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An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a 1, a 2,... a n}. [5] [6] [7]
The component diagram extends the information given in a component notation element. One way of illustrating a component's provided and required interfaces is through a rectangular compartment attached to the component element. [3] Another accepted way of presenting the interfaces is the ball-and-socket graphic convention.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The classes in a class diagram represent both the main elements, interactions in the application, and the classes to be programmed. In the diagram, classes are represented with boxes that contain three compartments: The top compartment contains the name of the class. It is printed in bold and centered, and the first letter is capitalized.
A sample UML class and sequence diagram for the Decorator design pattern. [7] In the above UML class diagram, the abstract Decorator class maintains a reference (component) to the decorated object (Component) and forwards all requests to it (component.operation()). This makes Decorator transparent (invisible) to clients of Component.
UML Diagrams used to represent the development view include the Package diagram and the Component diagram. [2] Physical view: The physical view (aka the deployment view) depicts the system from a system engineer's point of view. It is concerned with the topology of software components on the physical layer as well as the physical connections ...
Theorem: If A and B are sets, then there is a set A×B which consists of all ordered pairs (a, b) of elements a of A and b of B. Proof: The singleton set with member a, written {a}, is the same as the unordered pair {a, a}, by the axiom of extensionality. The singleton, the set {a, b}, and then also the ordered pair
r : E → {{x,y} : x, y ∈ V}, assigning to each edge an unordered pair of endpoint nodes. Some authors allow multigraphs to have loops , that is, an edge that connects a vertex to itself, [ 2 ] while others call these pseudographs , reserving the term multigraph for the case with no loops.