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Sequence of points that get progressively closer to each other
In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given
Cauchy_sequence
Metric geometry
mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively
Complete_metric_space
Finite or infinite ordered list of elements
Look-and-say sequence Thue–Morse sequence List of integer sequences Types ±1-sequence Arithmetic progression Automatic sequence Cauchy sequence Constant-recursive
Sequence
mathematics, a sequence of functions { f n } {\displaystyle \{f_{n}\}} from a set S to a metric space M is said to be uniformly Cauchy if: For all ε >
Uniformly_Cauchy_sequence
Criterion for infinite series
The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. This convergence
Cauchy's_convergence_test
Value approached by a mathematical object
A property of convergent sequences of real numbers is that they are Cauchy sequences. The definition of a Cauchy sequence { a n } {\displaystyle \{a_{n}\}}
Limit_(mathematics)
Value to which tends an infinite sequence
analysis is the Cauchy criterion for convergence of sequences: a sequence of real numbers is convergent if and only if it is a Cauchy sequence. This remains
Limit_of_a_sequence
French mathematician (1789–1857)
equations Cauchy–Schwarz inequality Cauchy sequence Cauchy surface Cauchy's theorem (geometry) Cauchy's theorem (group theory) Maclaurin–Cauchy test French
Augustin-Louis_Cauchy
Nonexistence of gaps in the number line
Cauchy completeness is the statement that every Cauchy sequence of real numbers converges to a real number. The rational number line Q is not Cauchy complete
Completeness of the real numbers
Completeness_of_the_real_numbers
by a Cauchy sequence of rational numbers. This representation is far from unique; every rational sequence that converges to x is a Cauchy sequence representing
Construction of the real numbers
Construction_of_the_real_numbers
Concept in mathematics
the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. The Cauchy product
Cauchy_product
Number representing a continuous quantity
common definitions of real numbers include equivalence classes of Cauchy sequences (of rational numbers), Dedekind cuts, and infinite decimal representations
Real_number
test Cauchy's convergence test Cauchy–Hadamard theorem Cauchy product Cauchy's radical test Cauchy ratio test Cauchy sequence Uniformly Cauchy sequence Maclaurin–Cauchy
List of things named after Augustin-Louis Cauchy
List_of_things_named_after_Augustin-Louis_Cauchy
Structure in functional analysis
progressively closer" is made rigorous by Cauchy nets or Cauchy filters, which are generalizations of Cauchy sequences, while "point x {\displaystyle x} towards
Complete topological vector space
Complete_topological_vector_space
Alternative decimal expansion of 1
are defined to be the sequences of rationals that have the Cauchy sequence property using this distance. That is, in the sequence x 0 {\displaystyle
0.999...
Normed vector space that is complete
length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within
Banach_space
Property of a sequence or series
define Cauchy sequences. Cauchy nets and filters are generalizations to uniform spaces. Even more generally, Cauchy spaces are spaces in which Cauchy filters
Modes_of_convergence
Mathematical inequality relating inner products and norms
vectors in sequence spaces), and integrals (via vectors in Hilbert spaces). The inequality for sums was published by Augustin-Louis Cauchy (1821). The
Cauchy–Schwarz_inequality
Mathematical theorem
showing that every Cauchy sequence has a rapidly converging Cauchy sub-sequence, that every Cauchy sequence with a convergent sub-sequence converges, and
Riesz–Fischer_theorem
Property of a partially ordered set
prove the least-upper-bound property using the assumption that every Cauchy sequence of real numbers converges. Let S be a nonempty set of real numbers
Least-upper-bound_property
Type of vector space in math
expressed using a form of the Cauchy criterion for sequences in H: a pre-Hilbert space H is complete if every Cauchy sequence converges with respect to this
