A Proof for the Collatz Conjecture

Abstract

It is well known that the following Collatz Conjecture is one of the unsolved problems in mathematics. Collatz Conjecture: For any positive integer $n>1$, the following recursive algorithm will convergent to 1 by a finite number of steps. A) If $n$ is an even number then $n/2 \to n$, B) If $n$ is an odd number then $3n+1 \to n$. This paper proposes a proof for the Collatz Conjecture by the elementary mathematical induction.