In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the lim {\displaystyle \lim }...

concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in...

mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can...

is the limit of the sequence (3, 3.1, 3.14, 3.141, 3.1415, ...), which is increasing. A related sequence is the sequence of decimal digits of π, that...

definition of a cluster or accumulation point of a sequence generalizes to nets and filters. The similarly named notion of a limit point of a sequence (respectively...

of the sequence are getting closer and closer together in a way that suggests that the sequence ought to have a limit in X. Nonetheless, such a limit...

mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input...

topology and related branches, a net or Moore–Smith sequence is a function whose domain is a directed set. The codomain of this function is usually some...

mathematics, the limit of a sequence of sets A 1 , A 2 , … {\displaystyle A_{1},A_{2},\ldots } (subsets of a common set X {\displaystyle X} ) is a set whose...

is that a uniformly convergent sequence of continuous functions has a continuous limit. The failure of a merely pointwise-convergent limit of continuous...

as a continued fraction. Using calculus, e may also be represented as an infinite series, infinite product, or other types of limit of a sequence. Euler...

In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely...

definition of the mathematical notion of limit Limit of a sequence One-sided limit, either of the two limits of a function as a specified point is approached...

central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard...

an iterated limit is a limit of a sequence or a limit of a function in the form lim m → ∞ lim n → ∞ a n , m = lim m → ∞ ( lim n → ∞ a n , m ) {\displaystyle...

specifically in the theory of generalized functions, the limit of a sequence of distributions is the distribution that sequence approaches. The distance...

gives a mild sufficient condition under which limits and integrals of a sequence of functions can be interchanged. More technically it says that if a sequence...

the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous. More precisely, let X be a topological...

summable and also the sequence ( a 1 , a 2 , a 3 , … ) {\displaystyle (a_{1},a_{2},a_{3},\ldots )} is summable, and otherwise, when the limit does not exist...

In mathematics, an ultralimit is a geometric construction that assigns a limit metric space to a sequence of metric spaces X n {\displaystyle X_{n}} ...

when a point is the limit of a sequence. Still, for some spaces that are too large in some sense, one specifies also when a point is the limit of more...

term of the sequence. In this sense, a limit ordinal is the limit of all smaller ordinals (indexed by itself). Put more directly, it is the supremum of the...

(and only if) the limit of the sequence f n ( x ) {\displaystyle f_{n}(x)} evaluated at each point x {\displaystyle x} in the domain of f {\displaystyle...

14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons...

particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability...

{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\a\ell &=b^{2}.\end{aligned}}} A parabola can be obtained as the limit of a sequence of ellipses where one focus...

In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the...

In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values...

kind of limit (a weak limit) of a sequence of functions, each member of which has a tall spike at the origin: for example, a sequence of Gaussian distributions...

rate of convergence and order of convergence of a sequence that converges to a limit are any of several characterizations of how quickly that sequence approaches...