Hilbert_space
Mathematics of real numbers and real functions
This property characterizes the Cauchy sequences in a metric space. Stated a little more carefully, a sequence is Cauchy if, for any error tolerance, all
Real_analysis
{\displaystyle Y.} Then f {\displaystyle f} is Cauchy-continuous if and only if, given any Cauchy sequence ( x 1 , x 2 , … ) {\displaystyle \left(x_{1}
Cauchy-continuous_function
Generalization of a sequence of points
only if it converges to x . {\displaystyle x.} A Cauchy net generalizes the notion of Cauchy sequence to nets defined on uniform spaces. A net x ∙ = (
Net_(mathematics)
Limit of some subsequence
space and there is a Cauchy sequence such that there is a subsequence converging to some x , {\displaystyle x,} then the sequence also converges to x
Subsequential_limit
Mathematical space with a notion of distance
difference. For example, uniformly continuous maps take Cauchy sequences in M1 to Cauchy sequences in M2. In other words, uniform continuity preserves some
Metric_space
Topics referred to by the same term
which every Cauchy sequence converges Complete uniform space, a uniform space where every Cauchy net in converges (or equivalently every Cauchy filter converges)
Completeness
Arithmetic operation
numbers. A real number is essentially defined to be the limit of a Cauchy sequence of rationals, lim a n {\displaystyle \lim a_{n}} . Addition is defined
Addition
Quotient of two integers
can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals (see Construction of the real
Rational_number
Uniform restraint of the change in functions
f:X\rightarrow R} is that it is Cauchy-continuous, i.e., the image under f {\displaystyle f} of a Cauchy sequence remains Cauchy. If X {\displaystyle X} is
Uniform_continuity
Field of knowledge
A Cauchy sequence consists of elements such that all subsequent terms of a term become arbitrarily close to each other as the sequence progresses (from
Mathematics
Philosphical view that existence proofs must be constructive
to the classical definition using Cauchy sequences, except with a constructive twist: for a classical Cauchy sequence, it is required that, for any given
Constructivism (philosophy of mathematics)
Constructivism_(philosophy_of_mathematics)
Riemannian manifold in which geodesics extend infinitely in all directions
not a complete metric space: any sequence in the plane converging to the origin is a non-converging Cauchy sequence in the punctured plane. There exist
Complete_manifold
On decreasing nested sequences of non-empty compact sets
the x k {\displaystyle x_{k}} form a Cauchy sequence. Since the metric space is complete this Cauchy sequence converges to some point x {\displaystyle
Cantor's_intersection_theorem
Property of geometry, also used to generalize the notion of "distance" in metric spaces
comparison. For example, the fact that any convergent sequence in a metric space is a Cauchy sequence is a direct consequence of the triangle inequality
Triangle_inequality
Number system extending the rational numbers
change the completion (different choices yield the same concept of Cauchy sequence, so the same completion). It is convenient, when the residue field
P-adic_number
Vector space of infinite sequences
… ) {\displaystyle 0,0,\ldots {\bigr )}} ) is a Cauchy sequence but it does not converge to a sequence in c 00 . {\displaystyle c_{00}.} Let K ∞ = { (
Sequence_space
Mathematical series with a finite sum
series converges. Cauchy condensation test. If { a n } {\displaystyle \left\{a_{n}\right\}} is a positive monotone decreasing sequence, then ∑ n = 1 ∞ a
Convergent_series
Provides integral formulas for all derivatives of a holomorphic function
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a
Cauchy's_integral_formula
Concept in general topology and analysis
analysis, a Cauchy space is a generalization of metric spaces and uniform spaces for which the notion of Cauchy convergence still makes sense. Cauchy spaces
Cauchy_space
Algebraic structure in linear algebra
By definition, in a Hilbert space, any Cauchy sequence converges to a limit. Conversely, finding a sequence of functions f n {\displaystyle f_{n}} with
Vector_space
Probability distribution
The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as
Cauchy_distribution
space X is said to be sequentially complete or semi-complete if every Cauchy sequence in S converges to an element in S. X is called sequentially complete
Sequentially_complete
Locally convex topological vector space that is also a complete metric space
topological vector space (TVS) that is complete as a TVS, meaning that every Cauchy sequence in X {\displaystyle X} converges to some point in X {\displaystyle
Fréchet_space
Topics referred to by the same term
The mathematical term fundamental sequence can refer to: In analysis, Cauchy sequence. In discrete mathematics and computer science, Unary coding. In
Fundamental_sequence
Mathematical theorem
Cauchy's limit theorem, named after the French mathematician Augustin-Louis Cauchy, describes a property of converging sequences. It states that for a
Cauchy's_limit_theorem
Theorem about metric spaces
that ( x n ) n ∈ N {\displaystyle (x_{n})_{n\in \mathbb {N} }} is a Cauchy sequence. In particular, let m , n ∈ N {\displaystyle m,n\in \mathbb {N} } such
Banach_fixed-point_theorem
Basic framework of mathematics
property may be expressed either as for every infinite sequence of real numbers, if it is a Cauchy sequence, it has a limit that is a real number, or as every
Foundations_of_mathematics
Smooth manifold with an inner product on each tangent space
{\displaystyle (M,d_{g})} is complete (every d g {\displaystyle d_{g}} -Cauchy sequence converges), All closed and bounded subsets of M {\displaystyle M} are
Riemannian_manifold
Subset of Euclidean space is compact if and only if it is closed and bounded
define a sequence ( x k ) {\displaystyle (x_{k})} such that each x k {\displaystyle x_{k}} is in T k {\displaystyle T_{k}} . This sequence is Cauchy, so it
Heine–Borel_theorem
Limit type in multivariable calculus
{\epsilon }{3}}} , which means that c n {\displaystyle c_{n}} is a Cauchy sequence which converges to a limit L {\displaystyle L} . In addition, as k
Iterated_limit
Theorem on the convergence of harmonic functions
The theorem is a corollary of Harnack's inequality. If un(y) is a Cauchy sequence for any particular value of y, then the Harnack inequality applied
Harnack's_principle
Real function with finite total variation
\mathbb {R} ^{+}} is lower semi-continuous: to see this, choose a Cauchy sequence of BV-functions { u n } n ∈ N {\displaystyle \{u_{n}\}_{n\in \mathbb
Bounded_variation
Axiomatic set theories based on the principles of mathematical constructivism
speaking of Cauchy sequences and their arithmetic. This is also the approach to analysis taken in Z 2 {\displaystyle {\mathsf {Z}}_{2}} . Any Cauchy real number
Constructive_set_theory
is not integrable. 6. On a metric space, a sequence x n {\displaystyle x_{n}} is called a Cauchy sequence if d ( x n , x m ) → 0 {\displaystyle d(x_{n}
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Mode of convergence of an infinite series
} As ∑ k = 1 n ‖ x k ‖ {\textstyle \sum _{k=1}^{n}\|x_{k}\|} is a Cauchy sequence of real numbers, for any ε > 0 {\displaystyle \varepsilon >0} and large
Absolute_convergence
Vector space with generalized dot product
1\right]\\kt&t\in \left(0,{\tfrac {1}{k}}\right)\end{cases}}} This sequence is a Cauchy sequence for the norm induced by the preceding inner product, which does
Inner_product_space
Criterion about convergence of series
follows from the triangle inequality.) For each x, the sequence Sn(x) is thus a Cauchy sequence in R or C, and by completeness, it converges to some number
Weierstrass_M-test
Vector space with a notion of nearness
Every Cauchy sequence is bounded, although Cauchy nets and Cauchy filters may not be bounded. A topological vector space where every Cauchy sequence converges
Topological_vector_space
Branch of mathematics
an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the formal theory of complex analysis. Poisson, Liouville
