DIY Life Web Search

Search results

  1. Results From The WOW.Com Content Network
  2. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    That is, xlim sup X n if and only if there exists a subsequence (X n k) of (X n) such that xX n k for all k. lim inf X n consists of elements of X which belong to X n for all except finitely many n (i.e., for cofinitely many n). That is, xlim inf X n if and only if there exists some m > 0 such that xX n for all n > m.

  3. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    Informally, a function f assigns an output f(x) to every input x. We say that the function has a limit L at an input p, if f(x) gets closer and closer to L as x moves closer and closer to p. More specifically, the output value can be made arbitrarily close to L if the input to f is taken sufficiently close to p.

  4. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    On the other hand, if X is the domain of a function f(x) and if the limit as n approaches infinity of f(x n) is L for every arbitrary sequence of points {x n} in Xx 0 which converges to x 0, then the limit of the function f(x) as x approaches x 0 is equal to L. [10] One such sequence would be {x 0 + 1/n}.

  5. Iterated limit - Wikipedia

    en.wikipedia.org/wiki/Iterated_limit

    In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form , = (,), (,) = ((,)),or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value ...

  6. Limit of a sequence - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_sequence

    Here, one can see that the sequence is converging to the limit 0 as n increases. In the real numbers , a number L {\displaystyle L} is the limit of the sequence ( x n ) {\displaystyle (x_{n})} , if the numbers in the sequence become closer and closer to L {\displaystyle L} , and not to any other number.

  7. Limit comparison test - Wikipedia

    en.wikipedia.org/wiki/Limit_comparison_test

    One can state a one-sided comparison test by using limit superior. Let a n , b n ≥ 0 {\displaystyle a_{n},b_{n}\geq 0} for all n {\displaystyle n} . Then if lim sup n → ∞ a n b n = c {\displaystyle \limsup _{n\to \infty }{\frac {a_{n}}{b_{n}}}=c} with 0 ≤ c < ∞ {\displaystyle 0\leq c<\infty } and Σ n b n {\displaystyle \Sigma _{n}b ...

  8. Limit of distributions - Wikipedia

    en.wikipedia.org/wiki/Limit_of_distributions

    Given a sequence of distributions , its limit is the distribution given by [] = []for each test function , provided that distribution exists.The existence of the limit means that (1) for each , the limit of the sequence of numbers [] exists and that (2) the linear functional defined by the above formula is continuous with respect to the topology on the space of test functions.

  9. Computation in the limit - Wikipedia

    en.wikipedia.org/wiki/Computation_in_the_limit

    One can think of limit computable functions as those admitting an eventually correct computable guessing procedure at their true value. A set is limit computable just when its characteristic function is limit computable. If the sequence is uniformly computable relative to D, then the function is limit computable in D.