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searching for Limit of a sequence 52 found (103 total)

Semi-major and semi-minor axes (2,374 words) [view diff] exact match in snippet view article find links to article

either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed

Horosphere (378 words) [view diff] exact match in snippet view article find links to article

hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and

Bochner measurable function (350 words) [view diff] exact match in snippet view article find links to article

in a Banach space is a function that equals almost everywhere the limit of a sequence of measurable countably-valued functions, i.e., f ( t ) = lim n →

Sofic group (355 words) [view diff] exact match in snippet view article find links to article

finitely generated group is sofic if it is the limit of a sequence of sofic groups. The limit of a sequence of amenable groups (that is, an initially subamenable

Ultralimit (2,462 words) [view diff] exact match in snippet view article find links to article

\{n:d(x_{n},x)\leq \epsilon \}\in \omega .} It is observed that, If an ω-limit of a sequence of points exists, it is unique. If x = lim n → ∞ x n {\displaystyle

Baire function (886 words) [view diff] exact match in snippet view article find links to article

limit of a sequence of Baire class 0 functions. In general, the Baire class α functions are all functions which are the pointwise limit of a sequence

Approximately finite-dimensional C*-algebra (3,201 words) [view diff] exact match in snippet view article find links to article

finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality

Area of a circle (5,892 words) [view diff] exact match in snippet view article find links to article

which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area

G-measure (352 words) [view diff] exact match in snippet view article find links to article

measure μ {\displaystyle \mu } that can be represented as the weak-∗ limit of a sequence of measurable functions G = ( G n ) n = 1 ∞ {\displaystyle

Indecomposable continuum (1,145 words) [view diff] exact match in snippet view article find links to article

often constructed as the limit of a sequence of nested intersections, or (more generally) as the inverse limit of a sequence of continua. The buckethandle

Complete class theorem (140 words) [view diff] exact match in snippet view article find links to article

limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a Bayesian procedure (or a limit of

Decision theory (3,216 words) [view diff] exact match in snippet view article find links to article

limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a Bayesian procedure (or a limit of

Regulated integral (891 words) [view diff] exact match in snippet view article find links to article

f : [a, b] → R is called a regulated function if it is the uniform limit of a sequence of step functions on [a, b]: there is a sequence of step functions

Weakly measurable function (601 words) [view diff] exact match in snippet view article find links to article

{\displaystyle B} is (strongly) measurable (that equals a.e. the limit of a sequence of measurable countably-valued functions) if and only if it is both

Measurable function (1,329 words) [view diff] exact match in snippet view article find links to article

real-valued measurable functions are all measurable as well. The pointwise limit of a sequence of measurable functions f n : X → Y {\displaystyle f_{n}:X\to Y}

Prefix order (625 words) [view diff] case mismatch in snippet view article find links to article

Models (DCM). pp. 25–29. Cuijpers, Pieter (2013). "The Categorical Limit of a Sequence of Dynamical Systems". EPTCS 120: Proceedings EXPRESS/SOS 2013. 120:

Intrinsic flat distance (894 words) [view diff] exact match in snippet view article find links to article

contained in Y but not necessarily equal to Y. For example, the GH limit of a sequence of spheres with a long thin neck pinch is a pair of spheres with

LF-space (2,770 words) [view diff] exact match in snippet view article find links to article

locally convex TVSs are "poorly behaved". For instance, the direct limit of a sequence (i.e. indexed by the natural numbers) of locally convex nuclear Fréchet

Laplacian of the indicator (4,269 words) [view diff] exact match in snippet view article find links to article

formulation of distribution theory, it is in practice regarded as a limit of a sequence of smooth functions; one may meaningfully take the Laplacian of a

Dirichlet function (770 words) [view diff] exact match in snippet view article find links to article

The Dirichlet function can be constructed as the double pointwise limit of a sequence of continuous functions, as follows: ∀ x ∈ R , 1 Q ( x ) = lim k

Montel space (1,338 words) [view diff] exact match in snippet view article find links to article

family of Montel spaces is a Montel space. The strict inductive limit of a sequence of Montel spaces is a Montel space. In contrast, closed subspaces

Axiom of countable choice (1,259 words) [view diff] exact match in snippet view article find links to article

function. Every accumulation point of a subset of a metric space is a limit of a sequence of points from the subset. The Rasiowa–Sikorski lemma MA ( ℵ 0 )

Inscribed square problem (1,939 words) [view diff] exact match in snippet view article find links to article

this argument has not been carried out to completion is that the limit of a sequence of squares may be a single point rather than itself being a square

DF-space (1,031 words) [view diff] exact match in snippet view article find links to article

convex sum of a sequence of DF-spaces is a DF-space. An inductive limit of a sequence of DF-spaces is a DF-space. Suppose that X {\displaystyle X} and

Classical Wiener space (1,216 words) [view diff] exact match in snippet view article find links to article

theorem; completeness is a consequence of the fact that the uniform limit of a sequence of continuous functions is itself continuous. Since it is both separable

Σ-algebra (5,381 words) [view diff] exact match in snippet view article find links to article

are defined as follows on σ-algebras. The limit supremum or outer limit of a sequence A 1 , A 2 , A 3 , … {\displaystyle A_{1},A_{2},A_{3},\ldots } of

Weakly simple polygon (399 words) [view diff] exact match in snippet view article find links to article

the polygonal boundary of a topological disk: this boundary is the limit of a sequence of polygons, offset from it within the disk. However, this type of

Hilbert's fifth problem (1,077 words) [view diff] exact match in snippet view article find links to article

manifolds: Every locally compact connected group is the projective limit of a sequence of Lie groups. Further, it is a Lie group if it has no small subgroups

Metrizable topological vector space (10,645 words) [view diff] exact match in snippet view article find links to article

induced by a metric (resp. pseudometric). An LM-space is an inductive limit of a sequence of locally convex metrizable TVS. A pseudometric on a set X {\displaystyle

Space-filling curve (1,965 words) [view diff] exact match in snippet view article find links to article

well-known space-filling curves are constructed iteratively as the limit of a sequence of piecewise linear continuous curves, each one more closely approximating

Jorge Luis Borges and mathematics (1,266 words) [view diff] exact match in snippet view article find links to article

Visualizing a measure zero set as the limit of a sequence of nested intervals. Pages in "The Book of Sand" have measure zero.

