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In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k. Eichler
Approximation in algebraic groups
Approximation_in_algebraic_groups
property (weak 'weak approximation', sic) for a variety V over a number field is weak approximation (cf. approximation in algebraic groups), for finite sets
Thin_set_(Serre)
Superstrong approximation is a generalisation of strong approximation in algebraic groups G, to provide spectral gap results. The spectrum in question is
Superstrong_approximation
In algebraic topology, the cellular approximation theorem states that a map between CW-complexes can always be taken to be of a specific type. Concretely
Cellular approximation theorem
Cellular_approximation_theorem
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
Conjecture in algebraic geometry
the resistant E8 case (see strong approximation in algebraic groups), thus completing the proof of Weil's conjecture. In 2011, Jacob Lurie and Dennis Gaitsgory
Weil's conjecture on Tamagawa numbers
Weil's_conjecture_on_Tamagawa_numbers
German mathematician (1928–2004)
His main publications were on quadratic forms and algebraic groups. Approximation in algebraic groups Betke–Kneser theorem Kneser–Tits conjecture Kneser's
Martin_Kneser
Cellular approximation theorem (algebraic topology) Dold–Thom theorem (algebraic topology) Eilenberg–Ganea theorem (homological algebra, algebraic topology)
List_of_theorems
Topics referred to by the same term
In mathematics, superstrong may refer to: Superstrong cardinal in set theory Superstrong approximation in algebraic group theory This disambiguation page
Superstrong
Rational-number approximation of a real number
number. In the 1840s, Joseph Liouville obtained the first lower bound for the approximation of algebraic numbers: If x is an irrational algebraic number
Diophantine_approximation
Topics referred to by the same term
Weak approximation may refer to: Weak approximation theorem, an extension of the Chinese remainder theorem to algebraic groups over global fields Weak
Weak_approximation
System of logic lacking the excluded middle law
) They have been further studied in the Argentinian algebraic logic school of Antonio Monteiro. De Morgan algebras are important for the study of the
De_Morgan_algebra
Algebra based on a vector space with a quadratic form
mod 8. This is an algebraic form of Bott periodicity. The class of Lipschitz groups (a.k.a. Clifford groups or Clifford–Lipschitz groups) was discovered
Clifford_algebra
How spheres of various dimensions can wrap around each other
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.
Homotopy_groups_of_spheres
Method for dividing a simplicial complex
subdivision is an important tool in algebraic topology. The barycentric subdivision is an operation on simplicial complexes. In algebraic topology it is sometimes
Barycentric_subdivision
Solving integer equations from all modular solutions
Hasse principle for algebraic groups was used in the proofs of the Weil conjecture for Tamagawa numbers and the strong approximation theorem. Local analysis
Hasse_principle
Branch of number theory
generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite
Algebraic_number_theory
Theory of getting acceptably close inexact mathematical calculations
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing
Approximation_theory
Field of mathematics
difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and
Numerical_linear_algebra
Continuous mappings can be approximated by ones that are piecewise simple
In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by
Simplicial approximation theorem
Simplicial_approximation_theorem
In algebraic group theory, a thin group is a discrete Zariski-dense subgroup of G(R) that has infinite covolume, where G is a semisimple algebraic group
Thin group (algebraic group theory)
Thin_group_(algebraic_group_theory)
a separated algebraic stack, which is roughly a "best possible" approximation to the stack by a separated algebraic space. All algebraic spaces are assumed
Keel–Mori_theorem
Classification scheme for mathematics
theory, proof theory, and algebraic logic) 05: Combinatorics 06: Order, lattices, ordered algebraic structures 08: General algebraic systems 11: Number theory
Mathematics Subject Classification
Mathematics_Subject_Classification
Mathematical subject
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example
Combinatorial_topology
Natural number
finite field of odd characteristic. In algebraic geometry, characteristic 3 is one of the small characteristics in which standard formulas may require
3
algebra with the language and problems of geometry. Fundamentally, it studies algebraic varieties. Algebraic graph theory a branch of graph theory in
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Branch of mathematics
systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of
Linear_algebra
Application of Clifford algebra
different algebraic and visual connotations coming from the word 'vector', this article avoids use of the word. Plane-based geometric algebra starts with
Plane-based_geometric_algebra
an algebraic lattice. Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub(A) for some algebra A. There is another algebraic lattice
Compact_element
Mathematics glossary
