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Also Cantor's proof that 2 n > n breaks down unless n is finite." — PM 2nd edition reprinted 1962:xiv, also cf. new Appendix C) In other words, the fact that an infinite list cannot realistically be specified means that the concept of "number" in the infinite sense (i.e. the continuum) cannot be described by the new theory proposed in PM ...
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should ...
Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies.That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different ...
In the United States, the book was released as Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. [1] [3] The book was released in the United States in October 1998 to coincide with the US release of Singh's documentary The Proof about Wiles's proof of Fermat's Last Theorem. [2] [7]
The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery.But its first chapter is Lakatos's own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–4 in the British Journal for the Philosophy of Science.
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99 Variations on a Proof is a mathematics book by Philip Ording, in which he proves the same result in 99 different ways. Ording takes an example of a cubic equation , x 3 − 6 x 2 + 11 x − 6 = 2 x − 2 , {\displaystyle x^{3}-6x^{2}+11x-6=2x-2,} and shows that its solutions are x = 1 {\displaystyle x=1} and x = 4 {\displaystyle x=4} using a ...
The Kuzari, full title Book of Refutation and Proof on Behalf of the Despised Religion [1] (Arabic: كتاب الحجة والدليل في نصرة الدين الذليل: Kitâb al-ḥujja wa'l-dalîl fi naṣr al-dîn al-dhalîl), also known as the Book of the Khazar (Hebrew: ספר הכוזרי: Sefer ha-Kuzari), [2] is one of the most famous works of the medieval Spanish Jewish ...