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An entity–relationship model (or ER model) describes interrelated things of interest in a specific domain of knowledge. A basic ER model is composed of entity types (which classify the things of interest) and specifies relationships that can exist between entities (instances of those entity types).
In systems analysis, a one-to-many relationship is a type of cardinality that refers to the relationship between two entities (see also entity–relationship model). For example, take a car and an owner of the car. The car can only be owned by one owner at a time or not owned at all, and an owner could own zero, one, or multiple cars.
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point set in the plane, the y-coordinates of the points, ordered by their x-coordinates, forms a sequence of numbers (unless two of the points have equal x-coordinates).
An entity–relationship model (ERM) is an abstract conceptual representation of structured data. Entity–relationship modeling is a relational schema database modeling method, used in software engineering to produce a type of conceptual data model (or semantic data model ) of a system, often a relational database , and its requirements in a ...
Barker's notation refers to the ERD notation developed by Richard Barker, Ian Palmer, Harry Ellis et al. whilst working at the British consulting firm CACI around 1981. The notation was adopted by Barker when he joined Oracle and is effectively defined in his book Entity Relationship Modelling as part of the CASE Method series of books.
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For some other Diophantine problems, the existence of a solution can be demonstrated through asymptotic lower bounds on the number of solutions, but this works best when the number of solutions grows at least polynomially, so the slower growth rate of Elsholtz and Tao's result makes a proof of this type less likely.