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The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and how they work. The book offers techniques for both reading and writing proofs, discusses techniques in proving if/then statements by contrapositive and proofing by contradiction, includes the negation statement, and/or, examines various theorems, such as the if and only-if, equivalence theorems, existence theorems, and the uniqueness theorems. In addition, the use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are also covered. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book accessible as well as invaluable.

Proof theory. --- Logic, Symbolic and mathematical

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"More than a century after its composition, Tractatus Logico-Philosophicus--Wittgenstein's first masterwork, and the only book he published during his lifetime--endures as the definitive modern text on what logic can and cannot do. Since its first English-language publication in 1922, this profoundly enigmatic work has inspired philosophers and non-philosophers alike. Consisting of 525 hierarchically numbered statements, each one "self-evident," Tractatus Logico-Philosophicus is imbued, as translator Damion Searls writes, with the kind of cryptic grandeur and awe-inspiring opacity we might expect--might want--from such an iconic philosopher. Yet earlier translations, in their efforts to excessively copy German phrasing and syntax, range from stilted, even redolently Victorian, to downright impenetrable. With this new translation and insightful introduction on the language of the book, Searls finally does justice to Wittgenstein's masterpiece, capturing the fluid and forceful prose of the original without sacrificing any of its philosophical rigor. Indeed, in freeing the translation from the grip of the German language--revisiting, especially, the nouns and impersonal verbs that don't convey in English the precision and intensity of the German--Searls renders Wittgenstein's philosophy clearer and more accessible than ever before. Featuring a preface by eminent Wittgenstein scholar Marjorie Perloff, this bilingual, facing-page edition promises to become the standard for generations to come." --

Logic, Symbolic and mathematical. --- Language and logic --- Language and logic. --- Langage et logique. --- Logique symbolique et mathématique. --- Langage et logique --- PHILOSOPHY / Epistemology. --- Philosophy. --- Philosophie. --- Wittgenstein, Ludwig,