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Set of values which satisfy a given set of equations
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations
Solution_set
Several equations of degree 1 to be solved simultaneously
the only solution. If the system has a singular matrix then there is a solution set with an infinite number of solutions. This solution set has the following
System_of_linear_equations
Finding values for variables that make an equation true
mathematics, to solve an equation is to find the solutions of an equation, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated
Equation_solving
Homogeneous mixture of a solute and a solvent
In chemistry, a solution is defined by IUPAC as "A liquid or solid phase containing more than one substance, when for convenience one (or more) substance
Solution_(chemistry)
Mathematical formula expressing equality
or two systems of equations are equivalent, if they have the same set of solutions. The following operations transform an equation or a system of equations
Equation
Mathematical set containing no elements
the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories
Empty_set
Initial set of valid possible values
computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization
Feasible_region
simplicity ignoring the set-theoretic issues): G has a left adjoint. G {\displaystyle G} preserves all limits, and the following solution set condition is satisfied:
Formal criteria for adjoint functors
Formal_criteria_for_adjoint_functors
Nazi plan for the genocide of Jews
The Final Solution or the Final Solution to the Jewish Question was a plan orchestrated by Nazi Germany during World War II for the genocide of individuals
Final_Solution
Types of solutions in mathematics
extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. A missing solution is
Extraneous and missing solutions
Extraneous_and_missing_solutions
Vectors mapped to 0 by a linear map
}}\\\end{alignedat}}} Thus the kernel of A is the same as the solution set to the above homogeneous equations. The kernel of a m × n matrix A over
Kernel_(linear_algebra)
popular solution set of the interval equation and this solution set will be applied in this article. In the multidimensional case the united solutions set is
Interval_finite_element
1985 book by Maltese Dr. Edward de Bono
develop a set of solutions, and to finally choose a solution through critical examination of the solution set. The meeting may start with everyone assuming
Six_Thinking_Hats
Optimization by removing non-optimal solutions to subproblems
candidate solutions by means of state-space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root
Branch_and_bound
Set of all Pareto efficient situations
represents the set of solutions where no solution outperforms any other solution in the set at every objective, and every solution not in the set is outperformed
Pareto_front
Polynomial with all terms of degree two
solution set of the equation xTAx + bTx = 1 depends on the eigenvalues of the matrix A. If all eigenvalues of A are non-zero, then the solution set is
Quadratic_form
Branch of ordinary differential equations
solution if the columns form a basis of the solution set. A matrix Φ ( t ) {\displaystyle \Phi (t)} is called a principal fundamental matrix solution
Floquet_theory
Limiting case which is different from the rest of the class
two to zero as it degenerates into a point. As another example, the solution set of a system of equations that depends on parameters generally has a fixed
Degeneracy_(mathematics)
Fractal constructible with L-systems
dragon. Having obtained the set of solutions to a linear differential equation, any linear combination of the solutions will, because of the superposition
Dragon_curve
Metaheuristic commonly used for optimization problems
elements to the problem's solution set from a list of elements ranked by a greedy function according to the quality of the solution they will achieve. To
Greedy randomized adaptive search procedure
Greedy_randomized_adaptive_search_procedure
Euclidean space without distance and angles
affine subspace is the solution set of an inhomogeneous linear system. The displacement vectors for that affine space are the solutions of the corresponding
Affine_space
by some authors) fails to have a unique solution at some point on the solution. The set on which a solution is singular may be as small as a single point
Singular_solution
Inequality which involves a linear function
included in the solution set when the inequality is strict. A simple procedure to determine which half-plane is in the solution set is to calculate the
Linear_inequality
Used to count, measure, and label
