Unformatted text preview: R , the task is to Fnd a smallest S such that S + = R . The beneFt is that S is smaller, while in some sense having the same information content as R , since R can be reconstructed from S . In general, there can be many solutions for S . We will return to this problem in the easier setting of partial orders in section 5. 4 Functions You have probably spent a large part of your mathematical education considering mathematical functions in one context or another. In this section, we formalize the notion of mathematical functions as special relations, giving the basic deFnitions, ways of constructing functions and properties for reasoning about functions. You have also been introduced to Haskell functions, which are examples of the computable functions. In future courses, you will learn about these computable functions. 30...
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 Spring '09
 Koskesh
 Math, Transitive closure, Mathematical Functions, computable functions, Kenyalike algorithm

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