Squeeze theorem (1,764 words) [view diff] exact match in snippet view article find links to article

similar, using the ε {\displaystyle \varepsilon } -definition of the limit of a sequence. The limit lim x → 0 x 2 sin ⁡ ( 1 x ) {\displaystyle \lim _{x\to

Spectral theory of compact operators (1,749 words) [view diff] exact match in snippet view article find links to article

the quotient map, z = 0. This is impossible because z is the norm limit of a sequence of unit vectors. Thus the lemma is proven. Concluding the Proof Proof

Ultraproduct (3,108 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \omega } above. In model theory and set theory, the direct limit of a sequence of ultrapowers is often considered. In model theory, this construction

Domain theory (2,689 words) [view diff] exact match in snippet view article find links to article

the least upper bound of the directed set. As in the case of the limit of a sequence, the least upper bound of a directed set does not always exist. Naturally

Dirac delta function (14,218 words) [view diff] no match in snippet view article find links to article

the delta function is often manipulated as a kind of limit (a weak limit) of a sequence of functions, each member of which has a tall spike at the origin:

Uniform boundedness principle (4,620 words) [view diff] exact match in snippet view article find links to article

The following theorem establishes conditions for the pointwise limit of a sequence of continuous linear maps to be itself continuous. Theorem—Suppose

Hyperbolic 3-manifold (2,217 words) [view diff] exact match in snippet view article find links to article

theorem implies that a manifold with m {\displaystyle m} cusps is a limit of a sequence of manifolds with l {\displaystyle l} cusps for any 0 ≤ l < m {\displaystyle

Quasi-fibration (1,143 words) [view diff] exact match in snippet view article find links to article

Theorem. Let p: E → B be a continuous map where B is the inductive limit of a sequence B1 ⊂ B2 ⊂ ... All Bn are moreover assumed to satisfy the first separation

Buffon's noodle (1,029 words) [view diff] exact match in snippet view article find links to article

+X_{n})=E(X_{1})+\cdots +E(X_{n}).} Regarding a curved noodle as the limit of a sequence of piecewise linear noodles, we conclude that the expected number

Scott domain (1,027 words) [view diff] exact match in snippet view article find links to article

in terms of partial data allows an algebra to be defined as the limit of a sequence of increasingly more defined partial algebras—in other words a fixed

Cauchy's integral formula (4,364 words) [view diff] exact match in snippet view article find links to article

particular the analyticity of the function. Likewise, the uniform limit of a sequence of (real) differentiable functions may fail to be differentiable

Integral (9,283 words) [view diff] exact match in snippet view article find links to article

In some cases such integrals may be defined by considering the limit of a sequence of proper Riemann integrals on progressively larger intervals. If

Ordinal number (6,704 words) [view diff] exact match in snippet view article find links to article

class, i.e., it cannot be a set). It is said to be closed when the limit of a sequence of ordinals in the class is again in the class: or, equivalently

Von Neumann bicommutant theorem (928 words) [view diff] exact match in snippet view article find links to article

show. Lemma. P ∈ M′. Proof. Fix x ∈ H. As Px ∈ cl(Mh), it is the limit of a sequence Onh with On in M. For any T ∈ M, TOnh is also in Mh, and by the continuity

Regular cardinal (1,441 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \omega } , so ω + ω {\displaystyle \omega +\omega } is the limit of a sequence of type less than ω + ω {\displaystyle \omega +\omega } whose elements

Real analysis (7,671 words) [view diff] exact match in snippet view article find links to article

used here in a metaphorical sense as a shorthand for taking the limit of a sequence of partial sums and should not be interpreted as simply "adding"

Manuel Felguérez (3,441 words) [view diff] exact match in snippet view article find links to article

Felguerez: El Limite de una Secuencia" [Corridor/Manuel Felguerez: The limit of a sequence]. Reforma (in Spanish). Mexico City. p. 21. "Reconoce el presidente

Viscosity solution (2,597 words) [view diff] exact match in snippet view article find links to article

{\displaystyle L^{\infty }} holds as follows: a locally uniform limit of a sequence of solutions (or subsolutions, or supersolutions) is a solution (or

Maximum principle (3,699 words) [view diff] exact match in snippet view article find links to article

attain a maximum value. However, it is possible for the pointwise limit of a sequence of functions without maxima to have a maxima. Nonetheless, if M has

College Scholastic Ability Test (4,133 words) [view diff] exact match in snippet view article find links to article

II. Differentiation III. Integration Elective subject Calculus I. Limit of a sequence II. Methods of differentiation III. Methods of integration Probability

Homomorphism density (2,300 words) [view diff] exact match in snippet view article find links to article

densities of graphs which satisfy certain property, since a graphon is a limit of a sequence of graphs. Many results in extremal graph theory can be described