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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 .
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
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 :
Capacity of a set, in Euclidean space, the total charge a set can hold while maintaining a given potential energy; Capacity factor, the ratio of the actual output of a power plant to its theoretical potential output; Storage capacity (energy), the amount of energy that the storage system of a power plant can hold
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 ...
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.
To invoke a method in an object, the object reference and method name are given, together with any arguments. Interfaces An interface provides a definition of the signature of a set of methods without specifying their implementation. An object will provide a particular interface if its class contains code that implement the method of that ...
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.: