# Zolar V

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1. ## Collatz Conjecture

I do recall the notation; unfortunately, I only briefly used the notation in a few of my classes. So I am familiar but probably not much past a familiarity. "I note that your paper is marked up nicely, which is good." - Thank you, i wrote it over the course of a few weeks as I learned how to use LaTex. I posted it here because I re-found the forum and remembered that this was a great place to have a good discussion. I believe a long time ago these forums were also integrated into LaTex or some other online math notation editor. I also don't really know where I would have posted this anyways. I did show my paper to a few math major friends of mine and we did have some discussion about it. They didn't seem to have the problems we are having here, so I wonder if I did some explanation to them verbally that I just entirely missed. "Are you saying that each of 3 and 5 eventually reduce to a power of 2 this way? Is that the idea?" - yes, every prime will eventually reduce to a power of 2. I am going to try to really define our function, or functions here so that it makes sense.
2. ## Hey guys im back!

Thank you! good to see old members are still active here!
3. ## Collatz Conjecture

I'm american, though the problem with my grammar is likely the product of not talking very much to anyone else.

7. ## Collatz Conjecture

As stated awkwardly: For any prime p > 2 the function G(p) = p + 1 (converges) to 2 after n iterations. So G(7) = 8 and 8 = 2^3. so each prime in 8 is 2. A better example i think: G(11) = 12 = 2*2*3 = (2*2 -1) *3 + 3 substep: G(3) = 4 = 2*2 So G(G(11)) = (2*2 -1) *3 + G(3) G(G(11)) = (2*2 -1) *3 + 2*2 The next step is to take out another prime and apply the function again (2*2 -1) *3 = (2*2 -1) + (2*2 -1) + (2*2 -1) or ((3-1)(2*2 -1)) + (2*2 -1) = ((3-1)(2*2 -1)) + 3 = 2*3 + 3 G(G(G(11)) = 2*3 + 3 + 2*2 = 2*3 + G(3) + 2*2 = 2*3 + 2*2 +2*2 = 2*3 + 2*2*2 you can then rewrite 2*3 as (2-1)*3 + 3 G(G(G(G(11))) = (2-1)*3 + 3 + 2*2*2 = (2-1)*3 + G(3) + 2*2*2 and of course (2-1)*3 = (1)*3 = 3 G(G(G(G(G(11)))) = 3 + 2*2 + 2*2*2 = G(3) + 2*2 + 2*2*2 = 2*2 + 2*2 + 2*2*2 so, 5 iterations cause G(11) to be a series of primes where each prime is 2. The purpose of G(p) = p + 1 is to reduce each prime within the composite number to 2. once we have our 2's then the application of n iterations of the second function H(x) = x/2 , results in 1. after n iterations of course. What this paper is trying to state is that G(p) = p + 1 is embedded in the odd function of the collatz conjecture. Since G(p) over some m iterations results in a 2^k number, it's clear that dividing by 2^k equals 1. thus the collatz conjecture always results in 1 after some m iterations.
8. ## Collatz Conjecture

That would be all from the first equation. the next part is to take the even equation from the collatz conjecture and apply it however many times it takes to reduce each 2 into a 1. The purpose of G(p) = p + 1 is to reduce each prime to 2.
9. ## Collatz Conjecture

You need to convert a non prime number into a composite of primes then extract a prime from that composite. p+1 is a composite number. p+1 = a*b*c*d*e.. where each of those are primes. What you need to do is then take (a*b*...*(d -1) ) *e + e E.G: http://www.wolframalpha.com/input/?i=(5*3*7)+%3D+(5*3+-1)*7+%2B+7 once you do that you can then utilize the function to reduce each prime E.G: G(5)= 5 +1 = 6 6 = 2*3 = (2-1)*3 +3 = 3 + 3 so 3+ 3 -> G(3+3) = G(3) + G(3) yes, x+1 is a composite number. you can then follow the rules of math to give you a expression that has a prime that you can use. any composite number can be rewritten as a product of primes. as such you can rewrite that expression of primes to be an even product of primes multiplied by a certain prime and added to that prime. E.G 486485 + 1 = 2*3*3*3*3*3*7*11*13 = (2*3^5*7*11-1)*13 + 13 Since you have a composite part and a prime part you can then apply the function on the prime part. Maybe you can see more of what I am trying to explain by taking a look at a few primes. G(p) = p + 1 where each prime in the composite number p+1 is less than p 7 -> 7+1 = 8 = 2*2*2 | 2,2,2 are < 7 11 -> 11+1 = 12 = 2*2*3 | 2,2,3 are <11 13 -> 13+1 = 14 = 2*7 | 2,7 are <13 17 -> 17+1 = 18 = 2*3*3 | 2,3,3 are < 17 19 -> 19+1 = 20 = 2*2*5 | 2,2,5 are <19 23- > 23+1 = 24 = 2*2*2*3 | 2,2,2,3 are < 23 ... and so on.
10. ## Collatz Conjecture

I edited it for -> instead of equals. to me "->" means a sort of action. G(p) = p + 1 is the function and G^n(p) = 2^n is the result of n iterations of the function. I tend to think in a very step oriented logical (if then) fashion. unfortunately I dont express myself very well.
11. ## Collatz Conjecture

Or differently stated: Consider a function f(x) = x + 1 where x is prime. then x+1 is a composite of primes where each individual prime is less than x. Suppose you applied f(x) to that resulting number for some m iterations. Then each resulting prime eventually tends to 2. That is to say the first iteration of f(x) produces a number whos primes are less than x, then each subsequent iteration produces a number who's primes are less than the first prime x and each subsequent prime that is plugged into the function. such that after a number of iterations the composite number is 2^m. of course after dividing 2^m by the even function m times that results in 1.
12. ## Collatz Conjecture

Thank you for your insight: Here is the prose version: Since the most important function within the collatz conjecture is F(x) = 3x + 1 , I really tried to understand what it was this function did to the problem. Two facts are present, any number is either prime or a composite of primes. Therefore I broke it down and looked at a different equation: G(y) = K + 1. For y prime. Notice the composite number K +1 is less than 2K, therefore all of the primes within the number are also less than K. Now since K + 1 is a composite number it can be rewritten as a multiplicative sets of primes. Moreso, you can reduce one set by 1 and extract a prime. E.G. 9 +1 = 10 = 2*5 → (2-1)5 + 5 Therefore you can extract a prime (E.G: 5) and plug it back into G(y). For each iteration you reduce the resulting composite number and after some M iteration you can reduce it to 2. Now given the original collatz function F(x) = 3x + 1 , you can rewrite this as F(x) = 2x + x+1 . Notice that we have an x+1 and that we can also rewrite any composite number in such a way as to extract a single prime to work with. Ergo F(x) = 2x + G(y). Since G(y) = K +1 for K prime and converges to 2 after M iterations. Then F(x) = 2x + G(y) → F(x) = 2 (x + 1) and again (x +1) is our G(y) so F(x) = 2(G(y)) → F(x) = 2*2 for some M,N iterations. Then of course you can apply the even collatz function and it converges naturally to 1. Side note: Any odd function of the form ax+1 also converges to 1 following the exact same logic, and the collatz odd function is just a case where a = 3. I also hope it’s well enough written that you can see my thoughts on it.
13. ## Collatz Conjecture

I would like you guys to take a serious look at the mathematics, instead of attacking the semantics. Is it really that difficult for you to comprehend what the paper is trying to state?
14. ## Collatz Conjecture

"That's utter nonsense. If you claim a proof of an open problem you can't make up all your own terminology." - precisely why I need to work with a true mathematician. G(p) = p + 1 -> G^n(p) = 2^n G^n(p) / 2^n = 1 What I was trying to say was that after n iterations, G(p) = 2+ 2+ 2.... = 2^m AND G(p) / 2^m = 1 Here is a simple online calculator that shows G^m (p) = 1 else multiply by 3 <- replace 3 with 1. https://www.dcode.fr/collatz-conjecture
15. ## Collatz Conjecture

yes typo. It should read 3*2*11 +11 . The point of the rewrite is to show that any integer can be rewritten such that it is a number + a prime. Of course the whole purpose is that when you have a number + a prime you can then use the prime reduction theorem upon the (+ prime) part. "Oh I see you're using the word "convergence" in a funny way." - yes, my abilities to write proofs are limited and inexperienced.
16. ## Collatz Conjecture

I meant to say that using the prime reduction theorem, the odd collatz function can be rewritten such that it is a 2^m number and thus divided by the even function m times results in 1. What do you mean limiting? I didn't limit the collatz conjecture by any means. "ps -- Line 41 is wrong. 99 does not equal 33. " correct, the line should read 3 * 2 *11 + 11
17. ## Collatz Conjecture

Well here, let me just post my pdf. Im quite serious about my proof. Rip it to pieces and tell me im an idiot please. Draft2.pdf
18. ## Collatz Conjecture

Is anyone here interested in the Collatz Conjecture? If so I believe I have the solution, seriously, and I need to work with someone who knows how to write a formal proof better than I. There are some errors in my proof, but the underlying principle is right. I only have my minors in mathematics, so my proof writing skills are subpar.
19. ## Force exerted by a magnet

Ahh, i remember this experiment and post! Forgive my inability to accomplish the experiment in question, I was preoccupied with serving in the air force. I picked an exponential function because at a 0 distance there would be a near maximum repelling force exerted, and at some distance (r) there would be a slight or nil force exerted. After (r) the rest of the distances would also have a very small force, whereas between 0 and (r) the forces would get a good bit stronger.
20. ## Hey guys im back!

After a long hiatus, nearly 7 years, I have returned. I went and joined the air force, got a bachelors of science, a minors in math and a minors in bio; and currently work in IT/ software engineering. Any of the old members still active?
21. ## Force exerted by a magnet

i don't seem to be able to stress this enough, I cant do it. it is a simple experiment, and im sure that the people who read this forum are likely to have access to/ or the supplies to accomplish it.
22. ## Force exerted by a magnet

Like i said, i don't have the equipment anymore. Right now performing the experiment by myself just isn't feasible. I picked exponential (in my initial hypothesis), Subsequently the data i collected even though it was jittery still supported this hypothesis.
23. ## Force exerted by a magnet

Hey fellas, I know its been a freaking long while since i posted or visited here last. But i was remembering an old experiment i did back in high school that i couldn't do right. I know that the data i was supposed to see was going to be a positive exponential increase. But my data was too jittery, mostly due to poor experiment setup and execution. Ok, this is what i was trying to find: If you have 2 permanent magnets ( i used 2 Neodymium barrel type magnets. 1 In Dia, 2 In height) How much force is one magnet being pushed away from the second magnet. My hypothesis: As the second magnet gets closer, the first magnet will be pushing away harder. Scaling exponentially, until there is no more space left between the two magnets. As distance between the two magnets decreases the force exerted by the first magnet to move away from the second one increases. My experiment design wasn't all that great as i had to basically jerryrig all of the devices together for unintended purposes. I used a grooved aluminum yardstick, (grove fit magnets pretty well and easily slid) and there was this electronic force scale that im pretty sure i had to turn on its side and attach to one end of the yard stick. Though, after calibrating, the only real issue was that i used my hand to slowly move the second magnet close. Several attempts were thwarted by jittery hand movements, and some were thwarted by the one magnet being pushed up instead of back. I set one magnet on the rail with the backside touching the force scale, while i placed the other magnet on the rail away from the first. i grasped the second magnet and slid it closer to the 1st. + = magnet - = Rail [ = force scale [+------------+ i moved the second magnet closer: [+----+ and so on. Also note, i used like sides as to repel one another. SO: now on to you guys. IF you would be so kind as to gather the data i was looking for. I don't have any of the equipment necessary, nor the magents either. I would really like it if you would also test several different sizes of magnets too. E.G: 1cm Diameter, 2cm long: 3cm diameter, 4cm long: 5cm diameter, 5cm long: 2cm diameter, 4cm long: 4cm diameter, 5cm long: 6cm diameter, 6cm long: 3cm diameter, 6cm long: 5cm diameter, 6cm long: 7cm diameter, 7cm long:

dix and psy

25. ## Zolar V

what is with all the freakin spam?

1. Software bug allows updates from banned users to appear. It's been reported. I'm deleting them manually, so it only happens intermittently.

2. FYI-The primary offender's account has been terminated with extreme prejudice. That should solve the immediate problem.

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