  In 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.
