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Probabilities --- Combinatorial analysis --- Probabilities. --- Combinatorial analysis. --- Analyse combinatoire --- Combinatorial probabilities --- Probabilités combinatoires --- Probabilités combinatoires.
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Stochastic processes --- Discrete mathematics --- Combinatorial probabilities --- Probabilités combinatoires --- 519.212 --- Probabilistic combinatorics --- Probabilities --- Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- Combinatorial probabilities. --- 519.212 Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- Probabilités combinatoires
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La logique est un domaine paradoxal: alors que l'on prétend y déterminer les règles à respecter pour ne pas tomber dans des paradoxes, c'est là que l'on en rencontre le plus ! Et ces paradoxes, qui font trembler les fondements des mathématiques, peuvent entraîner les calculs informatiques dans des maelströms infinis. Ce livre vous entraîne dans un parcours initiatique sur les chemins de l'indécidabilité, de l'aléatoire, de la déduction et de l'induction. Les découvertes récentes défrichent un univers où l'esprit tente de comprendre l'esprit, de le recréer et de s'en amuser.
Logic, Symbolic and mathematical --- Logique mathématique --- Proof theory --- Théorie de la démonstration --- Computational complexity --- Complexité de calcul (informatique) --- Logic, symbolic and mathematical --- Programmable logic devices --- Logic, Symbolic and mathematical. --- Logique mathématique. --- Proof theory. --- Théorie de la démonstration --- Computational complexity. --- Décidabilité (logique mathématique) --- Cryptographie --- Information theory. --- Information, Théorie de l'. --- Decidability (Mathematical logic) --- Turing, Machines de. --- Turing machines. --- Cryptographie. --- Cryptography. --- Paradoxe. --- Paradoxes. --- Combinatorial probabilities. --- Probabilités combinatoires.
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The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
Differential geometry. Global analysis --- Combinatorial probabilities --- Convergence --- Convergentie --- Mathematical sequences --- Numerical sequences --- Numerieke reeksen --- Reeksen (Wiskunde) --- Sequences (Mathematics) --- Suites (Mathématiques) --- Suites numériques --- Wiskundige reeksen --- Combinatorial probabilities. --- Convergence. --- Probabilités combinatoires --- Convergence (Mathématiques) --- Mathematical Theory --- Applied Mathematics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Suites (Mathématiques) --- Probabilités combinatoires --- Convergence (Mathématiques) --- Suites récurrentes (mathématiques) --- Recurrent sequences (Mathematics) --- Number theory. --- Computers. --- Number Theory. --- Theory of Computation. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Number study --- Numbers, Theory of --- Algebra --- Probabilistic combinatorics --- Probabilities --- Suites récurrentes (mathématiques) --- Nombres, Théorie des --- Systèmes dynamiques --- Theorie des nombres --- Theorie probabiliste
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