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Theory of Computation by George Tourlakis

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1.2 RELATIONS AND FUNCTIONS

Intuitively, a relation is a formula, Images(x, y, z). We say that a, b, c are related according to Images (x, y, z) just in case Images(a, b, c) is true. Influenced by the set theorist who wants to realize “everything” (even formulae) as some set, the modern mathematician views relations extensionally (by what they contain) as sets. For example, Images(x, y, z) naturally defines this set, its extension: {imagex, y, zimage : Images(x, y, z)}. One goes one step further and forgets the role of Images. As a result, we give a totally extensional definition of a relation as a set of tuples, disregarding how it may have been formed by a “defining property”.

1.2.0.4 Definition. A binary relation —or simply relation—R ...

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