Titlebook: Why Prove it Again?; Alternative Proofs i John W. Dawson, Jr. Book 2015 Springer International Publishing Switzerland 2015 Alternative Proo

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The Fundamental Theorem of Arithmetic, the factors. The theorem is often credited to Euclid, but was apparently first stated in that generality by Gauss. Note that the statement has two parts: First, every integer greater than 1 . a factorization into primes; second, any two factorizations of an integer greater than 1 into primes must b

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The Fundamental Theorem of Algebra,ce. Like the Pythagorean Theorem, the Fundamental Theorem of Algebra has been proved in many different ways since its enunciation by Euler in 1739. Unlike the Pythagorean Theorem, however, early attempts to prove the Fundamental Theorem of Algebra are not shrouded in the mists of antiquity, so we kn

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Other Case Studies,avor and that the informal criteria for distinguishing proofs described in Chapter?. serve that purpose well. I hope too that some of the proofs discussed in those chapters will have been new to most readers, who will have found them to possess both intrinsic interest and pedagogical value.This fina

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