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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)
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 total extermination
Final_Solution
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
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
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
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
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
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)
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
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
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
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
Criteria in Category theory of Mathematics
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
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
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
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
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)
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
South Korean battery maker
Energy Solution, the battery maker behind S.Korea's biggest IPO". Reuters. Seoul. Kim, Eun-jung (December 1, 2020). "LG Energy Solution sets sail to
LG_Energy_Solution
tournament solutions are the: Copeland set Smith set (a.k.a. Top cycle) Slater set[clarification needed] Bipartisan set Landau set Banks set Minimal covering
Tournament_solution
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
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
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
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
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
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
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)
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
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
Classical problem in combinatorics
cover all elements with only two sets: { {1, 2, 3}, {4, 5} }, but not with only one set. Therefore, the solution to the set cover problem for this U and
Set_cover_problem
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
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
Technology Solutions Holdings Set to Join S&P MidCap 400" (PDF). S&P Dow Jones Indices. August 12, 2022. Retrieved August 17, 2022. "Celsius Holdings Set to Join
List_of_S&P_400_companies
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
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
British independent record label
releasing discs on the label. In the mid 1990s he set up D.C. Recordings as a replacement for Vinyl Solution, with several other new offshoots catering for
Vinyl_Solution
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
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
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
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
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
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
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
1973 novel by Eric Norden
Ultimate Solution is a 1973 dystopian alternate history novel by journalist and former Playboy interviewer Eric Norden (pen name for Eric Pelletier). Set in
The_Ultimate_Solution
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
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
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
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
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
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
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
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
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
Australian asylum policy from 2001
The Pacific Solution is the name given to the government of Australia's policy of transporting asylum seekers to detention centres on island nations in
Pacific_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
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
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
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
Surface described by a 4th-degree polynomial
quartic surface: affine and projective. An affine quartic surface is the solution set of an equation of the form f ( x , y , z ) = 0 {\displaystyle f(x,y
Quartic_surface
Shape that blocks all lines of sight
opaque set is a system of curves or other set in the plane that blocks all lines of sight across a polygon, circle, or other shape. Opaque sets have also
Opaque_set
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)
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
Healthcare Set to Join S&P SmallCap 600" (PDF). May 11, 2026. Retrieved May 25, 2026. "Bright Horizons Family Solutions and Remitly Global Set to Join S&P
List_of_S&P_600_companies
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
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
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
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
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
Aspect of general relativity
Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
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
Navigation and surveillance technique
algorithms yield the same "correct" solution set (but perhaps one or more different sets of "incorrect" solutions). Of course, statistically larger measurement
Pseudo-range_multilateration
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 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
Australian rock band
Crime & the City Solution is an Australian rock band formed in late 1977 by singer-songwriter and mainstay Simon Bonney. They disbanded in 1979 leaving
Crime_&_the_City_Solution
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
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
Description of a quantum-mechanical system
{H}}_{n}} are the Hermite polynomials of order n {\displaystyle n} . The solution set may be generated by ψ n ( x ) = 1 n ! ( m ω 2 ℏ ) n ( x − ℏ m ω d d x
Schrödinger_equation
Solution of a simplified form of an equation
(dominate) the solution and excluding terms contributing only small modifications to this approximate solution. Following an initial solution, iteration of
Method_of_dominant_balance
Topics referred to by the same term
set, in dynamical systems, the set of points leading up to an attractor Von Neumann-Morgenstern solution or stable set, in cooperative games, a set of
Stable_set
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