Download PDFOpen PDF in browserProof of CollatzTheoremEasyChair Preprint 477713 pages•Date: December 23, 2020AbstractIn this article, we will show that Collatz is theorem and we proof it by method that we made in section 2 and 3. In section 1, first we introduction Collatz problem and idea of mathematician about this problem then we change the function of this problem and we make a new definition of Collatz set and generalize Collatz problem in the set theory. In section 2 we decrease all of natural numbers to $\mathbb{Z}_{10}$ and make a model with lemma that we said. Then in section 3 we say 3 properties of numbers that are in our models and then we make a new definition of coloring of graph to complete our model and make a new model to explain Collatz system with 3 numbers. Finally in section 4 we begin proof some part of first model and we use properties that we proved in section 3, to proof our model completely. Keyphrases: Collatz, Collatz Conjecture, Conjecture, Proof of Collatz, collatz system, collatz theorem, even number, finished proof, graph theory, number theory, odd number, output degree, subgraph