elliptic cohomology. En-algebra equivariant algebraic topology Equivariant algebraic topoloy is the study of spaces with (continuous) group action. etale étale
Glossary of algebraic topology
Glossary_of_algebraic_topology
Area of mathematics
mathematical and computer techniques in natural languages Computational algebraic geometry Computational group theory Computational geometry Computational
Computational_mathematics
History of a branch of mathematics
permutation group, a result known today as Cayley's theorem. In succeeding years, Cayley systematically investigated infinite groups and the algebraic properties
History_of_group_theory
Application of geometry in number theory
which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in R n , {\displaystyle \mathbb {R}
Geometry_of_numbers
Physics-mathematics connection
first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to
Particle physics and representation theory
Particle_physics_and_representation_theory
problem; Enumerators which generate sizable finite approximations to both finite and infinite algebraic objects and make it possible to carry out searches
Magnus (computer algebra system)
Magnus_(computer_algebra_system)
mathematics. Topological algebra arose in the early 20th century, studying algebraic structures such as topological groups and Lie groups. In the 1940s and 50s
History_of_algebra
Associative algebra together with a Lie bracket that satisfies Leibniz's law
Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure
Poisson_algebra
Vector space equipped with a bilinear product
or unital associative algebra, or in some subjects such as algebraic geometry, unital associative commutative algebra. Replacing the field of scalars by
Algebra_over_a_field
Tool in homological algebra
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral
Spectral_sequence
Mathematician
obstruction to the Hasse principle and weak approximation for homogeneous spaces of connected linear algebraic groups over number fields with connected geometric
Mikhail_Borovoi
Algebra in algebraic topology
In algebraic topology, a Steenrod algebra was defined by Henri Cartan (1955) to be the algebra of stable cohomology operations for mod p {\displaystyle
Steenrod_algebra
Platonov, V. P. (1969), "The problem of strong approximation and the Kneser–Tits hypothesis for algebraic groups", Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
Kneser–Tits_conjecture
Algebraic topology uses abstract algebra to study topological spaces
This is a list of algebraic topology topics. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces
List of algebraic topology topics
List_of_algebraic_topology_topics
Branch of mathematics
topic in algebraic topology, but nowadays is learned as an independent discipline. Besides algebraic topology, the theory has also been used in other areas
Homotopy_theory
Study of discrete mathematical structures
approximation, p-adic analysis and function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include:
Discrete_mathematics
Methods of calculating definite integrals
written in elementary form . It may be possible to find an antiderivative symbolically, but it may be easier to compute a numerical approximation than to
Numerical_integration
*-algebra of bounded operators on a Hilbert space
their algebraic tensor product. One can define a tensor product of von Neumann algebras (a completion of the algebraic tensor product of the algebras considered
Von_Neumann_algebra
Representation of C*-Algebras Chapter 11. Tensor Products Chapter 12. Approximation by Matrix Algebras Chapter 13. Crossed Products Chapter 14. Direct Integrals and
Fundamentals of the Theory of Operator Algebras
Fundamentals_of_the_Theory_of_Operator_Algebras
Mathematical group of the homotopy classes of loops in a topological space
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of
Fundamental_group
factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Natural number
geometrical measure of a connected linear algebraic group over a global number field, is 1 for all simply connected groups (those that are path-connected with
1
Branch of functional analysis
composition of mappings. The results obtained in the study of operator algebras are often phrased in algebraic terms, while the techniques used are often
Operator_algebra
Varying methods used to calculate pi
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning
Approximations_of_pi
Branch of mathematics
methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities, and in the 19th
Mathematical_analysis
Algebraic study of differential equations
Systems Of Algebraic Differential Equations" and two books, Differential Equations From The Algebraic Standpoint and Differential Algebra. Ellis Kolchin
Differential_algebra
American mathematician
Applications to Diophantine Approximations in Algebraic Groups. He is a professor at the University of California, Berkeley. His work lies in mathematical logic—particularly
Thomas_W._Scanlon
Norwegian mathematician (1863–1922)
theorem – Algebraic numbers are not near many rationals Plastic ratio – Number, approximately 1.3247 Word problem for groups – Problem in finite group theory
Axel_Thue
Notable events in the history of algebra
a timeline of key developments of algebra: Mathematics portal History of algebra – Historical development of algebra Archibald, Raymond Clare (December
Timeline_of_algebra
Branch of algebraic geometry
