How to Prove The Collatz Conjecture - Softcover

Fleming, Danny

Softcover

ISBN 10: 141160427X ISBN 13: 9781411604278

Publisher: Lulu.com, 2004

Synopsis

The first proof of the Collatz Conjecture.

About this title

About the Author

I have a Bachelor of Science in Mathematics and a Classical Studies Minor I received from Califorina State University in 1996.

Excerpt. © Reprinted by permission. All rights reserved.

... First, any even number will continue decreasing until it reaches 1 or an odd number. Once we reach this odd number x, we will have an even number after the 3x+1 rule is applied. Here is why: We know 3 is always odd by definition. And x is always odd because the 3x+1 rule is always used if x is odd. For the 3x part of 3x+1, we have an odd number (3) times another odd number (x). We know from Book IX Proposition 29 of Euclid's Elements that an odd number times another odd number is always odd. Examples, using 3 and any other positive odd integer for 3x+1 are: 3x3=9, 3x9=27, 3x81=243, 3x5=15, 3x19=57, etc. As expected, 9, 27, 243, 15, 57 are all odd ... Adding 1 to this proven odd 3x will always be an even number because any odd number plus 1 is even ... .

Edition details

• Publisher: Lulu.com
• Publication date: 2004
• Language: English
• ISBN 10: 141160427X
• ISBN 13: 9781411604278
• Binding: Paperback
• Number of pages: 149