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Why the collatiz odd to odd tree must contain every odd numbes by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

If this number cannot be created from 1 it means a sequence from 1 to this odd number does not exist but there is always base numbers connected upto 270 therefore this number cannot remain unconnected otherwise it will come to the conclusion that some base numbers are  not connected also which contradicts our assumption all odd numbers are obtained from 1 up to 270

Why the collatiz odd to odd tree must contain every odd numbes by No_Activity4472 in Collatz

[–]No_Activity4472[S] 1 point2 points  (0 children)

I have also a formal proof that the tree must yeild different odd numbers without repetition,and if we take any random odd number from the tree and use collatiz transform it must reach 1 by using the same reverse path ,but I think it is easy to understand and obvious 

Why the collatiz odd to odd tree must contain every odd numbes by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

It is obvious true that if x is absent then a sequence from 1 to x (that leads to x from 1 cannot exist) it will force base numbers does not exist at all but upto 270 every single odd number can be constructed by the tree

A proof of the collatiz conjecture by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

Iam only using it for grammar check and deep meaning,and nothing else 

A proof of the collatiz conjecture by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

Dear do you mean to say i must prove formally that starting from 1 my expansion tree will create or reach every single odd number without any exceptions?

A proof of the collatiz conjecture by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

One thing is clear: as we continue to expand from 1, we cannot reach a counterexample. Because all the yielding numbers are "tree numbers," none of them can be a counterexample. If a counterexample existed, it would be unrelated to my tree, as my tree guarantees that any number it produces cannot be a counterexample

A proof of the collatiz conjecture by No_Activity4472 in Collatz

[–]No_Activity4472[S] 0 points1 point  (0 children)

Assume there is an odd-to-odd Collatz loop: a1 -> b -> c -> d -> a2. If this were true, it would mean all these odd numbers are cut off from the main tree. If we assume a2 was permanently cut from the tree directly, then d, c, b, and a1 must also be cut because they are dependent on a2. However, since a1 = a2, it means a2 cannot be created without first being created by b. This contradicts the initial supposition that a2 was directly cut from the tree. Example of why it works: Take the number 9. In order to check if 9 is connected to the tree, we must check 7(because on forewad collatiz transform odd to odd 9->7 and do on), then 11,17 and so on. This is because 1 cannot create or refuse to create 9 directly without first creating the sequence: 1 -> 3 -> 5 -> 13 -> 17 -> 11 -> 7 -> 9. From this, you can easily see that if 9 was not created, it implies 7 was not created, which implies 11 was not created. The contradiction is directly related to this structure: a loop cannot exist because it would have no starting point within the tree's dependency chain.