Talk:Collatz conjecture

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I am proposing a major edit to this page.

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

The added text is in ALL CAPS (will be changed to sentence structure once officially added to text). The added text is from the recently published paper “Hahn, Kirk O., 2024, Analysis of Collatz Conjecture Rules, Theoretical Mathematics & Applications, Volume 14, Issue 1, 1 – 76.” I am the author of this paper, so I tried to maintain a neutral “voice” with the information. No hype or exaggeration. We are all scientists or scientists-in-training when it comes to evaluating the changes to the page, so we must adhere to the “scientific method”. Which means in this case that all disclosed information in the paper is assumed to be true, since the paper has been published in a peer-reviewed, AMS registered journal. The journal is not the most prestigious but it is good enough to be included in the thousands of mathematical journals. The disclosure is assumed true unless someone with facts or evidence shows a mistake or error in the calculations or conclusions. Opinions, beliefs or feelings have no place in science. I encourage all commenters, whether positive or negative, to read the paper first [1]. We can only have an informed discussion with everybody knowing the facts. I will answer any questions that the commenters may have for me.

--------------------------------------------

Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such problems."[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics".[8] FORTUNATELY, THEY WERE NOT CORRECT.

IN 2024, KIRK HAHN DISCLOSED THAT THE COLLATZ CONJECTURE WAS TRUE FOR ALL POSITIVE INTEGERS.[40] THE PAPER SHOWED WITH FORMAL MATHEMATICAL PROOFS THAT THE SOLUTION INCLUDES ALL POSITIVE INTEGERS, ALL POSITIVE INTEGERS EVENTUALLY GO TO “1” WHEN THE COLLATZ RULES ARE USED TO ITERATE THE NUMBERS, IT IS MATHEMATICAL IMPOSSIBLE TO FORM LOOPS, EXCEPT FOR THE 4-2-1 MINOR LOOP AND NO POSITIVE INTEGER CONTINUOUSLY GOES UP TOWARD INFINITY WITHOUT EVENTUALLY DECREASING TO “1”.

ADDITIONALLY, THE POSITIVE INTEGERS FORM A SIMPLE AND PREDICTABLE DENDRITIC (TREE-LIKE) PATTERN WHEN APPROPRIATELY GRAPHED.

[INSERT FIGURE OF DENDRITIC PATTERN]

THIS OBSERVATION LEAD TO THE PRODUCTION OF A GENERAL EQUATION FOR THE COLLATZ CONJECTURE THAT IS ABLE TO CALCULATE ALL THE PARAMETERS. THE EQUATION IS ABLE TO CALCULATE THE NUMBER OF STEPS FROM THE INITIAL POSITIVE INTEGER TO REACHING “1”, THE INTERMEDIATE VALUES DURING ITERATION AND THEIR PRECISE LOCATION ON THE DENDRITIC PATTERN AND SHOWS ALL POSITIVE INTEGERS GOES TO “1”. IT CAN EVEN CALCULATE THE ENTIRE ITERATION WITH ONLY KNOWING THE INITIAL POSITIVE INTEGER.

[INSERT FIGURE OF GENERAL EQUATION]

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Since 3n + 1 is even whenever n is odd, one may instead use the "shortcut" form of the Collatz function:

Figure of equation

This definition yields smaller values for the stopping time and total stopping time without changing the overall dynamics of the process. HOWEVER, IT SHOULD BE REMEMBERED THAT THE RULE FOR ODD NUMBERS IS NOT THIS “SHORTCUT”, BUT JUST 3N+1. COMBINING THE ODD AND EVEN STEPS MAY SHORTENED THE NUMBER OF STEPS, But IT ALSO OBSCURES THE TRUE RELATIONSHIP OF THE NUMBERS WHEN DEVELOPING A PROOF OF THE CONJECTURE.

40. HAHN, KIRK O., 2024, ANALYSIS OF COLLATZ CONJECTURE RULES, THEORETICAL MATHEMATICS & APPLICATIONS, VOLUME 14 ISSUE 1, 1 – 76 45.50.231.56 (talk) 17:20, 13 August 2024 (UTC)[reply]

Sorry, Wikipedia is not the right place to promote your own original research.