the real numbers can be extended to the complex numbers. The complete solution set of a polynomial of degree two or higher can include the square roots
Number
Problem in process of sharing surplus
that the solution to a bargaining problem should satisfy. It is useful when both parties are willing to cooperate in implementing the fair solution. Such
Cooperative_bargaining
Algorithmic process of solving equations
equation set { f(1,y) = f(x,2) } is a syntactic first-order unification problem that has the substitution { x ↦ 1, y ↦ 2 } as its only solution. Conventions
Unification (computer science)
Unification_(computer_science)
Comprehensive list of Magic: The Gathering card sets since its inception in 1993
The trading card game Magic: The Gathering has released a large number of sets since it was first published by Wizards of the Coast. After the 1993 release
List of Magic: The Gathering sets
List_of_Magic:_The_Gathering_sets
Solution with a precisely known concentration of something
chemistry, a standard solution (titrant or titrator) is a solution containing an accurately known concentration. Standard solutions are generally prepared
Standard_solution
Chemical solution in solid form
A solid solution, a term commonly used for metals, is a homogeneous mixture of two compounds in solid state and having a single crystal structure. Many
Solid_solution
Fractal named after mathematician Benoit Mandelbrot
The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/) is a two-dimensional set. It is defined in the complex plane as the complex numbers c {\displaystyle c} for
Mandelbrot_set
Concept in integral mathematics
the solution to the relaxed linear program can be used to gain information about the solution to the original integer program. Consider the set cover
Linear_programming_relaxation
2025 documentary film by Andrew Jarecki and Charlotte Kaufman
The Alabama Solution is a 2025 American documentary film directed by Andrew Jarecki and Charlotte Kaufman. It follows the prison system in Alabama from
The_Alabama_Solution
Concept from linear programming
the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds
Basic_feasible_solution
Dilute solution used as an antiseptic
Dakin's solution is a dilute solution of sodium hypochlorite (0.4% to 0.5%) and other stabilizing ingredients, traditionally used as an antiseptic, e
Dakin's_solution
Indian multinational technology company
2016. "Tally Solutions launched new channel partner programme". indiatimes.com. 9 March 2015. Retrieved 4 July 2016. "Tally Solutions Set to Transform
Tally_Solutions
Measure of the level of acidity or basicity of an aqueous solution
scale used to specify the acidity or basicity of aqueous solutions. Acidic solutions (solutions with higher concentrations of hydrogen (H+) cations) are
PH
Algorithm for solving systems of linear equations
system of linear equations, then these operations do not change the solution set. Therefore, if one's goal is to solve a system of linear equations, then
Gaussian_elimination
Isolated point in the solution set of a polynomial equation in two real variables
An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are isolated point and hermit point
Acnode
Proposed diplomatic solution for the Israeli–Palestinian conflict
The two-state solution is a proposed approach to resolving the Israeli–Palestinian conflict, by creating two states on the territory of the former Mandatory
Two-state_solution
Iterative design process
making it a more attractive option for problems with a large or unknown solution set. It is also facilitated with tools in commercially available CAD packages
Generative_design
Educational publishing company
PLCs, which requires that applicants meet a set of criteria and reapply annually. Four times per year, Solution Tree publishes AllThingsPLC Magazine, which
Solution_Tree
Formal rule for predicting how a game will be played
\Gamma } , let S G {\displaystyle S_{G}} be the set of strategy profiles of G {\displaystyle G} . A solution concept is an element of the direct product Π
Solution_concept
Roots of multiple multivariate polynomials
set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of
System of polynomial equations
System_of_polynomial_equations
is an integer optimal dual solution. Edmonds and Giles showed that if a polyhedron P {\displaystyle P} is the solution set of a TDI system A x ≤ b {\displaystyle
Total_dual_integrality
Combinatorial optimization problem
consists in finding the maximal solution set (S) of non-conflicting activities, or more precisely there must exist no solution set S' such that |S'| > |S| in
Activity_selection_problem
Set of arguments where two or more functions have the same value
mathematics, an equaliser is a set of arguments where two or more functions have equal values. An equaliser is the solution set of an equation. In certain
Equaliser_(mathematics)
Optimization problem
exact solution. Set-partitioning—This approach models the VRP as a set cover problem, in which the locations make up the universe and the set of all
Vehicle_routing_problem
Classical problem in combinatorics
elements with only two sets: { {1, 2, 3}, {4, 5} }, see picture, but not with only one set. Therefore, the solution to the set cover problem for this
Set_cover_problem
Set of software subsystems or components needed to create a complete platform
In computing, a solution stack, also called software stack and tech stack is a set of software subsystems or components needed to create a complete platform
Solution_stack
Mathematical statement that two values are not equal
chains (where ∧ {\displaystyle \land } can be read as "and"); the set of its solutions is shown in blue in the picture (the red, green, and orange line
Inequation
Technique in computer vision
at the two points. Implementations of these solutions are available in open source software. Given a set of n 3D points in a world reference frame and
Perspective-n-Point
Concept in differential equation mathematics
growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions
Regular_singular_point
Complexity class
algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC. Although a solution to an NP-complete problem can be verified
NP-completeness
Critical point where a periodic solution arises
is said to occur when varying a parameter of the system causes the set of solutions (trajectories) to change from being attracted to (or repelled by) a
Hopf_bifurcation
South Korean battery maker
LG Energy Solution Ltd. (LGES; Korean: 주식회사 엘지에너지솔루션) is a battery company headquartered in Seoul, South Korea. LGES is one of the largest battery makers
LG_Energy_Solution
transformations that maps every solution of the system to another solution of the same system. In other words, it maps the solution set of the system to itself
Lie_point_symmetry
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Type of logic puzzle
limited number of solution sets then that can lead to useful clues. For instance, a 30-in-seven sum only has two solution sets: {1,2,3,4,5,6,9} and {1,2
Kakuro
Political party in Greece
The Greek Solution (Greek: Ελληνική Λύση, romanized: Ellinikí Lýsi) is a political party in Greece founded by Kyriakos Velopoulos. The party is right-wing
Greek_Solution
Type of number
pseudoperfect numbers sometimes may provide solutions to Znám's problem, in which all elements of the solution set are prime. For instance, the prime factors
Primary_pseudoperfect_number
Type of functional equation (mathematics)
mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential
Differential_equation
Basic notion of sameness in mathematics
{\displaystyle x=5} as its only solutions. The terminology is used similarly for equations with several unknowns. The set of solutions to an equation or system
Equality_(mathematics)
Topological space that locally resembles Euclidean space
topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has
Manifold
In mathematics, vector subspace
continuous linear functionals). Descriptions of subspaces include the solution set to a homogeneous system of linear equations, the subset of Euclidean
Linear_subspace
Describes the transverse intersection properties of a smooth family of smooth maps
Df_{s}(x)=n} for all solutions x ∈ X {\displaystyle x\in X} of f s ( x ) = y {\displaystyle f_{s}(x)=y} , then the solution set f s − 1 ( { y } ) {\displaystyle
Transversality_theorem
Concept in the solution of linear partial differential equations
In mathematics, a fundamental solution for a linear partial differential operator L is a formulation in the language of distribution theory of the older
Fundamental_solution
American bioanalysis corporation
microplate reader in 1987 and since then has continually broadened its solution set through a combination of internal research and development efforts as
Molecular_Devices
Logic puzzle
leads to a different set of ages for the children. We can utilize the fundamental property of arithmetic to find potential solution sets. The prime factors
Ages_of_Three_Children_puzzle
Objective function of evolutionary algorithm
as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms
Fitness_function
resolution, the algebra of value sets relies on narrowing rules. Narrowing rules allow the elimination of values from a solution set which are inconsistent with
Narrowing of algebraic value sets
