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The solution set of a given set of equations or inequalities is the set of all its solutions, a solution being a tuple of values, one for each unknown, that satisfies all the equations or inequalities. If the solution set is empty, then there are no values of the unknowns that satisfy simultaneously all equations and inequalities.
The Kissing Number Problem. A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to ...
More generally, the solution set to an arbitrary collection E of relations (E i) (i varying in some index set I) for a collection of unknowns (), supposed to take values in respective spaces (), is the set S of all solutions to the relations E, where a solution () is a family of values (()) such that substituting () by () in the collection E makes all relations "true".
Euler diagram for P, NP, NP-complete, and NP-hard set of problems (excluding the empty language and its complement, which belong to P but are not NP-complete) Main article: P versus NP problem The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time ), an algorithm ...
The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant k such that the following promise problem (L yes, L no) is NP-hard: L yes = {G: the value of G is at least 1 − δ} L no = {G: the value of G is at most ε} where G is a unique game whose answers come from a set of size k.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
The answer, he said, reveals how the job seeker sees themselves, how they see other people, and whether they are focused on themselves, other people, or tasks. One candidate answered it honestly ...
If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that produces the correct answer for any input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally ...