Items related to How to Prove The Collatz Conjecture
Synopsis
The first proof of the Collatz Conjecture.
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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 ... .
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- PublisherLulu.com
- Publication date2004
- ISBN 10 141160427X
- ISBN 13 9781411604278
- BindingPaperback
- LanguageEnglish
- Number of pages149
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