Mathematical Proof of Collatz Conjecture

International Journal of Mathematics Trends and Technology (IJMTT)  
© 2021 by IJMTT Journal  
Volume67 Issue7  
Year of Publication : 2021  
Authors : Nishad T M 

10.14445/22315373/IJMTTV67I7P521 
MLA Style: Nishad T M"Mathematical Proof of Collatz Conjecture" International Journal of Mathematics Trends and Technology 67.7 (2021):178182.
APA Style: Nishad T M(2021). Mathematical Proof of Collatz Conjecture International Journal of Mathematics Trends and Technology, 178182.
Abstract
Lothar Collatz introduced Collatz Conjecture in 1937. No one succeeded in proving this conjecture. In this article a convincing mathematical proof is introduced. Initially it is proved that for every natural number n in N={1,2,3,..}, the set An exists where An ={x/x is a term in Hailstone sequence starting with n}. Later it is proved thatthe intersections of An and Am is not empty foreverynatural number n≠m, m,n >1. Then it is observed that the countable intersection of all An contains A0= {1}.This observation brings the conclusion that for all Hailstone sequences starting with any positive integer n ,there exists a a term 1 in the Hailstone sequence.This conclusion implies that for any positive integer n, the Hailstone sequence starting with n eventually ends in 1.
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Keywords : Collatz conjecture, Lothar Collatz, Hailstone sequence, 3n+1, n/2 function,Proof of Collatz Conjecture