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  2. Limit (mathematics) - Wikipedia

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

    On one hand, the limit as n approaches infinity of a sequence {a n} is simply the limit at infinity of a function a(n) —defined on the natural numbers {n}. 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 X − x 0 which ...

  3. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    Limits involving infinity are connected with the concept of asymptotes. These notions of a limit attempt to provide a metric space interpretation to limits at infinity. In fact, they are consistent with the topological space definition of limit if

  4. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions

  5. Extended real number line - Wikipedia

    en.wikipedia.org/wiki/Extended_real_number_line

    Using this characterization of extended-real neighborhoods, limits with tending to + or , and limits "equal" to + and , reduce to the general topological definition of limits—instead of having a special definition in the real number system.

  6. 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 ...

  7. Limit of a sequence - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_sequence

    A limit of a sequence of points () in a topological space is a special case of a limit of a function: the domain is in the space {+}, with the induced topology of the affinely extended real number system, the range is , and the function argument tends to +, which in this space is a limit point of .

  8. Beyond Infinity (mathematics book) - Wikipedia

    en.wikipedia.org/wiki/Beyond_Infinity...

    Beyond Infinity : An Expedition to the Outer Limits of Mathematics is a popular mathematics book by Eugenia Cheng centered on concepts of infinity.It was published by Basic Books and (with a slightly different title) by Profile Books in 2017, [1] [2] [3] and in a paperback edition in 2018. [4]

  9. Indeterminate form - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_form

    A limit taking one of these indeterminate forms might tend to zero, might tend to any finite value, might tend to infinity, or might diverge, depending on the specific functions involved. A limit which unambiguously tends to infinity, for instance lim x → 0 1 / x 2 = ∞ , {\textstyle \lim _{x\to 0}1/x^{2}=\infty ,} is not considered ...