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 }...
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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...
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mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are...
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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...
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mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input...
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Accumulation point (redirect from Limit point of a set)
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...
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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...
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Net (mathematics) (redirect from Limit of a net)
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...
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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...
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Uniform convergence (redirect from Uniform limit)
is that a uniformly convergent sequence of continuous functions has a continuous limit. The failure of a merely pointwise-convergent limit of continuous...
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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...
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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...
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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...
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specifically in the theory of generalized functions, the limit of a sequence of distributions is the distribution that sequence approaches. The distance...
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Ordinal number (redirect from Transfinite sequence)
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...
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In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely...
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14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons...
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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}} ...
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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...
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Pointwise convergence (redirect from Pointwise convergent sequence)
(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...
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central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard...
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the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous. More precisely, let X be a topological...
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Continuous function (redirect from Continuity at a point)
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...
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This is a list of calculus topics. Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation...
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Real analysis (redirect from Theory of functions of a real variable)
particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability...
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Series (mathematics) (redirect from Sequence of series)
the sequence of its partial sums has a limit L. In this case, one usually writes L = ∑ n = 0 ∞ a n . {\displaystyle L=\sum _{n=0}^{\infty }a_{n}.} A series...
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Graphon (redirect from Graph limit)
study of dense graphs. Graphons arise both as a natural notion for the limit of a sequence of dense graphs, and as the fundamental defining objects of exchangeable...
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In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the...
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{\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...
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degeneracy pressure, compared to main sequence stars, which resist collapse through thermal pressure. The Chandrasekhar limit is the mass above which electron...
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