abstract development of algebraic geometry. Over finite fields, étale cohomology provides topological invariants associated to algebraic varieties. p-adic Hodge
Arithmetic_geometry
Cryptanalytic attacks using a system of multivariate equations
Algebraic attack is a method of algebraic cryptanalysis by which a set of algebraic equations can be used to solve a cryptographic Boolean function that
Algebraic_attack
German mathematician
group theory, algebraic topology, ergodic theory of group actions, and operator algebras. Thom received in 2000 his Certificate of Advanced Study in Mathematics
Andreas_Thom_(mathematician)
Math relation that is reflexive and symmetric
In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all
Tolerance_relation
Israeli mathematician
the rank of algebraic varieties over large algebraic fields, Geyer-Jarden theorem about torsion points on elliptic curves over large algebraic fields, and
Moshe_Jarden
variety by a group: a quotient variety, say, would be a coarse approximation of a quotient stack. The notion is of fundamental importance in the study of
Quotient_stack
Type of mathematical expression
functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic
Polynomial
of these approximation methods can be expressed in purely linear algebraic or functional analytic terms as matrix or function approximations. Others are
Gaussian process approximations
Gaussian_process_approximations
Algebra Colloquium Algebra i Logika Algebra Universalis Algebraic & Geometric Topology Algebraic Combinatorics American Journal of Mathematics American
List_of_mathematics_journals
Concept in mathematics
Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding
Sparse_approximation
Mathematical theorem
constructed for filtered spaces in the book Nonabelian algebraic topology cited below, which develops basic algebraic topology, including higher analogues
Eckmann–Hilton_argument
Curves of genus > 1 over the rationals have only finitely many rational points
Faltings' theorem is a result in arithmetic geometry, according to which a non-singular algebraic curve of genus greater than 1 over the field Q {\displaystyle
Faltings'_theorem
Algorithms for zeros of functions
studied in numerical analysis. However, for polynomials specifically, the study of root-finding algorithms belongs to computer algebra, since algebraic properties
Root-finding_algorithm
development of mathematics. It involves determining either a numerical approximation or a closed-form expression of the roots of a univariate polynomial
Polynomial_root-finding
Setting of relativistic physics in geometric algebra
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics
Spacetime_algebra
In the theory of von Neumann algebras, the Kaplansky density theorem, due to Irving Kaplansky, is a fundamental approximation theorem. The importance
Kaplansky_density_theorem
Matrix group
residually finite. An important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether
Congruence_subgroup
Methods of mathematical approximation
problem. Formally, we have for the approximation to the full solution A , {\displaystyle \ A\ ,} a series in the small parameter (here called ε)
Perturbation_theory
Branch of topology
and Terry A. Loring, Deformations of topological spaces predicted by E-theory, In Algebraic methods in operator theory, p. 316–327. Birkhäuser 1994.
Shape_theory_(mathematics)
Study of the properties of codes and their fitness
Analysis on Finite Groups and Applications. Cambridge University Press. p. 195. ISBN 978-0-521-45718-7. Blahut, Richard E. (2003). Algebraic Codes for Data
Coding_theory
computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Topology glossary List of topologies List of topology topics List of geometric topology topics List of algebraic topology topics Publications in topology
List of general topology topics
List_of_general_topology_topics
Representation of mathematical space
has various applications both in and outside of mathematics, for instance in algebraic topology, in complex analysis, and in modeling. On the one hand, it
Triangulation_(topology)
Mathematics award
varieties." 2021 Bhargav Bhatt – "For outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Mathematical functions that quantify complexity
equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the classical
Height_function
studies connection between degree of approximation and smoothness Universal differential equation — differential–algebraic equation whose solutions can approximate
List of numerical analysis topics
List_of_numerical_analysis_topics
Russian mathematician
lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf
Grigory_Margulis
Branch of mathematics
been split in many subfields that depend on the underlying methods—differential geometry, algebraic geometry, computational geometry, algebraic topology
Geometry
Type of classification in algebra
Archimedean property. Alajbegovic, J.; Mockor, J. (1992), Approximation Theorems in Commutative Algebra: Classical and Categorical Methods, NATO ASI Series
Archimedean_group
Algebraic structure associated with a topological space
spread of homology groups brought a change of terminology and viewpoint from "combinatorial topology" to "algebraic topology". Algebraic homology remains
Homology_(mathematics)
Mathematics used in ancient Mesopotamia