See above: Collatz 2nd loop proven impossible in 5 stepsof easy logic. Uwappa (talk) 17:45, 13 August 2024 (UTC)[reply]

This is not "original research" as defined by Wikipedia. It is research that has been published in a peer-reviewed journal, as such, it is no different than any other published paper. It is true I have proposed the edit but it is from a published paper. 45.50.231.56 (talk) 19:35, 13 August 2024 (UTC)[reply]

It is from a journal never deemed worthy of indexing in MathSciNet, and removed from indexing in zbMATH in 2017. These are indexes that aim to include all respectable mathematics journals, from which I conclude that their deliberate exclusion means they think it is not a respectable mathematics journal. —David Eppstein (talk) 21:21, 13 August 2024 (UTC)[reply]

Unsurprisingly, the publisher (Scienpress Ltd) was on Beall's List. --JBL

For some reason its doi prefix, 10.47260, does not appear to be marked as predatory by User:Headbomb's script for that. Maybe it should be? —David Eppstein (talk) 17:48, 14 August 2024 (UTC)[reply]

Added. Headbomb {t · c · p · b} 18:18, 14 August 2024 (UTC)[reply]

This is your opinion, but it is not a requirement of either Wikipedia’s policy or rules. As I mentioned, TMA is not the most prestigious Math journal; however, it meets the minimum qualifications for a reliable source for Wikipedia. Wikipedia defines a “reliable source” has being “published” [yes], peer-reviewed [yes], and not a predatory journal [yes]. Additionally, TMA is listed in the AMS Digital Mathematics Registry, the journal is deposited with the National Librarian of the National Library of New Zealand, it is published in both online and print versions, it is 1 of 14 journals in four general categories published by Scientific Press International Limited and has ISSN numbers for both print (1792-9687) and online (1792-9709). TMA is not a “predatory journal”. It only has a modest publication fee, compared to other journals that charge thousands of dollars ($3,370 for J. Number Theory). The Beall's List is just one man’s opinion of potential predatory journals and publishers. The reason for a reliable source is the conclusion that the papers in this type of journal will also have higher probability of being reliable. In this case, all the information in the published paper is self-verifiable. Any reader of the paper can determine for themselves if the information is true by repeating the disclosed math. The level of math in the paper is high school level, which most people reading this page can do without any advance math knowledge. If the information is unreliable, then point out the errors in the calculations or conclusions. Therefore, let us discuss the disclosed mathematics. Is it true or false? 45.50.231.56 (talk) 19:33, 14 August 2024 (UTC)[reply]

"it meets the minimum qualifications for a reliable source for Wikipedia"

As a predatory journal, it does not meet WP:RS. See WP:VANPRED in particular. Headbomb {t · c · p · b} 19:41, 14 August 2024 (UTC)[reply]

It's largely irrelevant to our discussion here of whether we can include this material, but if you must know, I believe the arguments in the paper to be invalid. The reason is that, although the paper assumes that the arguments to the Collatz iteration are positive, it never uses that assumption. Therefore, if it provided a valid argument, that argument would apply equally well to the application of the Collatz iteration to negative integers. But we know from Collatz conjecture § Iterating on all integers that for negative integers there are at least four different Collatz cycles. —David Eppstein (talk) 19:48, 14 August 2024 (UTC)[reply]

The conjecture only pertains to positive integers, so negative numbers are not included in the analysis of the conjecture. 45.50.231.56 (talk) 05:45, 15 August 2024 (UTC)[reply]

[...] it meets the minimum qualifications for a reliable source for Wikipedia. No, it really doesn't.

Therefore, let us discuss the disclosed mathematics. That's not what we're here for. Like, at all. XOR'easter (talk) 22:51, 14 August 2024 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

only integers

The definition says: "If the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1.". So, you can not choose non-integers for the Collatz conjecture and the sections Iterating on rationals with odd denominators, 2-adic extension and Iterating on real or complex numbers need to be removed. 94.31.89.138 (talk) 18:01, 20 August 2024 (UTC)[reply]

And the section talks about it being an extension of the map.Naraht (talk) 18:03, 23 September 2024 (UTC)[reply]

All of these sections define clearly and properly what they mean and are adequately sourced. —David Eppstein (talk) 18:39, 23 September 2024 (UTC)[reply]

References

What is/are the references/citations that disclose the information in paragraph "Iterating on all integers"? 45.50.231.56 (talk) 15:11, 23 September 2024 (UTC)[reply]

I think much of this can be found in Lagarias 1985 section 2.6 and its references. —David Eppstein (talk) 17:26, 23 September 2024 (UTC)[reply]

Prime numbers

There is no section on how 3n+1 conjecture may do anything with prime numbers; could use one.

Example: proving 3n+1 conjecture means there is no infinite Nnext=(3n+1)/2 sequence of prime numbers that just won't stop appearing.

Seriously, proving 3N+1 is real means proving curious sequences like this one are impossible. 81.89.66.133 (talk) 08:06, 20 December 2024 (UTC)[reply]

Collatz-graph is a tree

Collatz-graph is connected and acyclic.

Content:

1.Formulas for forward and backward sequences.

2.Family tree

3.Collatz sequence tree

4.Conclusion.

Exploring other mathematical sequences:

5. (3*N+5)/2^m

6. Juggler sequence

https://sourceforge.net/projects/trial-collatz-proof/ Kavalenka (talk) 13:55, 29 December 2024 (UTC)[reply]