Search results
Results from the WOW.Com Content Network
If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
The following proposition says that for any set , the power set of , ordered by inclusion, is a bounded lattice, and hence together with the distributive and complement laws above, show that it is a Boolean algebra.
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".
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 ...
A coanalytic set is the complement of an analytic set cofinal A subset of a poset is called cofinal if every element of the poset is at most some element of the subset. cof cofinality cofinality 1. The cofinality of a poset (especially an ordinal or cardinal) is the smallest cardinality of a cofinal subset 2.
A derived binary relation between two sets is the subset relation, also called set inclusion. If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B. For example, {1, 2} is a subset of {1, 2, 3}, and so is {2} but {1, 4} is not. As implied by this definition, a set is a subset of itself.
The cofinite topology or the finite complement topology is a topology that can be defined on every set . It has precisely the empty set and all cofinite subsets of X {\displaystyle X} as open sets. As a consequence, in the cofinite topology, the only closed subsets are finite sets, or the whole of X . {\displaystyle X.}
That is, for any sets ,, and , one has = () = () Inside a universe , one may define the complement of to be the set of all elements of not in . Furthermore, the intersection of A {\displaystyle A} and B {\displaystyle B} may be written as the complement of the union of their complements, derived easily from De Morgan's laws : A ∩ B = ( A c ...