|
Bounded Set
In mathematical analysis and related areas of mathematics, a set is called ''bounded'' if all of its points are within a certain distance of each other. Conversely, a set which is not bounded is called ''unbounded''. The word "bounded" makes no sense in a general topological space without a corresponding metric. '' Boundary'' is a distinct concept: for example, a circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. A bounded set is not necessarily a closed set and vice versa. For example, a subset ''S'' of a 2-dimensional real space R''2'' constrained by two parabolic curves ''x''2 + 1 and ''x''2 - 1 defined in a Cartesian coordinate system is closed by the curves but not bounded (so unbounded). Definition in the real numbers A set ''S'' of real numbers is called ''bounded from above'' if there exists some real number ''k'' (not necessarily in ''S'') such that ''k'' ≥ '' s'' for all ''s'' in ''S''. The number ''k'' is calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounded Unbounded
Boundedness or bounded may refer to: Economics * Bounded rationality, the idea that human rationality in decision-making is bounded by the available information, the cognitive limitations, and the time available to make the decision * Bounded emotionality, a concept within communication theory that stems from emotional labor and bounded rationality Linguistics * Boundedness (linguistics), whether a situation has a clearly defined beginning or end Mathematics * Boundedness axiom, the axiom schema of replacement * Bounded deformation, a function whose distributional derivatives are not quite well-behaved-enough to qualify as functions of bounded variation, although the symmetric part of the derivative matrix does meet that condition * Bounded growth, occurs when the growth rate of a mathematical function is constantly increasing at a decreasing rate * Bounded operator, a linear transformation ''L'' between normed vector spaces for which the ratio of the norm of ''L''(''v'') t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
