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- Are there specific numbers for which the Collatz Conjecture is proven . . .
For all those infinite sequences the Collatz-conjecture is immediately proven - the Collatz-transformation (in its Syracuse-formulation) goes in reverse direction of the arrows, for instance 3 → 5 3 → 5 and then inside the row which contains the 5 5 left towards its head, which is 1 1 and which is thus the root of the whole doubly infinite
- How to know when the Collatz conjecture has been proved?
The Collatz conjecture has moreover a property that most conjectures like Goldbach or Riemann do not have If there is a diverging trajectory , we might not be able to prove that within ZFC It is not clear how we should decide in general whether a given sequence eventually terminates
- What is the importance of the Collatz conjecture?
The Collatz conjecture is the simplest open problem in mathematics You can explain it to all your non-mathematical friends, and even to small children who have just learned to divide by 2
- solution verification - Criticism of proof attempt: Collatz Conjecture . . .
Therefore the Collatz Conjecture is true Every number will inevitably transform down to 1 1 Sorry for the difficult to read LaTeX, kind of a new user, but feel free to criticize away about anything! And thanks all for everyone's help
- solution verification - Collatz Conjecture: Reasoning about the . . .
I've been thinking about the possibility of a divergent collatz sequence for the Collatz Conjecture In other words, the possibility that neither a trivial nor non-trivial cycle is ever reached I
- Newest collatz-conjecture Questions - Mathematics Stack Exchange
Sep 24, 2023 at 23:15 abstract-algebra collatz-conjecture Sep 4, 2023 at 10:08 sequences-and-series elementary-number-theory modular-arithmetic collatz-conjecture Sep 3, 2023 at 2:32
- Is the Collatz conjecture in - Mathematics Stack Exchange
Case 0: The Collatz conjecture is false because some Collatz sequence is periodic with a period other than 4, 2, 1 4, 2, 1 In that case, the Collatz conjecture is provably equivalent to 0 = 1 0 = 1 over any theory with enough power to encode and decode the witnessing sequence up to its first repetition (e g PA or I Σ1 Σ 1)
- Is this a possible part of the solution to the Collatz Conjecture
A disproof of Collatz is virtually hopeless : We know that nontrivial loops would be awfully long , so to find a nontrivial loop is virtually hopeless Even if we hit a start value leading to a divergent trajectory , we have no way to prove that this trajectory actually is diverging It could break down at very high levels and finally reach 1 1 So, the best hope is a proof of Collatz , but
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