Collatz Sequence Proof (2nd Way)

One person: This proof is completely wrong because the induction is incorrect. If the Collatz function enters the cycle {1, 4, 2} for all numbers in {1, 2, 3, ..., r} where r is an even number, then the third case (iii) only proves that even numbers r+2, r+4, ..., 2r enter the cycle {1, 4, 2}. It does not prove that even numbers greater than 2r enter the cycle {1, 4, 2}, so you cannot use this assumption in the fourth case (iv) when considering the even number 3n+1. My Answer1: Your question is wrong because the term after r is r+2, not 2r. Same Person: You need to do your own research and read peer-reviewed papers on this postulate. Start with the comprehensive paper by Lagarias, as well as Tao's paper, which proves that almost all Collatz sequences eventually become bounded by an increasing function. My Answer 2: I don't need advice. I do not need follow others' steps because I am under control of solving Collatz. Same Person: Both are experts on the Collatz postulate, while you are not. My Answer 3: No need for attack. I have millions of honorable professors are looking at my humble solutions at YouTube, X.com, my books at Amazon.com, my documentary film by Film maker Dr. Aaron Dye, Washington University.