How to know when the Collatz conjecture has been proved?
2022年1月24日 · Complete Proof of the Collatz Conjecture, Farzali Izadi (maybe this is Farzali Izadi's linkedin profile) Solution to Collatz's Conjecture, Jose William Porras; The Visual Pattern in the Collatz Conjecture and Proof of No Non-Trivial Cycles, Fabian S. Reid; Wikipedia states that the conjecture is not proved, while for example Porras' proof is ...
Status of the Nichols claim to proof of the Collatz conjecture ...
2022年1月30日 · This re-arrangement gives another (Collatz) tree which has the same pitfalls as the classical (Collatz) tree: It fails to show the presence of all natural numbers in the tree (it uses the same argument as the classical tree), it fails to show there are no cycles (several trees), it fails to show there are no infinite sequences.
Where is the flaw in this "proof" of the Collatz Conjecture?
2017年10月31日 · We now know a number can only violate the Collatz Conjecture if it's of the form N+1 = 32k - 1. At this point, a pattern is quickly emerging: First, a number could only violate the Collatz Conjecture if it was of the form N+1 = 4k - 1; Next, a number was shown that it could only violate the Collatz Conjecture if it was of the form N+1 = 8k - 1
solution verification - Criticism of proof attempt: Collatz …
2022年8月26日 · If you can find an m and p such that (3 m - 2 m)/(2 p - 3 m) = Integer, you will have disproven the non-existence of loops in the Collatz conjecture, beyond the trivial case, m = 1 and p = 2. The integer will be the value of the smallest odd element of a loop, and the loop will contain m odd elements, such that O 1 < O 2 < ...< O m-1 < O m .
What does proving the Collatz Conjecture entail?
From the get go: i'm not trying to prove the Collatz Conjecture where hundreds of smarter people have failed. I'm just curious. I'm wondering where one would have to start in proving the Collatz Conjecture. That is, based on the nature of the problem, what's the starting point for …
number theory - What is the importance of the Collatz conjecture ...
So, the Collatz conjecture seems to say that there is some sort of abstract quantity like 'energy' which cannot be arbitrarily increased by adding 1. That is, no matter where you start, and no matter where this weird prime-shuffling action of adding 1 takes you, eventually the act of pulling out 2s takes enough energy out of the system so that ...
discrete mathematics - Is this a proof of the Collatz Conjecture ...
2017年1月19日 · $\begingroup$ Sentences like "in this paper, we provide a self-consistent argument to support the validity of the Collatz conjecture" and "the existence of diverging trajectories can be however ruled out by invoking an argument of internal consistency" strongly set off my bullshit detector - they're usually a good sign that a "proof" is nothing more than a …
number theory - What progress has been made on the Collatz …
2022年1月12日 · As of the date of this post the conjecture has been confirmed to be true up to $$682 \times 2^{60}\left(\approx 2^{69.41}\right).$$ In terms of proving it Terence Tao published a paper titled "Almost all orbits of the Collatz map attain almost bounded values." "Almost all"! How exciting is that! But who knows, maybe we are still further than we ...
proof theory - If the Collatz Conjecture is unsolvable is it true ...
2017年6月1日 · Incidentally, the statements for which PA-unprovability implies truth are those which are equivalent in PA to a $\Pi^0_1$ sentence; it is not known whether the Collatz conjecture is equivalent over PA to a $\Pi^0_1$ sentence, so currently no way is known for turning a proof of the PA-undisprovability of Collatz into a proof of the Collatz ...
Probability and the Collatz Problem - Mathematics Stack Exchange
But we have checked for all numbers less than four and the Collatz function converges, so there is no number that will diverge. I know this is a very sketchy sketch of a “proof”. I just want to know what you think. If it is nonsense please say so. Edit: I also tried a different Collatz-style iterations, with $3x-1$ instead of $3x+1$. As far ...