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In mathematics, a finitary relation has a finite number of "places". In set theory and logic, a ''relation'' is a property that assigns truth values to -tuples of individuals. Typically, the property describes a possible connection between the components of a -tuple. For a given set of -tuples, a truth value is assigned to each -tuple according to whether the property does or does not hold. An example of a ''ternary relation'' (i.e., between three individuals) is: " was introduced to by ", where is a 3-tuple of persons; for example, "Beatrice Wood was introduced to Henri-Pierre Roché by Marcel Duchamp" is true, while "Karl Marx was introduced to Friedrich Engels by Queen Victoria" is false. ==Informal introduction== ''Relation'' is formally defined in the next section. In this section we introduce the concept of a relation with a familiar everyday example. Consider the relation involving three roles that people might play, expressed in a statement of the form "''X'' thinks that ''Y'' likes ''Z'' ". The facts of a concrete situation could be organized in a table like the following: Each row of the table records a fact or makes an assertion of the form "''X'' thinks that ''Y'' likes ''Z'' ". For instance, the first row says, in effect, "Alice thinks that Bob likes Denise". The table represents a relation ''S'' over the set ''P'' of people under discussion: : ''P'' = . The data of the table are equivalent to the following set of ordered triples: : ''S'' = . By a slight abuse of notation, it is usual to write ''S''(Alice, Bob, Denise) to say the same thing as the first row of the table. The relation ''S'' is a ''ternary'' relation, since there are ''three'' items involved in each row. The relation itself is a mathematical object defined in terms of concepts from set theory (i.e., the relation is a subset of the Cartesian product on ), that carries all of the information from the table in one neat package. Mathematically, then, a relation is simply an "ordered set". The table for relation ''S'' is an extremely simple example of a relational database. The theoretical aspects of databases are the specialty of one branch of computer science, while their practical impacts have become all too familiar in our everyday lives. Computer scientists, logicians, and mathematicians, however, tend to see different things when they look at these concrete examples and samples of the more general concept of a relation. For one thing, databases are designed to deal with empirical data, and experience is always finite, whereas mathematics at the very least concerns itself with potential infinity. This difference in perspective brings up a number of ideas that may be usefully introduced at this point, if by no means covered in depth. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「finitary relation」の詳細全文を読む スポンサード リンク
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