My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 31st, 2017, 12:10 AM   #1
Senior Member
 
Joined: Mar 2017
From: .

Posts: 266
Thanks: 4

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.
Mariga is offline  
 
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
collatz, conjecture, proof



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Proof to Collatz conjecture. Mariga Number Theory 200 December 7th, 2017 09:50 PM
On the Collatz Conjecture JwClaassen Number Theory 0 March 18th, 2017 09:47 AM
About Collatz conjecture vlagluz Number Theory 10 November 5th, 2014 12:27 AM
The marvellous proof of the collatz conjecture lwgula Number Theory 2 October 30th, 2014 03:02 PM
Collatz conjecture & More (Please Help) Aika Number Theory 6 April 29th, 2012 07:34 AM





Copyright © 2017 My Math Forum. All rights reserved.