PROOF OF THE COLLATZ CONJECTURE USING THE REVERSE ALGORITHM

The Collatz conjecture has remained unsolved for a long time. In this paper, a proof of this conjecture will be presented. We know that almost all numbers will eventually reach one through the steps of the Collatz algorithm. Terence Tao has previously proven this. This paper demonstrates that all numbers will reach one by using Tao's proof. If almost all numbers reach one, then the probability that a randomly chosen number from the set of positive integers will reach one is one. The probability that a number will not reach one is zero. The probability of selecting the elements of the number sequences associated with a number n that violates the conjecture from the set of positive integers is a non-zero value such as c. However, this contradicts the proof that almost all numbers reach one. Therefore, there is no such number n that violates the conjecture, and the conjecture is true for all numbers. In order to prove that the probability of selecting the elements of the number sequences associated with a number n that violates the conjecture from the set of positive integers is a non-zero value like c, we examine the sequences associated with one. If the probability of selecting the elements of some branches of these sequences from the set of positive integers is a non-zero value, we reach the desired proof.