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is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set. A set that is not a finite set is called an infinite set. For example, the set of all positive integers is infinite:
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations,
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 ...
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 ...
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".
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
In mathematics, a field of sets is a mathematical structure consisting of a pair (,) consisting of a set and a family of subsets of called an algebra over that contains the empty set as an element, and is closed under the operations of taking complements in , finite unions, and finite intersections.
Hilbert proved the theorem (for the special case of multivariate polynomials over a field) in the course of his proof of finite generation of rings of invariants. [1] The theorem is interpreted in algebraic geometry as follows: every algebraic set is the set of the common zeros of finitely many polynomials.