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If the solution set of an equation is restricted to a finite set (as is the case for equations in modular arithmetic, for example), or can be limited to a finite number of possibilities (as is the case with some Diophantine equations), the solution set can be found by brute force, that is, by testing each of the possible values (candidate ...
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 and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
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.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
In Quine's set-theoretical writing, the phrase "ultimate class" is often used instead of the phrase "proper class" emphasising that in the systems he considers, certain classes cannot be members, and are thus the final term in any membership chain to which they belong. Outside set theory, the word "class" is sometimes used synonymously with "set".
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