Finitary

In mathematics or logic, a finitary operation is an operation of finite arity, that is an operation that takes a finite number of input values. By contrast, an operation that may take an infinite number of input values is said to be infinitary. In standard mathematics, an operation is, by definition, finitary. Therefore these terms are used only in the context of infinitary logic. In mathematics or logic, a finitary operation is an operation of finite arity, that is an operation that takes a finite number of input values. By contrast, an operation that may take an infinite number of input values is said to be infinitary. In standard mathematics, an operation is, by definition, finitary. Therefore these terms are used only in the context of infinitary logic. A finitary argument is one which can be translated into a finite set of symbolic propositions starting from a finite set of axioms. In other words, it is a proof (including all assumptions) that can be written on a large enough sheet of paper. By contrast, infinitary logic studies logics that allow infinitely long statements and proofs. In such a logic, one can regard the existential quantifier, for instance, as derived from an infinitary disjunction.