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A finitary argument is one which can be translated into a finite set of symbolic propositions starting from a finite [1] 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 mathematics education, Finite Mathematics is a syllabus in college and university mathematics that is independent of calculus.A course in precalculus may be a prerequisite for Finite Mathematics.
Towards the end of the 20th century John Penn Mayberry developed a system of finitary mathematics which he called "Euclidean Arithmetic". The most striking tenet of his system is a complete and rigorous rejection of the special foundational status normally accorded to iterative processes, including in particular the construction of the natural ...
In mathematics, a finitary relation over a sequence of sets X 1, ..., X n is a subset of the Cartesian product X 1 × ... × X n; that is, it is a set of n-tuples (x 1, ..., x n), each being a sequence of elements x i in the corresponding X i. [1] [2] [3] Typically, the relation describes a possible connection between the elements of an n-tuple.
However, infinitary operations are sometimes considered, [1] in which case the "usual" operations of finite arity are called finitary operations. A partial operation is defined similarly to an operation, but with a partial function in place of a function.
The above concept of relation [a] has been generalized to admit relations between members of two different sets (heterogeneous relation, like "lies on" between the set of all points and that of all lines in geometry), relations between three or more sets (finitary relation, like "person x lives in town y at time z "), and relations between ...
President-elect Donald Trump is set to take office on Jan. 20. Once he takes the reins, a number of economic changes could ensue. Trump has proposed slapping tariffs on goods the U.S. imports from ...
If this transfinite induction is accepted as a finitary method, then one can assert that there is a finitary proof of the consistency of Peano arithmetic. More powerful subsets of second-order arithmetic have been given consistency proofs by Gaisi Takeuti and others, and one can again debate about exactly how finitary or constructive these ...