My Math Forum Proof to Collatz Conjecture.

 Number Theory Number Theory Math Forum

 March 30th, 2017, 11:10 PM #1 Banned Camp   Joined: Mar 2017 From: . Posts: 338 Thanks: 8 Math Focus: Number theory Proof to Collatz Conjecture. Consider any positive integer n from which the sequence is formed. n has a probability of 0.5 of either being odd or even. If even, we divide it by two. If odd, we multiply it by three, add one and then divide the result by two since the resulting number must be even. This is same as multiplying n by 1.5 and adding 0.5. The resulting integer, say m, will hence either be n/2 or 1.5n+0.5 and also has a probability of 0.5 of being either even or odd. The 0.5 that is added has considerable effect on outcome only if n is 1 (which can explain the repeating cycle when the sequence reaches 1). In this case we will neglect it. Since n has equal chances of being odd or even, it therefore has equal chances of being divided by 2 or being multiplied by 1.5, and so is m and the rest of the outcomes. The factor by which the outcomes are divided by is greater than the factor they are multiplied with and hence, the sequence will converge.

 Tags collatz, conjecture, proof

,
,

math forum proof collatz

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Mariga Number Theory 207 March 20th, 2018 08:32 PM JwClaassen Number Theory 0 March 18th, 2017 08:47 AM vlagluz Number Theory 10 November 4th, 2014 11:27 PM lwgula Number Theory 2 October 30th, 2014 02:02 PM Aika Number Theory 6 April 29th, 2012 06:34 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top