include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation of 2 {\displaystyle
Babylonian_mathematics
Extension of quantum field theory to curved spacetime
are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Awarded every year by the American Mathematical Society
"Equivalence relations on algebraic cycles and subvarieties of small codimension". Algebraic Geometry – Arcata 1974. Proceedings of Symposia in Pure Mathematics
Leroy_P._Steele_Prize
thought of as an approximation of the map f {\displaystyle f} . Now, a birational class of f {\displaystyle f} is a family of group homomorphisms indexed
Bivariant_theory
Theoretical object in mathematics
groups are simple algebraic groups over F1: Given a Dynkin diagram for a semisimple algebraic group, its Weyl group is the semisimple algebraic group
Field_with_one_element
Theory in number theory
Anabelian geometry is a theory in arithmetic geometry which describes the way in which the algebraic fundamental group of a certain arithmetic variety
Anabelian_geometry
doctorate Anastasia Stavrova, Russian expert in algebraic groups, non-associative algebra, and algebraic K-theory Jackie Stedall (1950–2014), British
List_of_women_in_mathematics
Generalisation of a sheaf; a fibered category that admits effective descent
particularly useful in studying moduli spaces. There are inclusions: schemes ⊆ algebraic spaces ⊆ Deligne–Mumford stacks ⊆ algebraic stacks (Artin stacks)
Stack_(mathematics)
it has good reduction at p and in addition the p-torsion has rank d. Quasi-algebraic closure The topic of quasi-algebraic closure, i.e. solubility guaranteed
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Physical theory with fields invariant under the action of local "gauge" Lie groups
the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there
Gauge_theory
Italian mathematician and philosopher (1765–1822)
solvability of algebraic equations. Ruffini introduced notions like the order of an element, conjugacy, and cycle decomposition in permutation groups, making
Paolo_Ruffini
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
Surname or Lastname
English (also established in Ireland)
English (also established in Ireland) : from a pet form of the personal name Pell.English (also established in Ireland) : nickname from Old French pele ‘bald’.
Boy/Male
French, German, Polish
Long
Surname or Lastname
English (common in East Anglia)
English (common in East Anglia) : occupational name for a servant or a shepherd, from Middle English grÅm(e) ‘boy’, ‘servant’ (of uncertain origin), which in some places was specialized to mean ‘shepherd’.
Surname or Lastname
English (rare in England)
English (rare in England) : variant of Hug 1.
Male
Croatian
, goodness.
Surname or Lastname
English (found chiefly in the West Midlands and in Ireland)
English (found chiefly in the West Midlands and in Ireland) : habitational name from Hodnet in Shropshire, or any of various places called Hoddnant in Wales. The place names are from Welsh hawdd ‘pleasant’, ‘peaceful’ + nant ‘valley’, ‘stream’.
Surname or Lastname
Swedish (common in Finland)
Swedish (common in Finland) : ornamental name formed with the common surname suffix -in and an unexplained first element.German : unexplained.English : unexplained.Spanish (FarÃn) : unexplained.
Surname or Lastname
English (rare in England)
English (rare in England) : apparently a habitational name from Huccaby in Devon, possibly so named from Old English woh ‘crooked’ + byge ‘river bend’, or Uckerby in North Yorkshire, named with an unattested Old Norse personal name, Úkyrri or Útkári, + býr ‘farmstead’.
Surname or Lastname
English (also established in Ireland)
English (also established in Ireland) : habitational name from for example Barcroft in Haworth, West Yorkshire, so named with Old English bere ‘barley’ + croft ‘paddock’, ‘smallholding’.This is the name of a family established in Ireland by William Barcroft (1612–96). They can be traced to the parish of Barcroft, Lancashire, in the reign of Henry III (1216–72).
Surname or Lastname
English (also found in Wales)
English (also found in Wales) : patronymic from the Middle English personal name Jenk, a back-formation from Jenkin with the removal of the supposed Anglo-Norman French diminutive suffix -in.Joseph Jenks (1602–83), the descendant of an old Welsh family, was born in England and traveled to Saugus, near Lynn, MA, in 1642 to assist in the development of America’s first iron works. His son, Joseph Jenckes (sic), followed in 1650, founded Pawtucket, RI, and raised four sons who held places of respect and distinction in RI, including one who served as governor for five years.
Surname or Lastname
English (also frequent in Wales)
English (also frequent in Wales) : patronymic from the personal name Watkin.
Surname or Lastname
English (common in West Yorkshire)
English (common in West Yorkshire) : habitational name from Hainworth in West Yorkshire, named from the Old English personal name Hagena + Old English worð ‘enclosure’.English (common in West Yorkshire) : habitational name from Ainsworth in Lancashire, from the Old English personal name Ægen + worð ‘enclosure’. Names such as de Haynesworth and de Heynesworth occur in the surrounding area in the 14th century.
Surname or Lastname
English (formerly common in Kent)
English (formerly common in Kent) : unexplained. This name seems to have died out in Britain.
