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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