/sci/ - Science & Math » Thread #12619687

26KiB, 350x202, c65bbc12-46cb-4fcf-901f-62392a05d4f3_collatz1.jpg

View Same Google iqdb SauceNAO

Anonymous Sat 23 Jan 21:50:19 2021 No.12619687 View Reply Original Report

Quoted By: >>12619698 >>12619715 >>12619748 >>12620201 >>12620686 >>12621037 >>12621123

>this one extremely simple concept stumps all of the Earth's greatest minds

Anonymous

Anonymous Sat 23 Jan 2021 21:51:25 No.12619695 Report

Quoted By:

If you are unfamiliar with the conjecture and what I mean by this.

Nobody can confirm or deny this conjecture as being true or not.

Anonymous

Anonymous Sat 23 Jan 2021 21:51:35 No.12619698 Report

Quoted By: >>12619708

>>12619687
not me though

Anonymous

Anonymous Sat 23 Jan 2021 21:53:30 No.12619708 Report

Quoted By: >>12619791

>>12619698
Is the conjecture true or false?

Anonymous

Anonymous Sat 23 Jan 2021 21:54:55 No.12619715 Report

Quoted By: >>12619781 >>12619797 >>12619865 >>12620985

>>12619687
Lmao I looked at the proof techniques some attempts use and the general class of iterated arithmetic problems are not solvable in any way. Nobody knows a fucking thing about how any of it works, even the best number theorists are just throwing every mathematical tool at the problem and seeing what sticks.

Particle Physicist

Particle Physicist Sat 23 Jan 2021 22:00:09 No.12619748 Report

Quoted By: >>12619770

>>12619687
It seems fairly intuitive to assert as true. This isn't a formal proof, but it should be good enough.
>Evens and Odds are equally distributed amongst the natural numbers.
>Half the time, dividing an even number by 2 will yield an even number
>Every time, multiplying by 3 and adding 1 to an odd number yield an even number
>In 2/3 of the cases, we return an even number after the operation
>Use recursive geometric series to find the average amount by which even operation reduces number (if even, reduce again)
>On average, odd operation triples value and adds 1
>If, on average, even operation reduces by more, then even wins
>infinite iterations, you hit 1.

Anonymous

Anonymous Sat 23 Jan 2021 22:06:20 No.12619770 Report

Quoted By:

>>12619748
>encounters another cycle around 56trillion-trillion-trillion
>so few number link to it, its effects on teh average go away towards infinity
>fuck'n el! shrekt again!

Anonymous

Anonymous Sat 23 Jan 2021 22:10:41 No.12619781 Report

Quoted By:

>>12619715
There's a lot of this stuff around number theory. I think we're looking at a gap in mathematics the size of, say, calculus, before it was invented, when people were forced to throw the kitchen sink at any geometry problems involving curves.

Anonymous

Anonymous Sat 23 Jan 2021 22:15:11 No.12619791 Report

Quoted By: >>12619823

>>12619708
yes

Anonymous

Anonymous Sat 23 Jan 2021 22:16:16 No.12619797 Report

Quoted By: >>12619852

>>12619715
It will generate a progressively larger set of numbers based on the first. As these numbers increase in value, they are more likely to have factors that are increasing powers of 2, and thus will be more likely to decrease by a larger proportion, keeping the generated sequence as a someone what low range of values. As these numbers are pseudorandonly generated, they will eventually generate a number that is a factor of 2, at which point the sequence will move directly to 1. What confuses people about this? It's just probabilities of generating numbers that are powers of 2 increasing as the value increases.

Anonymous

Anonymous Sat 23 Jan 2021 22:21:42 No.12619821 Report

Quoted By:

Number theory has a lot of intractable conjectures and theorems with relatively simple statements.

Anonymous

Anonymous Sat 23 Jan 2021 22:22:25 No.12619823 Report

Quoted By: >>12621099

>>12619791
So you can't determine whether the conjecture is true or false...

Anonymous

Anonymous Sat 23 Jan 2021 22:28:18 No.12619845 Report

Quoted By:

>(2n+1)3+1
>(2n)/2
i can see how you keep getting bigger until you reach a number that's the powers of 2 which gives one but how do i write this like a formal answer and continue from here?

Anonymous

Anonymous Sat 23 Jan 2021 22:29:55 No.12619852 Report

Quoted By:

>>12619797
>these numbers are pseudorandonly generated
asserting
>they will eventually generate a number that is a factor of 2
asserting
>It's just probabilities of generating numbers that are powers of 2 increasing as the value increases.
asserting

Get out of here, brainlet statistician.

Anonymous

Anonymous Sat 23 Jan 2021 22:30:06 No.12619853 Report

Quoted By: >>12620552

However the conjecture is solved, it will say something profoundly deep about dynamical systems. The 1-2 cycle is a discrete vortex, which is the same problem underlying turbulence in fluid dynamics.

Anonymous

Anonymous Sat 23 Jan 2021 22:34:00 No.12619865 Report

Quoted By: >>12620173

>>12619715
Collatz, Goldbach, twin primes, impossible.

Anonymous

Anonymous Sat 23 Jan 2021 23:56:59 No.12620173 Report

Quoted By: >>12620676

>>12619865
Goldbach and twin primes ask about primes, which is one family of number theory questions.
Collatz asks a question about dynamical systems over $\mathbb{Z}$ , which is closer to a question about the mandelbrot set or some other shit than anything about the primes. Dynamical systems in general are unsolvable without some kind of new paradigm we don't have yet, like how questions about polynomials weren't answerable before discovering group theory.