Mathematical_analysis
Measurement on a normed vector space
\sup\{z^{\intercal }x:\|x\|_{2}\leq 1\}=\|z\|_{2}.} (This follows from the Cauchy–Schwarz inequality; for nonzero z , {\displaystyle z,} the value of x {\displaystyle
Dual_norm
Mathematical set with some added structure
space, we can define bounded sets and Cauchy sequences. A metric space is called complete if all Cauchy sequences converge. Every incomplete space is isometrically
Space_(mathematics)
Formula in complex analysis
complex analysis, Cauchy's estimate gives local bounds for the derivatives of a holomorphic function. These bounds are optimal. Cauchy's estimate is also
Cauchy's_estimate
Group that is a topological space with continuous group operations
indices i , j ≥ i 0 . {\displaystyle i,j\geq i_{0}.} A Cauchy sequence is a Cauchy net that is a sequence. If B {\displaystyle B} is a subset of an additive
Topological_group
Mathematical expression
analogous to the construction of an irrational number as the limit of a Cauchy sequence of rational numbers. Because of analogies like this one, the theory
Continued_fraction
System of numbers with non-finite quantities
Cauchy complete, meaning that relativizing the ∀ ∃ ∀ {\displaystyle \forall \exists \forall } definitions of Cauchy sequence and convergent sequence to
Levi-Civita_field
Submanifold of Lorentzian manifold
In the mathematical field of Lorentzian geometry, a Cauchy surface, also called more properly Cauchy hypersurface, is a certain kind of submanifold of a
Cauchy_surface
Ranges of numbers contained in each other
In a follow-up, the fact, that Cauchy sequences are convergent (and that all convergent sequences are Cauchy sequences) can be proven. This in turn allows
Nested_intervals
Line formed by the real numbers
space: The real line is a complete metric space, in the sense that any Cauchy sequence of points converges. The real line is path-connected and is one of
Number_line
Theorem in mathematics
\|x_{n+1}-x_{n}\|<\delta /2^{n}} . Thus ( x n ) {\displaystyle (x_{n})} is a Cauchy sequence tending to x {\displaystyle x} . By construction f ( x ) = y {\displaystyle
Inverse_function_theorem
Mathematical construction of a set with an equivalence relation
regular Cauchy sequences equipped with the usual notion of equivalence. Predicates and functions of real numbers need to be defined for regular Cauchy sequences
Setoid
Infinite sum
comparisons to flattened-out versions of a series leads to Cauchy's condensation test: if the sequence of terms a n {\displaystyle a_{n}} is non-negative and
Series_(mathematics)
On closed convex subsets in Hilbert space
\left(c_{n}\right)_{n=1}^{\infty }} is a Cauchy sequence. Since C {\displaystyle C} is complete, the sequence is therefore convergent to a point m ∈ C
Hilbert_projection_theorem
Metric on a smooth statistical manifold
square-integrable. Square integrability is equivalent to saying that a Cauchy sequence converges to a finite value under the weak topology: the space contains
Fisher_information_metric
Function which measures the "size" of elements in a field or integral domain
|xm − xn| < ε. Cauchy sequences form a ring under pointwise addition and multiplication. One can also define null sequences as sequences (an) of elements
Absolute_value_(algebra)
Type of topological space in mathematics
(endowed with the topology from R), since any neighborhood contains a Cauchy sequence corresponding to an irrational number, which has no convergent subsequence
Locally_compact_space
Mode of convergence of a function sequence
methods. When put into the modern language, what Cauchy proved is that a uniformly convergent sequence of continuous functions has a continuous limit.
Uniform_convergence
Mathematical theorem
4M\delta +2\delta .} Hence the sequence { g n } {\displaystyle \{g_{n}\}} forms a Cauchy sequence in the uniform norm on K {\displaystyle K}
Riemann_mapping_theorem
Mathematical function with no sudden changes
f ( x n ) ) {\displaystyle \left(f\left(x_{n}\right)\right)} is a Cauchy sequence, and c {\displaystyle c} is in the domain of f {\displaystyle f} .