Narrowing_of_algebraic_value_sets
Thai businessman (1946–2025)
to as Krungsri Bank) (SET:BAY), Siam City Cement (SET:SCCC), Allianz Ayudhya Capital (SET:AYUD), Matching Maximize Solution (SET:MATCH), Media Studio,
Krit_Ratanarak
Method for bounding the errors of numerical computations
increase in the range stems from the solution of areas that do not take the form of an interval vector. The solution set of the linear system { x = p y =
Interval_arithmetic
23, 2024. "Texas Pacific Land Set to Join S&P 500, Mueller Industries to Join S&P MidCap 400 and Atlas Energy Solutions to Join S&P SmallCap 600" (PDF)
List_of_S&P_500_companies
30, 2024. "Texas Pacific Land Set to Join S&P 500, Mueller Industries to Join S&P MidCap 400 and Atlas Energy Solutions to Join S&P SmallCap 600" (PDF)
List_of_S&P_400_companies
Structure in convex geometry
solution set to the linear program defined by each. The linear program in which the goal is to maximize linear objective function w has solution set F
Normal_fan
Complement of an open subset
Consequently, solution sets of continuous equations are closed: if f : X → R {\displaystyle f:X\to \mathbb {R} } is continuous, then the zero set { x ∈ X :
Closed_set
Study of mathematical algorithms for optimization problems
engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more
Mathematical_optimization
Algorithm on systems of polynomials
polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one of the systems
Triangular_decomposition
DLT Solutions is an American company in Herndon, Virginia. It is a value-added reseller of software and hardware and professional services provider to
DLT_Solutions
solutions are the: Copeland set Smith set (aka Top cycle) Slater set[clarification needed] Bipartisan set Landau set Banks set Minimal covering set Tournament
Tournament_solution
1985 Canadian children's fantasy film
The Peanut Butter Solution (French title: Opération beurre de pinottes) is a 1985 Canadian children's fantasy film directed by Michael Rubbo. The second
The_Peanut_Butter_Solution
Solution of some Diophantine equation
principal contributors to its solution) states that a set of integers is Diophantine if and only if it is computably enumerable. A set of integers S is computably
Diophantine_set
Calculations needed to move a robot arm to a given position and orientation
In the engineering field of robotics, an arm solution is a set of calculations that allow the real-time computation of the control commands needed to
Arm_solution
Theorem in projective geometry
because any point in the intersection of the solution sets of f and g will also be in the solution set of h. Again given the hexagon on a conic of Pascal's
Pascal's_theorem
algorithm. Given a well-bounded, convex body (K; n, R, r) given as the solution set of a system of linear inequalities, one can find an ellipsoid E(A,a)
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
Mathematical solution
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives
Weak_solution
Basic concepts of algebra
clearly has no solution. There are also systems which have infinitely many solutions, in contrast to a system with a unique solution (meaning, a unique
Elementary_algebra
Type of multi-objective optimization
exist a set of weights w 1 > w 2 > ⋯ > w n {\displaystyle w_{1}>w_{2}>\cdots >w_{n}} such that the set of lexicographically-optimal solutions is identical
Lexicographic_optimization
Generalized Condorcet set
other pairwise victory. Miller, Nicholas R. (February 1980). "A New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches
Landau_set
Condition of an optimization problem which the solution must satisfy
constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. The following is a simple optimization
Constraint_(mathematics)
Proposed resolution of the Israeli–Palestinian conflict
The one-state solution is a proposed approach to the Israeli–Palestinian peace process that envisions a single state within the boundaries of the former
One-state_solution
American payment protection and management company
RDR - as part of its post-purchase solution set for merchants and issuers. Verifi provides post-purchase solutions designed to prevent, deflect, or automatically
Verifi
Practice in IT management
overlap." As the technologies mature APM is now being viewed as a complete solution set. Maximum productivity can be achieved more efficiently through event
Business transaction management
Business_transaction_management
Mathematical optimization algorithm
g_{k}(x)\geq 0} that define the feasible region, that is, the set of all x to search for the optimal solution. Given a point x {\displaystyle x} in the feasible