Anonymous

Anonymous Sun 24 Jan 2021 00:05:18 No.12620201 Report

Quoted By: >>12620538

>>12619687
Starting from 0 proves this to be false

Anonymous

Anonymous Sun 24 Jan 2021 01:38:57 No.12620538 Report

Quoted By:

>>12620201
Well it's a good thing the conjecture is over all numbers greater than 0 isn't it?

Anonymous

Anonymous Sun 24 Jan 2021 01:41:24 No.12620552 Report

Quoted By:

>>12619853
Interesting. I feel like there's a huge hole in math around this area (dynamic systems, primes) that will get solved by inventing a new way of looking at math, as radical a break perhaps as calculus or algebra.

Anonymous

Anonymous Sun 24 Jan 2021 02:08:16 No.12620676 Report

Quoted By:

>>12620173
Oh I see.

Anonymous

Anonymous Sun 24 Jan 2021 02:10:39 No.12620686 Report

Quoted By: >>12620866

>>12619687
Doesn't work for infinity.

Anonymous

Anonymous Sun 24 Jan 2021 03:05:33 No.12620866 Report

Quoted By: >>12620881

>>12620686
Infinity is not a number

Anonymous

Anonymous Sun 24 Jan 2021 03:11:23 No.12620881 Report

Quoted By:

>>12620866
It is under finale infinitism.
unless you don't accept the idea of number density.
which would cause a contradiction in well established beliefs such as differentiation and integration.
where h is the most dense number.

Anonymous

Anonymous Sun 24 Jan 2021 03:51:17 No.12620985 Report

Quoted By: >>12621024

>>12619715
Number theory is infamous for insanely hard problems that are solved trivially using some completely unrelated theory.
>general class of iterated arithmetic problems are not solvable in any way
source?

Anonymous

Anonymous Sun 24 Jan 2021 04:02:50 No.12621024 Report

Quoted By:

>>12620985
https://en.wikipedia.org/wiki/Collatz_conjecture#Undecidable_generalizations
the generalization is undecidable

Anonymous

Anonymous Sun 24 Jan 2021 04:04:59 No.12621029 Report

Quoted By:

Just as a heads-up to some of you, a lot of you can intuitively see that because it is changing to evens and odds and powers of two that it would naturally go down to one, but there are cases in alternate formulas where the function keeps looping.

Like it will go to one value and then repeat itself, and there is no actual proof yet surprisingly that demonstrates the Collatz Conjecture has to necessarily be true. It is technically possible it is false even, and that is why people are trying to solve it.

Anonymous

Anonymous Sun 24 Jan 2021 04:06:30 No.12621037 Report

Quoted By: >>12621109

>>12619687
What are some other number concepts that also simple and fun like this?

Anonymous

Anonymous Sun 24 Jan 2021 04:34:02 No.12621099 Report

Quoted By:

>>12619823
The proof is trivial, but it would not fit into the word count of a post here so it is left as an exercise to the reader.

Anonymous

Anonymous Sun 24 Jan 2021 04:39:03 No.12621109 Report

Quoted By: >>12621122 >>12621248

>>12621037
2 interesting ones I know:
1) Every even integer greater than 2 can be represented as the sum of 2 primes (oldest unsolved problem?).
2) No 3 positive integers a,b,c satisfy $a^n + b^n = c^n$ when $n > 2$

There's also the ABC conjecture which our god proved but I don't think that one is terribly simple.

Anonymous

View Same Google iqdb SauceNAO 1607960306204.png, 656KiB, 680x555

Anonymous Sun 24 Jan 2021 04:46:35 No.12621122 Report

Quoted By:

>>12621109
I just wanted to remind you that as of January 15 2021 /ourguy/ is safe
http://www.kurims.kyoto-u.ac.jp/~motizuki/anpi-kakunin-jouhou.html

Anonymous

Anonymous Sun 24 Jan 2021 04:46:42 No.12621123 Report

Quoted By: >>12621132

>>12619687
Let k = -2
Since k is even, divide by 2:
-1.
Since this is odd, multiply by 3 and add 1:
We get -3 + 1 = -2.
We have arrived at our starting point.
This is an infinite loop.
Therefore, the conjecture is false.
QED

Anonymous

Anonymous Sun 24 Jan 2021 04:52:06 No.12621132 Report

Quoted By: >>12621141

>>12621123
OP is a fag so he posted a shitty image, but the the question is only concerning positive integers.

Anonymous

Anonymous Sun 24 Jan 2021 04:56:24 No.12621141 Report

Quoted By: >>12621148 >>12621152

>>12621132
Kek. Yeah OP chose the worst possible pic.

Let me try proving the case for positive integers:
Let k be any positive integer.
The instructions say to perform operations on the previous term.
There exists no previous term.
The conjecture is not well defined, so it's false.
QED

Anonymous

Anonymous Sun 24 Jan 2021 04:58:18 No.12621148 Report

Quoted By:

>>12621141
Wait that would mean it is vacuously true

Anonymous

Anonymous Sun 24 Jan 2021 05:00:02 No.12621152 Report

Quoted By:

>>12621141
kek

Anonymous

View Same Google iqdb SauceNAO 0E7F1C0B-7DFC-4216-AEA0-4C5265BE (...).jpg, 25KiB, 682x449

Anonymous Sun 24 Jan 2021 05:50:35 No.12621248 Report

Quoted By:

>>12621109
Like a campfire story
>Every even integer greater than 2 can be represented as the sum of 2 primes... but there’s no proof for it
Aaaaah!

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches