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In mathematics, the capacity of a set in Euclidean space is a measure of the "size" of that set. Unlike, say, Lebesgue measure , which measures a set's volume or physical extent, capacity is a mathematical analogue of a set's ability to hold electrical charge .
create_with_capacity(n): creates a new set structure, initially empty but capable of holding up to n elements. add(S,x): adds the element x to S, if it is not present already. remove(S, x): removes the element x from S, if it is present. capacity(S): returns the maximum number of values that S can hold.
Objects can contain other objects in their instance variables; this is known as object composition. For example, an object in the Employee class might contain (either directly or through a pointer) an object in the Address class, in addition to its own instance variables like "first_name" and "position".
Let X be a set (that is, an object in Set), which will be the basis of the free object to be defined. A free object on X is a pair consisting of an object A {\displaystyle A} in C and an injection i : X → U ( A ) {\displaystyle i:X\to U(A)} (called the canonical injection ), that satisfies the following universal property :
java.util.Collection class and interface hierarchy Java's java.util.Map class and interface hierarchy. The Java collections framework is a set of classes and interfaces that implement commonly reusable collection data structures. [1] Although referred to as a framework, it works in a manner of a library. The collections framework provides both ...
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 ...
Let be a set family (a set of sets) and a set. Their intersection is defined as the following set family: := {}. We say that a set is shattered by if contains all the subsets of , i.e.:
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.