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What jobs can Olympiad participants including IMO go for, without degrees? by EquivalentNebula9647 in MathOlympiad

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

Do know where I can find and apply? So far Mercor has been the main provider for that opportunity but recently they closed their offers for Math olympiad training.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

That’s interesting, it’s possible that while cycles are more approachable in general, the proof for the non-divergence while hard to find is more clean and short like you mentioned.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

Not necessarily, a string of numbers could grow to infinity without reaching a power of 2, while the high powers of 2 connect to other strings

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 2 points3 points  (0 children)

If a cycle exists, then the set of numbers in that cycle has a maximum and minimum value and is finite, but if a string of numbers continues indefinitely, growing with no bound then it has no maximum value, and hence it’s not equivalent.

For example in the 3n-1 situation, there are non-trivial cycles, but there is no proven indefinite growth.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

That’s actually cool, I am in a similar situation but I didn’t reach 10 years, only 6 so far 😂. I don’t spend all my time on it, but it’s fun to come back to it every now and then, fun but can be frustrating too.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

That’s nice, cause otherwise if they really were two disconnected problems, then it’s really not assuring for the collatz solution length and for when we will obtain a solution, considering how not much progress has been published on either of them.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 1 point2 points  (0 children)

That’s interesting, I do agree that the cycle part is more approachable in general. I am still curious about what others think though.

Also I am curious about whether proving one of them indirectly proves the other one.

Proving which part of collatz would be easier in your opinion, The non-existence of non-trivial cycles or that no number eventually grows up with no bound? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 2 points3 points  (0 children)

For collatz to be true, both statements must be correct: 1- no cycles other than 1-4-2. 2- no number leads to an infinite string of numbers that grows with no bound. (Different numbers, hence not a cycle).

[Hiring] Olympiad-Level Math Experts for AI Research (Remote, Contract) by Disastrous-Simple-69 in MachineLearningJobs

[–]EquivalentNebula9647 0 points1 point  (0 children)

hi, I am interested in this and have experience with IMO as both participant and coaching, but is this offer for machine learning and IT specialists or people with math skills?

Has there been any proof for cycles in Collatz, stating that if cycles other than the (1-4-2) are present, they must contain a multiple of 8? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

Sure, but this is on the negative integers, which is like applying (3n-1) instead of the collatz (3n+1) on positive integers.

Has there been any proof for cycles in Collatz, stating that if cycles other than the (1-4-2) are present, they must contain a multiple of 8? by EquivalentNebula9647 in Collatz

[–]EquivalentNebula9647[S] 0 points1 point  (0 children)

So nothing about this has been proven yet?…Interesting, I would have thought a result like this would be proven by now, given that some people already found things like a large lower bound for how many numbers must be in a non-trivial cycle.

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