Concepts inThe theory of joins in relational databases
Relational algebra
Relational algebra, an offshoot of first-order logic, deals with a set of finitary relations that is closed under certain operators. These operators operate on one or more relations to yield a relation. Relational algebra is a part of computer science.
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Subset
In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.
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Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.
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Relational database
A relational database is a collection of data items organized as a set of formally described tables from which data can be accessed easily. A relational database is created using the relational model. The software used in a relational database is called a relational database management system (RDBMS). A relational database is the predominant choice in storing data, over other models like the hierarchical database model or the network model.
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Lossless data compression
Lossless data compression is a class of data compression algorithms that allows the exact original data to be reconstructed from the compressed data. The term lossless is in contrast to lossy data compression, which only allows an approximation of the original data to be reconstructed, in exchange for better compression rates. Lossless data compression is used in many applications. For example, it is used in the ZIP file format and in the Unix tool gzip.
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Multivalued function
In mathematics, a multivalued function is a left-total relation; that is, every input is associated with at least one output. Strictly speaking, a "well-defined" function associates one, and only one, output to any particular input. The term "multivalued function" is, therefore, a misnomer because functions are single-valued. Multivalued functions often arise from functions which are not injective. Such functions do not have an inverse function, but they do have an inverse relation.
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Lossy compression
In information technology, "lossy" compression is a data encoding method that compresses data by discarding (losing) some of it. The procedure aims to minimize the amount of data that needs to be held, handled, and/or transmitted by a computer. The different versions of the photo of the dog at the right demonstrate how much data can be dispensed with, and how the images become progressively coarser as the data that made up the original one is discarded (lost).
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Set (mathematics)
A set is a collection of well defined and distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.
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