Continuous_function
Topological space with a notion of uniform properties
Instead of working with Cauchy sequences, one works with Cauchy filters (or Cauchy nets). A Cauchy filter (respectively, a Cauchy prefilter) on a uniform
Uniform_space
Divergent sequence – see limit of a sequence or divergent series Convergent sequence – see limit of a sequence or convergent series Cauchy sequence – a sequence
List_of_real_analysis_topics
Function type in graph theory
We now say that a sequence of graphs ( G n ) {\displaystyle (G_{n})} is convergent under the cut distance if it is a Cauchy sequence under the cut distance
Graphon
Generalization of the real numbers
proper sets) and continuous functions can be defined. An equivalent of Cauchy sequences can be defined as well, although they have to be indexed by the class
Surreal_number
Mathematical analysis
this is called the Cauchy real number. In that language, regular rational sequences are degraded to a mere representative of a Cauchy real. Equality of
Constructive_analysis
Convergence test for infinite series
the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing sequence f (
Cauchy_condensation_test
Existence and uniqueness of solutions to initial value problems
a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem
Picard–Lindelöf_theorem
Method of proof in mathematics
exhaustive search, and so a is a well defined sequence, constructively. Moreover, because a is a Cauchy sequence with a fixed rate of convergence, a converges
Constructive_proof
objects and continuous maps as morphisms. Cauchy sequence A sequence {xn} in a metric space (M, d) is a Cauchy sequence if, for every positive real number r
Glossary_of_general_topology
Topics referred to by the same term
measure Cauchy-regular function (or Cauchy-continuous function,) a continuous function between metric spaces which preserves Cauchy sequences Regular
Regular
Boundary condition for generalized functions
C^{\infty }({\bar {\Omega }})} the sequence u k | ∂ Ω {\textstyle u_{k}|_{\partial \Omega }} is a Cauchy sequence in L p ( ∂ Ω ) {\textstyle L^{p}(\partial
Trace_operator
Generalization of compactness
of a finite ε-net. A metric space is totally bounded iff every sequence admits a Cauchy subsequence; in complete metric spaces, a set is compact if and
Totally_bounded_space
Infinite series whose terms alternate in sign
the partial sums S m {\displaystyle S_{m}} form a Cauchy sequence (i.e., the series satisfies the Cauchy criterion) and therefore they converge. The argument
Alternating_series
Mathematical model of the time dependence of a point in space
This convention is also related to the study of limit points and Cauchy sequences. Mathematics and discrete convention: all maps are defined as the evolution
Dynamical_system
Surjective homomorphism
precisely a continuous function with dense image, since the image of a Cauchy sequence determines the image of its limit point: for example the inclusion
Epimorphism
Determining convergence in mathematics
( S n ) n = 1 , 2 , … {\displaystyle (S_{n})_{n=1,2,\ldots }} is a Cauchy sequence, and so must converge to a limit. Therefore, ∑ a n {\displaystyle \sum
Direct_comparison_test
Generalized function whose value is zero everywhere except at zero
articles in 1827. Cauchy defined an infinitesimal in Cours d'Analyse (1827) in terms of a sequence tending to zero. Namely, such a null sequence becomes an infinitesimal
Dirac_delta_function
Term in mathematics
last, the convergence of Cauchy sequences. The proofs are quite nontrivial. Among these five characterizations, the Cauchy-sequence perspective turns out
Characterization (mathematics)
Characterization_(mathematics)
Theorem stating that pointwise boundedness implies uniform boundedness
x ) , h 2 ( x ) , … {\displaystyle h_{1}(x),h_{2}(x),\ldots } is a Cauchy sequence in Y {\displaystyle Y} is of the second category in X , {\displaystyle
Uniform_boundedness_principle
Concept in mathematics
shown that the sequence { ∫ X s n d μ } n = 1 ∞ {\displaystyle \left\{\int _{X}s_{n}\,d\mu \right\}_{n=1}^{\infty }} is a Cauchy sequence in the Banach
Bochner_integral
Branch of mathematical analysis
often Banach algebras since Cauchy sequences can be taken to be convergent. Then the function theory is enriched by sequences and series. In this context
Hypercomplex_analysis
CAUCHY SEQUENCE
CAUCHY SEQUENCE
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : topographic name for someone who lived by a causeway, Middle English caucey (from Old Norman French cauciée); the ending of the word was in time assimilated by folk etymology to Middle English way.
Boy/Male
Australian, Norse, Scottish
Relic
Girl/Female
Arabic
Going Up
Boy/Male
Scottish English
True and bold. Also 'bald'. Introduced from England and Germany during the Norman conquest, the...
Girl/Female
American, Australian
Storage Place
Girl/Female
Irish
Vigilant.