Surname or Lastname
English (frequent in eastern England)
English (frequent in eastern England) : ethnic name from Norman French aleman ‘German’ or alemayne ‘Germany’ (Late Latin Alemannus and Alemannia, from a Germanic tribal name that probably originally meant ‘all the men’). In some cases the surname may be from the region of Normandy known as Allemagne (south of Caen), probably named as a Germanic-speaking enclave in a Celtic area in Roman times. In North America, the form Allman has probably absorbed some cases of cognates from other languages, in particular Spanish Aleman and French Alleman.German (Allmann) : variant of Allemann (see Alleman) or in some cases probably an Americanized form of the same name.
Surname or Lastname
English (also found in Ireland)
English (also found in Ireland) : from a pet form of Lamb 1 and 2.
Female
Irish
Irish form of French Madeline, MADAILÉIN means "of Magdala."
Surname or Lastname
English (common in Lancashire)
English (common in Lancashire) : habitational name from Sharples Hall near Bolton, probably so called from Old English scearp ‘sharp’, i.e. ‘steep’ + lǣs ‘pasture’.
Female
Irish
Variant spelling of Irish Gaelic LÃadan, LÃADÃIN means "grey lady."
Surname or Lastname
Scottish (also found in Ireland)
Scottish (also found in Ireland) : reduced form of McDow. This surname is borne by a sept of the Buchanans.English : variant of Daw.Americanized spelling of Dutch Douw, an Old Frisian personal name.Americanized spelling of German Dau.Henry Dow (1634–1707), NH soldier and statesman, was born at Ormsby in Norfolkshire, England. His father migrated with his family to Watertown in the colony of Massachusetts Bay in 1637 and moved to Hampton in the province of NH in 1644. Henry became an influential and prosperous figure in Hampton. He married twice and had four sons.
Surname or Lastname
English (found mainly in Wales)
English (found mainly in Wales) : variant of Glasscock 2.
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Bringer of Life
Girl/Female
Hindu, Indian
Newest
Boy/Male
Indian, Punjabi, Sikh
Love for the Learned One
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : variant of Hollingsworth.
Girl/Female
Muslim/Islamic
Respect
Girl/Female
American, Christian, Greek, Hindu, Indian, Swedish, Tamil, Telugu
Pure; Chaste; Holy; Goddess of Mary
Boy/Male
Latin Italian
Worthy of praise; of value. Saint Anthony is the patron sain of poor people. Famous Bearer:...
Girl/Female
Hindu, Indian, Traditional
Earth; Ganges
Girl/Female
Hindu, Indian
Lord of Yug
Boy/Male
Tamil
Rising to fame and honor
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
APPROXIMATION IN-ALGEBRAIC-GROUPS
n.
An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc.
prep.
With reference to a limit of time; as, in an hour; it happened in the last century; in all my life.
n.
A continual approach or coming nearer to a result; as, to solve an equation by approximation.
n.
A value that is nearly but not exactly correct.
prep.
With reference to space or place; as, he lives in Boston; he traveled in Italy; castles in the air.
n.
The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating.
adv.
With approximation; so as to approximate; nearly.
prep.
With reference to physical surrounding, personal states, etc., abstractly denoted; as, I am in doubt; the room is in darkness; to live in fear.
v. t.
To perform by algebra; to reduce to algebraic form.
n.
One versed in algebra.
a.
Alt. of Algebraical
prep.
A prefix from Eng. prep. in, also from Lat. prep. in, meaning in, into, on, among; as, inbred, inborn, inroad; incline, inject, intrude. In words from the Latin, in- regularly becomes il- before l, ir- before r, and im- before a labial; as, illusion, irruption, imblue, immigrate, impart. In- is sometimes used with an simple intensive force.
a.
Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings.
adv.
Not out; within; inside. In, the preposition, becomes an adverb by omission of its object, leaving it as the representative of an adverbial phrase, the context indicating what the omitted object is; as, he takes in the situation (i. e., he comprehends it in his mind); the Republicans were in (i. e., in office); in at one ear and out at the other (i. e., in or into the head); his side was in (i. e., in the turn at the bat); he came in (i. e., into the house).
adv.
By algebraic process.
n.
One of the terms in an algebraic expression.
n.
A rule or principle expressed in algebraic language; as, the binominal formula.
adv.
With privilege or possession; -- used to denote a holding, possession, or seisin; as, in by descent; in by purchase; in of the seisin of her husband.
a.
Resembling, or approximating to, a hemisphere in form.
prep.
With reference to movement or tendency toward a certain limit or environment; -- sometimes equivalent to into; as, to put seed in the ground; to fall in love; to end in death; to put our trust in God.