup ,phi of the family. Less trivially, it can be shown that a uniform structure that
  40. Inf In is the largest meeting of tails of the sequence, and the outer limit LIM, sup ,In is the smallest joining of tails of the sequence. *Let In be the meet of the
  41. 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 elements of the
  42. 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 sequence of subsets:: :\
  43. Norm | | ƒ | |, is defined in it. Such a norm may be defined as | | ƒ | | =, sup , known as the sup reme norm. This is indeed a well-defined norm, since
  44. One deals with real numbers or any other totally ordered set. To show that a =, sup ,(S),one has to show that an is an upper bound for S and that any other upper
  45. A_|^: = \lineup_ | a_n|^. We take R to be infinite when this latter LIM, sup ,is zero. Conversely, if we start with an annulus of the form A = and a
  46. In the construction above we take the smallest possible ball B, we see that the, sup ,norm of the extended sequence does not grow (although the image of the
  47. Then occur is 0,that is, : :\Pr\left (\lineup_ E_n\right) = 0. \, Here," LIM, sup ," denotes limit sup erior of the sequence of events, and each event is a set of
  48. Is also known as meet. If the sup reme of a set S exists, it can be denoted as, sup ,(S) or, which is more common in order theory, by \sees. Likewise, infima are
  49. Set. Functions 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
  50. 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 topology (i.e.

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