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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 ...
Perfect set. In general topology, a subset of a topological space is perfect if it is closed and has no isolated points. Equivalently: the set is perfect if , where denotes the set of all limit points of , also known as the derived set of . In a perfect set, every point can be approximated arbitrarily well by other points from the set: given ...
Complete measure, a measure space where every subset of every null set is measurable. Completion (algebra), at an ideal. Completeness (cryptography) Completeness (statistics), a statistic that does not allow an unbiased estimator of zero. Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting them.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
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".
Total order. In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric).
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