Active-set_method
Term used in information technology
enterprise solution architecture (ESA). Greefhorst and Proper (2013): An architecture of a solution, where a solution is a system that offers a coherent set of
Solution_architecture
called a polytope. Analytically, a convex polyhedron is expressed as the solution set for a system of linear inequalities, aiTx ≤ bi, where ai are vectors
N-dimensional_polyhedron
Difference between the dimensions of mathematical object and a sub-object
then the codimension of the solution set is at most the number of constraints. We do not expect to be able to find a solution if the predicted codimension
Codimension
Problem of finding the best feasible solution
the set of all possible points or solutions that satisfy the problem's constraints, targets, or goals. These points represent the feasible solutions that
Optimization_problem
opinion on the Wall. Secondly, it would violate the vision of a two-state solution set forth in the Oslo Accords. Thirdly, the permanent and day-to-day control
Proposed Israeli annexation of the West Bank
Proposed_Israeli_annexation_of_the_West_Bank
1941 science fiction short story by Robert A. Heinlein
"Solution Unsatisfactory" is a 1941 science fiction short story by American writer Robert A. Heinlein - predicting the development and conclusion of the
Solution_Unsatisfactory
SOLUTION SET
SOLUTION SET
Girl/Female
Tamil
Good or Happy condition, Solution
Boy/Male
Arabic, Muslim
Wish; Accord; Resolution
Girl/Female
Arabic, Muslim
Determination; Resolution
Girl/Female
Arabic, Muslim
Determination; Resolution
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Strategy; Idea; Trick; Solution; A Device; Planning
Boy/Male
Muslim
Resolution, Firm will
Girl/Female
Muslim
Determination, Resolution
Girl/Female
Hindu
Good or Happy condition, Solution, Fortune
Girl/Female
Tamil
Good or Happy condition, Solution, Fortune
Boy/Male
Indian
Resolution, Firm will
Boy/Male
Tamil
Perfect isolation, Salvation
Boy/Male
Arabic, Muslim
Root; Element; Resolution
Boy/Male
Muslim
Root, Element, Resolution
Boy/Male
Hindu
Perfect isolation, Salvation
Boy/Male
Bengali, Indian
Resolution
Girl/Female
Hindu
Good or Happy condition, Solution
Boy/Male
Arabic
Prudence; Resolution
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Creation; Evolution; Construction
Boy/Male
Indian, Sanskrit
Evolution; Progress
SOLUTION SET
SOLUTION SET
Boy/Male
American, British, English, German
Strong as a Bear
Male
Scandinavian
Variant spelling of Scandinavian Erland, ERLEND means "foreigner, stranger."
Girl/Female
Indian
Snow queen.
Boy/Male
Muslim
Nice, Admirable
Female
Finnish
Finnish name derived from the word mieli which can have many MIELIKKI meanss ("desire, feeling, heart, mind, mood, pleasure"), but its central meaning is "mind."Â In mythology, this is the name of a goddess of forests and healing, whose symbol is the unicorn.Â
Male
Scandinavian
Scandinavian form of Old Norse Rögnvaldr, ROGNVALD means "wise ruler."
Boy/Male
Indian
Help, Support, Victory
Girl/Female
Arabic, Muslim
A Star
Boy/Male
Native American
Flat iron.
Boy/Male
Hindu, Indian
The Biggest; Name of Lord Shiva
SOLUTION SET
SOLUTION SET
SOLUTION SET
SOLUTION SET
SOLUTION SET
n.
The state of being dissolved or disintegrated; resolution; disintegration.
n.
That which is resolved or determined; a settled purpose; determination. Specifically: A formal expression of the opinion or will of an official body or a public assembly, adopted by vote; as, a legislative resolution; the resolutions of a public meeting.
n.
The act or process by which a body (whether solid, liquid, or gaseous) is absorbed into a liquid, and, remaining or becoming fluid, is diffused throughout the solvent; also, the product reulting from such absorption.
n.
A solution; an explanation.
n.
The termination of a disease; resolution.
n.
Evolution of one's self; development by inherent quality or power.
n.
The act of resolving or making clear; resolution; solution.
n.
The act of unfolding or unrolling; hence, in the process of growth; development; as, the evolution of a flower from a bud, or an animal from the egg.
n.
Adverse action of will; unwillingness; -- opposed to volition.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
n.
A liquid medicine or preparation (usually aqueous) in which the solid ingredients are wholly soluble.
n.
The act or process of solving; solution; as, the resolution of an equation or problem.
n.
release; deliverance; discharge.
n.
See Fehling's solution, under Solution.
n.
To analyse, or determine the strength of, by means of standard solutions. Cf. Standardized solution, under Solution.
n.
See Exsolution.
n.
A crisis.