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  2. Limit inferior and limit superior - Wikipedia

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

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  3. 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 ...

  4. 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.

  5. 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.

  6. Interchange of limiting operations - Wikipedia

    en.wikipedia.org/wiki/Interchange_of_limiting...

    Examples abound, one of the simplest being that for a double sequence a m,n: it is not necessarily the case that the operations of taking the limits as m → ∞ and as n → ∞ can be freely interchanged. [4] For example take a m,n = 2 m − n. in which taking the limit first with respect to n gives 0, and with respect to m gives ∞.

  7. Cauchy's limit theorem - Wikipedia

    en.wikipedia.org/wiki/Cauchy's_limit_theorem

    Cauchy's limit theorem, named after the French mathematician Augustin-Louis Cauchy, describes a property of converging sequences.It states that for a converging sequence the sequence of the arithmetic means of its first members converges against the same limit as the original sequence, that is () with implies (+ +) / .

  8. Tom Clancy's H.A.W.X 2 - Wikipedia

    en.wikipedia.org/wiki/Tom_Clancy's_H.A.W.X_2

    The game features a story campaign which can be played solo or with cooperation of three other players. The player is often in control of Major Alex Hunter, a pilot from High Altitude Warfare – Experimental (HAWX) squadron but gets to play one or two missions as other pilots, including Captain Dimitri Ivanovich Sokov of Russian Air Force, Lieutenant Colin Munro of the British Royal Navy and ...

  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.