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### 1.2 RELATIONS AND FUNCTIONS

Intuitively, a relation is a formula, (x, y, z). We say that a, b, c are related according to (x, y, z) just in case (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, (x, y, z) naturally defines this set, its extension: {x, y, z : (x, y, z)}. One goes one step further and forgets the role of . 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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