Problems - Ideas - Solutions: Proof of the Collatz Conjecture (Paperback)

This book is at first glance a proof of the well-known conjecture of Lothar Collatz on the Syracuse sequence.However, in fact, this book is about finding consistency and regularity in the world around us.Without any doubt, there will be many criticisms about the inconclusiveness of the proof, the presence of errors, the presence of inaccuracies, the presence of unnecessary minor details, inappropriate mathematical presentation, etcHowever, both computing projects to search for a counterexample will be stopped because of the obvious allegiance to the Conjecture of Collatz is after the project management will familiarize themselves with the material of the bookMoreover, there will be new correct proofs of the validity of the Collatz Conjecture, which are quite possibly shorter and more correctly stated mathematicallyHowever, all these new proofs will be very important to use the tool of Modified Reduced Sequences of Collatz, the tool of Canonical Tree of Collatz, the tool of Branches and Trunks of Collatz Tree, the tool of Vertical and Horizontal Sequences, the tool of Direct and Reverse structures of Collatz and other tools outlined in the bookProbably the tool of Vertical and Horizontal numbers as well as the tool of the types of the Collatz will be used in attempts to solve other unsolved problems of number theory.The most important value of the material presented in the book is precisely in the detection of the tool types of the Collatz and it is in the detection of the tool Horizontal and Vertical numbers.The material of the book shows how, as a result of minor transformations, the chaos of the "hailstone numbers" behavior turns into a coherent and regular picture.The study of the Canonical Tree of the Collatz and the Direct And Reverse structures of the Collatz in itself is a very interesting direction in the development of number theory in particular and in the harmony and regularity of the world in General.The material of the book is clear and accessible to any school child from 11-12 years.The material of the book can be a source of a huge number of tasks for programming Olympiads.On the example of the problem of correctness of The Collatz conjecture about the Syracuse sequence, I want to draw attention to the following circumstance and propose a new paradigm for solving any problems (not only in mathematics, but also in engineering and in General in all human activities)The fact is that until now, mankind has meant two intellects, namely the usual human intelligence and artificial intelligence of computers.While there is actually many times more powerful intellect than both of the above mentioned intellects, namely there is a Collective intellect.A proof of the validity of the Collatz hypothesis, devoid of any drawbacks, could have been obtained within a few weeks if the Collective Intellect had set itself the task of building such a proofTherefore, another goal of this book is the author's desire to create and develop a paradigm of Collective Intellect.Currently, the most important prerequisite for the creation and development of the paradigm of Collective Intellect has appeared.It's about the rapidly growing ability of people to communicate in virtual reality.In the very near future I want to create appropriate virtual platforms based on Second Life, Sansar, Decentraland or any other virtual reality.However, while such virtual platforms are not created, I suggest everyone to leave their questions and comments in the blog howwewanttolive.livejournal.comIn this blog I will answer any questions and comments on the material of this book as well as on all other topics covered in this blog.