Boy/Male
British, English
Good with Bow and Arrow; A Diminutive of Archibald; True and Bold
Boy/Male
Irish
Observant; alert; vigorous.
Boy/Male
Irish
Observant; alert; vigorous.
Girl/Female
Greek American French Latin Irish English
Form of the Greek Catherine meaning 'pure'.
Girl/Female
Native American
To catch up with.
Girl/Female
American, Assamese, Christian, English, German, Greek, Indian, Italian, Kannada, Latin, Marathi, Swedish
Pure
Surname or Lastname
English
English : occupational name for a maker of beds or bedding, from Middle English couche ‘bed’ (see Couch) + man.
Surname or Lastname
English
English : perhaps a variant spelling of Cosby.
Male
Spanish
Pet form of Spanish Jesús, CHUCHO means "God is salvation."
Boy/Male
American, Australian, German
Man
Boy/Male
Spanish
Bringer of peace.
Girl/Female
Hindu, Indian
Wonderful
Surname or Lastname
Cornish and Welsh
Cornish and Welsh : nickname for a red-haired man, from cough, coch ‘red(-haired)’. Compare Gough.English : metonymic occupational name for a maker of beds or bedding, or perhaps a nickname for a lazy man, from Middle English, Old French couche ‘bed’, a derivative of Old French coucher ‘to lay down’, Latin collocare ‘to place’.
Female
English
English pet form of French Catharine, CATHY means "pure."
CAUCHY SEQUENCE
CAUCHY SEQUENCE
Girl/Female
Hebrew English
Lily.
Boy/Male
Arabic, Muslim
Mighty of the Faith; Glory of Religion
Boy/Male
Indian, Punjabi, Sikh
Protector of Lion
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
The All; Goddess Durga; Universal; Complete; Born in the Month of Shravan
Girl/Female
Muslim/Islamic
Beauty the planet venus
Girl/Female
American, Australian, Chinese, Christian, French, German, Greek, Latin
Nobility; Similar to Alice; Noble Sort
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Ganesh
Biblical
most intelligent father,father of strength,also called ABIEL
Biblical
a destroyer,angel of the bottomless pit
Surname or Lastname
English
English : patronymic from Hake 1.
CAUCHY SEQUENCE
CAUCHY SEQUENCE
CAUCHY SEQUENCE
CAUCHY SEQUENCE
CAUCHY SEQUENCE
v. t.
Lying on its side; thus, a chevron couche is one which emerges from one side of the escutcheon and has its apex on the opposite side, or at the fess point.
superl.
Showing impertinent boldness or pertness; transgressing the rules of decorum; treating superiors with contempt; impudent; insolent; as, a saucy fellow.
n.
A small species of agouti (Dasyprocta acouchy).
v. t.
To communicate to; to fasten upon; as, the fire caught the adjoining building.
n.
That which is caught or taken; profit; gain; especially, the whole quantity caught or taken at one time; as, a good catch of fish.
n.
Something desirable to be caught, esp. a husband or wife in matrimony.
v. i.
To hold, or meet in, a caucus or caucuses.
v. t.
To reach in time; to come up with; as, to catch a train.
v. t.
To treat by pushing down or displacing the opaque lens with a needle; as, to couch a cataract.
v. t.
To take or receive; esp. to take by sympathy, contagion, infection, or exposure; as, to catch the spirit of an occasion; to catch the measles or smallpox; to catch cold; the house caught fire.
v. t.
To come upon unexpectedly or by surprise; to find; as, to catch one in the act of stealing.
n.
A humorous canon or round, so contrived that the singers catch up each other's words.
n.
That by which anything is caught or temporarily fastened; as, the catch of a gate.
superl.
Expressive of, or characterized by, impudence; impertinent; as, a saucy eye; saucy looks.
v. i.
To take hold; as, the bolt does not catch.
a.
Arched; as, archy brows.
v. t.
To seize with the senses or the mind; to apprehend; as, to catch a melody.
v. t.
To seize after pursuing; to arrest; as, to catch a thief.
imp. & p. p.
of Catch