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Counterexamples in Probability and Statistics is a mathematics book by Joseph P. Romano and Andrew F. Siegel. It began as Romano's senior thesis at Princeton University under Siegel's supervision, and was intended for use as a supplemental work to augment standard textbooks on statistics and probability theory.
Models And Counter-Examples (Mace) is a model finder. [1] Most automated theorem provers try to perform a proof by refutation on the clause normal form of the proof problem, by showing that the combination of axioms and negated conjecture can never be simultaneously true, i.e. does not have a model. A model finder such as Mace, on the other ...
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Counterexamples in Probability is a mathematics book by Jordan M. Stoyanov. Intended to serve as a supplemental text for classes on probability theory and related topics, it covers cases where a mathematical proposition might seem to be true but actually turns out to be false.
For example, suppose that after a while, the mathematician above settled on the new conjecture "All shapes that are rectangles and have four sides of equal length are squares". This conjecture has two parts to the hypothesis: the shape must be 'a rectangle' and must have 'four sides of equal length'.
Both can be run simultaneously from the same input, [2] with Prover9 attempting to find a proof, while Mace4 attempts to find a (disproving) counter-example. Prover9, Mace4, and many other tools are built on an underlying library named LADR ("Library for Automated Deduction Research") to simplify implementation.
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Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr.. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties.