#Collatz-like Conjecture

[math1089]

Exploring Collatz-Like Functions: The Power of 3n – 1

The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe. Karl Pearson Be careful! Do not attempt to solve this math problem – it’s very tempting, but it leads to never-ending cycles. Here’s how it works: Start with a positive integer. If it’s even, divide it…

[cheezyharu]

Prove:

3x + 1

3x = -1

=> x = -1/3

I'm not a math teacher, you know~? If anything, you should've ask that math teacher over at @redrawthecolorlessworld cause I am not taking my time to prove that! :>

[squareallworthy]

I love it when academics use "we" to refer to their entire discipline. Like "We have a new lower bound for the Collatz conjecture" or "We have some powerful new tools for genome analysis." Yes. You and your homies, where "homies" means a worldwide community of like-minded people going back hundreds, maybe thousands of years. Those are good homies to have.

[regexkind]

Solve the Collatz conjecture

Last night I saw the Supreme Fascist descending from The Throne to my home with a great sack, and when the sack was poured out a great torrent of integers came forth and hid themselves like mice in the corners of my house. As I watched I spied one of them going into the boarded-up vents, down into the crawlspace; I knew instinctively that this was one which, when the Collatz rule was applied, would stably loop somewhere high, high above the triple 1-2-4. But when I woke and checked down there there was just water. I need to fucking fix my vapor barrier, Max. I haven't got time for a fucking quest

[jadagul]

The other night, I proved the Collatz conjecture in a dream.

Well, more specifically, someone else came up with a proof of the Collatz conjecture, in my dream. And in my dream, I read the argument and figured out why it didn't work.

And like it wasn't a very good argument; it's exactly the sort of sloppy argument that people present when they think they've proven the Collatz conjecture.

But what I think is interesting about this is that I remember the argument. And I remember finding the flaw in the argument. And it really was a mostly-coherent argument, and that really was the flaw in the argument! That's much more sophisticated abstract reasoning than I thought we generally got in dreams.

[grungler]

idg why mathematicians go to such effort to prove obvious shit, just learned about Collatz conjecture and it being 'unsolved" and it seems so obviously true like why bother??

if every time its even the number is divided that shit has like 40% chance of stacking, but every time its odd it goes 3 times higher but adds a 1 so it cant combo, of course it'll eventually get to 1?? Does the P in PHD stand for preschool?

Like if youre having trouble with that maybe go back to proving 1+1=2 with your good will hunting ass

[kitscodingblog]

Welcome to my Coding Adventure!

So after a bunch of big changes in my life I decided to start coding and learning Python. For what reasons? I'm not sure, beyond the fact that I really like it. I also found out that its used a lot in Network Security (Ethical Hacking and all that) so I've been diving into that too.

I was reading something about keeping a blog to help keep a record of your own personal journey, and I figured its been a long time since i kept a blog, so why not start one for this?

So if you're interested, feel free to follow and keep up with me. I don't know how well I'll keep this up so here's hoping! I'm really enjoying it so far!

More under the cut (a lot more)

I started a few weeks ago (maybe longer, but for real-real like three weeks ago) after uplifting my whole life and moving up the East Coast. I've always wanted to learn to code, and I really enjoy working with computers, so this felt like a good time to give it a go.

I tried to code while I was in college, but it always made me feel really dumb and I never could get the hang of it. I wasn't the kind of person to push through the difficulties, and being surrounded by people who were so, so much better than me didn't help. I felt like I was way, way behind everyone and there was no way for me to catch up.

If I could tell my old self one thing, it's to just keep trying. We will actually start to get it, it just takes time.

I've been using a few books to help me, and like with most things I do, while following along I totally understand, but as soon as I'm left to my own devices, I suddenly don't remember anything. I was struggling to do basic problems, and I felt like I just wasn't grasping it. How can I do these problems when I don't know what I'm doing??

And after a few weeks of beating myself up, I finally felt like I got it with this last problem.

I had to make a code that would use the Collatz Conjecture. At first I had no idea what it wanted from me, but after looking up what that even meant I got it. The code ALMOST worked so I googled and found a few examples online, which helped em trouble shoot my code and I did it!

This was the first time I felt like I had a rough idea of not only what to do, but how to do it! It felt like taking my first steps forwards and I feel a lot better now. It made me feel like I can figure this out!

Anyway, we're gonna do more coding today. I might create a Virtual Machine on my laptop or desktop and try the network hacking thing out. It seems really cool and also terribly, scary haha!

I hope you enjoy my ramblings about coding! if not uhh. Sorry I guess?

[bubbloquacious]

7, 23, 45, 71 👀

From Real's Math Ask Meme.

7. What do you like about math?

The creativity :) I can make up whatever I want and play around with it, and no matter what way I try to solve a problem, to unkink a tangle in a structure, I know it will give the same answer.

1↋. Will P=NP? Why or why not?

It can't be true right? Like that would be crazy. One joke that people make occasionally is like what if the equivalence between P and NP problems is independent of the Zermelo-Frænkel axioms, like the continuum hypothesis, wouldn't that be wild. I'm not so sure this could happen! So there's this idea that the Collatz conjecture is not independent of ZFC, because if it is false, then it is provably false; if there is a number that ends up in a loop that does not contain zero, then trying every number in sequence will eventually get you a disproof.

The same thing doesn't quite work for P = NP, but it's similar. If it is true, then you can try every Turing machine in sequence, and see if it solves an NP-complete problem in polynomial time, so it is provably true. It's not exactly right, because you need to show that the machine solves the problem for any input size, which is not necessarily computable. But it seems like a proof like that might work, which is why I feel like P = NP is not independent of ZFC.

39. Are you a Formalist, Logicist, or Platonist?

Answered here.

5↋. 👀

👀

[rlyehtaxidermist]

assuming immortality, would you attempt tackling some of the big-name conjectures like Goldbach/Collatz/abc/Riemann early on? or would you leave them off and keep doing your own thing mostly

I'd definitely keep a designated notebook for them, but I wouldn't make a huge priority of it; though definitely more of an effort than I do now, even if just to be one of the people poised to understand it when there's a breakthrough, mine or no

[pulim-v]

If you could be famous, what would you wanna be famous for? The talent would be built in, like for example if you’d wanna be a singer, you’d just instantly become a good singer

If you were stuck on a deserted island and had to choose a person to be stuck with, who would you choose

I'd like being famous as a researcher tbh, possibly some hyper specific math achievement like solving the Collatz conjecture (either that or being an artist but we don't talk about that lmao)

Probably my irl best friend, it'd make me not go insane that quickly and we could probably work together decently well

[topoillogical]

One of my funner opinions is that one should try to solve any unsolved math problem that calls to them. I think it's good for the soul

Try and figure out where to start! How would one even go about proving twin primes? Or, just pick a place and start there. Say "suppose there are finitely many mersenne primes, and let M be the largest". What does that imply? Suppose there is a cycle in the Collatz conjecture. Can you say anything about it? No? Why?

Just like... let yourself think about it and poke at it and you'll get a better understanding of why it's so hard, and maybe learn something new, and maybe have a good time

[lunarsilkscreen]

The Collatz Conjecture

Is designed in a way to avoid prime numbers. All prime numbers are odd, except for 2. So when you add 1 you avoid all primes, and you divide by two, until you reach a prime, then multiply by 3 and add 1. This has the added benefit of avoiding breaking the number into a decimal.

A simpler proof would be to just add by one without multiplying by three.

You would have to prove that there are enough prime numbers in a sequence of 3x+1 in order to say that it's not true for every integer. So you would have to prove x starting on a prime would never ever not be prime in 3x+1.

And since the intention of 3x+1 is to eventually avoid all prime numbers, it's more than likely true.

[mathemon]

I do math for fun when I'm bored.

I find joy in the collatz conjecture.

I like taking two coprime numbers and finding their additive cycle (∀a∀b|b>a≥2∧(∄d|d≥2∧d||a∧d||b)->∀n|n≥(a-1)*(b-1),n=xa+yb where a,b,d and n are all positive integers and x and y are non-negative integers)

I did the pi day challenges.

I want to see what (0≤x≤4, x²-2x+1≤y≤2x+1, 2y-x-1≤z≤x+y) looks like.

I made it part of my Tumblr name.

(just don't ask me to do statistics.)

I didn't wanna derail the other post but I still wanna spread some love for my favourite subject...

Reblog if you've ever felt genuine joy or excitement from doing and/or thinking about math

[necarion]

It would be really funny to have a time machine and use it to introduce Pythagoras to the Collatz and Twin Primes conjectures. "I have made this remarkable discovery, but cannot prove it isn't false. A man of learning like yourself should make short work of this."

[i-iii-iii-vii]

every once i while i mention how i feel at home & twistor theoretically hugged & completely safe/well understood when i'm with my mutuals. today i'm welcoming baudelaire to our little group.

i'm asking myself if the ppl i call mutuals even though they died long ago, were writing (and, ohh, they were, jeezus, they were. iykyk.) about such a pathological psycho-emotional sociopathic behavior in great detail, describing every algorithm, using the common notation, sculpting peculiarly a morphology which is obviously recognizable (well, to me.)(and..who?) (ﾉﾟ⊿ﾟ)ﾉ (ʃᵕДᵕʅ) (ﾉ∧￩ ι) - does it mean they knew of the generalizability / the significance already? because that implies they had archieved a wholesome and robust knowledge of their own wreckage. which is supercool and can turn out very well as in hermann hesse's case.. but as most of em left the building with the head-in-the-oven-bus or the blow-my-head-off-plane(departure at quantum gate) or my fav nightmare*: completed their life→death transistion but nobody noticed as they kept on walkin' earth like christmas turkeys without filling (iff those turkeys usually came as zombies) and the funeral took place several decades later when existence(level n/a) got rid of the turkey's leftovers via the neighbor's dog whatsoever - i conclude: 1. from my frame of reference the knowledge of largest order of magnitude isn't actually of largest order of magnitude (c'mon it's obvious, there's not a lot missing, it just has to add up! -said everyone trying to prove the collatz conjecture, too). 2. no pain no gain but the pain load is exhaused, therefore continue at *⁽ᶠᵃᵛ ⁿⁱᵍʰᵗᵐᵃʳᵉ⁾ possibly correlating the fact that 3. must be ignored on all instances, as 3.'s statement is not very scientific as it implies the nonexistence of free will which is provenly false. 3. it's a pathological function. and weierstrass will be weierstrass. inevitably. even if the function knows where it started, that it's nowhere differentiable and that it shows continuity everywhere and even if it knows it is indeed true and it's fine that it exists and that it's actually super cool and wiggly and not at all the devil's work like gauss said.

wow how i hate the involment of emotion/sociology. really good for nothing╰(･◡･╰) destabilizes every integral ╰(°ㅂ°)╯ fine, so i'm doing that by parts again

(°∇°╬) 凸(°^°*)

as someone who exclusively writes non-fiction (code, preferably javascript/python/C++ and currently - because of a strong affection/enthusiasm/serious hyperfixation - it's mostly mathematics - of which i'm now an undergrad student (∩˃⌔˂∩)♡), maybe a little essayesk from time to time or even wandering the paths of leibnitzian metaphysics (C:\\vbox\leibnitzian metaphysics) - while always 3+1 dimensionally platonistically pure and way past the 140 character limit. but a good proof wouldn't write itself significantly shorter.. (have you read the one of gödel on formally undecidable propositions of principia mathematica & rel. systems?)(and have you read russell's on 1+1=2 ?). as i tend to translate/generalize mathematics to help me understand external human behavior as well as deconstructing the significance (disproving prev) of the immense emotional impact concerning the integrity of my own ol' machine, it could be summarized as: i write abstracts. still, definite non-fiction. so with absolutely no training in the field of novels and prose, i can only assume (though with a probability=the collatz conjecture beeing true) (like, almost surely ;)) the constructability of my conclusion by interconnecting the abstracts would return true or halt or loop indefinitely, if it would throw an illegal exception - well, definitely it would, but would it sigkill & kernel_panic or would it libunwind*? maybe we feel we must know but well, we might never. as a somewhat openly liberal david hilbert could have said.

and that's just a little excerpt of me, as i'm *walking each frame, looking for a place to stop.

oh and btw: p=np

look, you leave riemann drive here & now that's not far at all, it's actually on your way, you'll bump into it near the exit, right there on the left, maxwell's 2nd / collatz blvd.