Irrationality Without Number Theory
نویسنده
چکیده
منابع مشابه
Irrationality and Cognition
The strategy of this paper is to throw light on rational cognition and epistemic justification by examining irrationality. Epistemic irrationality is possible because we are reflexive cognizers, able to reason about and redirect some aspects of our own cognition. One consequence of this is that one cannot give a theory of epistemic rationality or epistemic justification without simultaneously g...
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1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.1.1 History of irrationality . . . . . . . . . . . . . . . . . . . . 10 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 12 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 13 1.2.3 Irr...
متن کاملUniversity of Natural Sciences Introduction to Diophantine Methods: Irrationality and Transcendence
1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 10 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 11 1.2.3 Irrationality of e √ 2 (Following a suggestion of D.M. Masser) . . . . . . . ...
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We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, we show that there exists a four-term real linear recurrence relation whose solutions allow us to produce a tractable equivalent criterion for the quadratic irrationality of ζ(3), where ζ is the classic Zeta function of Riemann or, for that matter, the quadratic...
متن کاملIntroduction to Diophantine Methods Irrationality and Trancendence
1 Irrationality 3 1.1 Simple proofs of irrationality . . . . . . . . . . . . . . . . . . . . 3 1.2 Variation on a proof by Fourier (1815) . . . . . . . . . . . . . . . 10 1.2.1 Irrationality of e . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.2 The number e is not quadratic . . . . . . . . . . . . . . . 11 1.2.3 Irrationality of e √ 2 (Following a suggestion of D.M. Masser) . . . . . . . ...
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تاریخ انتشار 1990