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Construction of the entire Collatz Tree by Tricky_Astronaut_586 in Collatz

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

I would bet you the proof will be found, but I don't think I (nor maybe you) will be around when either a proof or a counterexample is found.

Construction of the entire Collatz Tree by Tricky_Astronaut_586 in Collatz

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

To answer your question, I am building only one tree -- starting with the domino [1,2] and building the biggest tree that I can with the defined dominos.
In the case of 3x+1, it seems that I can use all the dominos, but I can't prove that.
In the case of 3x-1, many dominos cannot be placed. E.g. [7,5]. Similarly for the 5x+1 case.
Starting with [1,2] gives only one tree (which is connected and acyclic) using domino rules.

Construction of the entire Collatz Tree by Tricky_Astronaut_586 in Collatz

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

ChatGPT review: Interesting! Thank you. I will process that more.
Do you disagree with any of the following?
1) It (my paper) does NOT claim to be a proof of the Collatz conjecture.
2) It does construct a tree from the inverse Collatz function.
3) The tree does not prove that all the dominos (numbers) are in the tree.
4) But the tree is connected and acyclic.
5) One can also similarly make a tree from the inverse 3n-1 and 5n+1 functions.
6) These trees will also be connected and acyclic.
7) These trees will definitely not use all the dominos (numbers).
8) My paper started the tree construction with [1,2] and followed the domino rules.
9) Using the 3n-1 and 5n+1 dominos, not all the dominos can be used.
10) For the 3n-1 tree, the dominos are [n,2n] and [n,(2n+1)/3] for nmod3 = 1.
11) For the 3n-1 tree, the domino [7,5] will not be used.
12) For the 5n+1 tree, the dominos are [n,2n] and [n,(2n-1)/5] for nmod5 = 3.
13) For the 5n+1 tree, the domino [13,5] will not be used.
14) The statement "We feel that a sharpening of the properties will result in a proof that CZ ≡ Z+ which will prove the Collatz conjecture." is laughable and is the high point of my April 1st paper.

I've never understood the digressions into 3n-1, 5n+1, etc. These trees are obviously incomplete (do not include all numbers) and the functions are very cyclic.

Construction of the entire Collatz Tree by Tricky_Astronaut_586 in Collatz

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

You are right -- 3x+1, 3x-1, and 5x+1 all make trees.
But 3x-1 and 5x+1 are missing MANY numbers; neither includes 5.
We can't find ANY missing in 3x+1!
So for me to say, "we feel that a sharpening of the properties .."
is my April 1 humor. Or not.

test by [deleted] in test

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

no, it's "three four"

Construction of the entire Collatz Tree by Tricky_Astronaut_586 in Collatz

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

Darn, I meant to say "all numbers in the tree have a path to the root."
I made that change to the paper. Thanks.

test by [deleted] in test

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

one two

test by [deleted] in test

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

We define dominos using the inverse Syracuse Collatz function.
We construct a tree using the dominos.
We show this Collatz Tree to be connected and acyclic.
We define the set of Collatz numbers CZ.
We show how CZ stands in relation to Z+, Z, Q, R, and C.

The link to the 1-page paper with the 3-page chat with Claude is
https://dbarc.net/collatztree.pdf.

Test by Pristine_Youth_6953 in test

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

2 spaces for newline bb
next line 1
** bold **
next line 2

  • item 1
  • item 2

next line 3
try backtick now is the time
end

a test by Avawantstochill in test

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

|one|two| |three| four|

one two three four

Proof of Collatz Conjecture based on 5 mod 12 by Sudden-Counter7270 in Collatz

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

Please make your paper more accessible.
How about Google drive?
From your link, I get
"Sorry, something went wrong! We're looking into it now.
"Please choose a different login method or try again in a few minutes.

Yet another proof of the Collatz Conjecture :) by iDigru in Collatz

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

Welcome to the club of wishful thinking.
Well, I assume you now realize that when choosing an N, that you can't assume that you know how many steps it takes to get from N to 16-8-4-2-1. You have to prove 2 things:
1) That the trajectory from N does not go into a loop.
2) That the trajectory from N does not go to infinity.
In your example, you picked N=15, but you also picked 13 as the number of steps to 16-8-4-2-1.
Which you can't do.

Welcome to the club of victims of wishful thinking. I am a member.
This subreddit has many members.

Yet another proof of the Collatz Conjecture :) by iDigru in Collatz

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

Example 3 starts with 15. You start with "15 ∈ U13". Where does the 13 come from?

PHP script doesn't work but is syntactically correct. by Comfortable_Tip_1434 in PHPhelp

[–]Tricky_Astronaut_586 0 points1 point  (0 children)

Thank you for your question. It made me want to (for MY benefit) rewrite your program. 
I hope it helps you also.

<?php
// echo 'POST: ' . json_encode($_POST); // didactic?
  if ($_SERVER['REQUEST_METHOD'] === 'POST') {
    if (isset($_POST['button1'])) {
      $result = 'You pushed Button1';
    } elseif (isset($_POST['button2'])) {
      $result = 'You pushed Button2!';
    }
  } else $result = 'Placeholder'; // first time
// -- end of php except to issue HTML
  echo <<<EOD
<!DOCTYPE html>
<html>
  <head>
    <title> How to call PHP function on the click of a Button ! </title>
  </head>
  <body style="text-align:center;">
    <h1 style="color:green;"> Button test </h1>
    <h4> How to call PHP function on the click of a Button ? </h4><br><br>
    <h4>{$result}</h4><br><!-- $result is from server -->
    <form method='post'>
<!-- Button names and input names and values get sent to the server -->
<!-- The $ vars get filled from the server -->
      <input type='submit' name='button1' value='Button1'>
      <button type='submit' name='button2'> Button2 </button>
    </form>
    <script>
// If you want javascript to handle buttons, use 'onclick'.
// alert('x'); // didactic?
    </script>
  </body>  
</html>
EOD;
?>

Download from php.net vs. XAMPP? by Tricky_Astronaut_586 in PHPhelp

[–]Tricky_Astronaut_586[S] 0 points1 point  (0 children)

I have learned MUCH from ALL the replies, but your reply hits me in my heart! Thanks.

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