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.
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