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gonnzo
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Message 12446 - Posted: 3 Jun 2011, 20:13:47 UTC

"The Collatz conjecture was proposed by Lothar Collatz in 1937. It is also known as the "3n + 1 problem" because of its deceptively-simple definition.

Now mathematician Gerhard Opfer of the University of Hamburg, who was a student of Collatz, says he has proved the conjecture true."

http://www.newscientist.com/blogs/shortsharpscience/2011/06/simple-number-puzzle-possibly.html?DCMP=OTC-rss&nsref=online-news

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Message 12447 - Posted: 4 Jun 2011, 2:43:40 UTC
Last modified: 4 Jun 2011, 2:45:58 UTC

Well, its not been verified yet, thats `our` job so keep on crunching :¬)

This has been verified for numbers up to 5.76 x 10^18 (nearly 6 billion billion), but without a proper mathematical proof there is always the possibility that an incredibly large number could violate Collatz's rule.

Opfer claims to have achieved this proof, which is set out in a paper on the University of Hamburg's preprint server - but the result has yet to be peer-reviewed and could prove incorrect. The paper has been submitted to the journal Mathematics of Computation for review.

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Message 12450 - Posted: 4 Jun 2011, 13:30:19 UTC

I wonder if Herr Opfer happens to mention (or is aware of) this project. The higher and higher we step, the more likely it is there will be a number so large it somehow breaks the pattern, at which point one could look at the construction of the number and possibly derive a pattern by which one could prove the conjecture false. Of course the converse is more likely at this point, given we are in a ridiculously high range right now.

Still...
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Message 12454 - Posted: 5 Jun 2011, 17:17:10 UTC - in response to Message 12447.
Last modified: 5 Jun 2011, 17:20:36 UTC

Well, its not been verified yet, thats `our` job so keep on crunching :¬)


Why do you say that this demonstration is not valid?

edit: just found someone else claiming the proof is incomplete

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Message 12455 - Posted: 5 Jun 2011, 19:43:31 UTC - in response to Message 12454.

More debunking here.

http://mathlesstraveled.com/2011/06/04/the-collatz-conjecture-is-safe-for-now/

Still crunching.

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Message 12458 - Posted: 5 Jun 2011, 23:25:03 UTC - in response to Message 12455.

Well, its not been verified yet, thats `our` job so keep on crunching :¬)


If the collatz conjecture would be true, we would never proof it with brute-force. The other case would be possible for "small" numbers.

Doesn't forget that this project is for developing for cuda programms for the boinc infrastructure. The developer choose a simply programmable problem for their programm to extend their knowledge in this area.

There are a lot of gpu project, which are helpfull for mankind, like Folding@Home, GPU-Grid.

See http://www.rechenkraft.net/wiki/index.php?title=Projekt%C3%BCbersicht/en

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Message 13586 - Posted: 3 Mar 2012, 18:58:24 UTC

So, has anyone stopped to consider that, with infinite numbers fueling the algorithm, the algorithm has no choice but to reach 1 at some point? Even if you flipped a coin an infinite number of times, the percentage of heads vs. tails would most likely reach 1% of one or the other eventually. Bearing that in mind, it becomes quantum mathematics because it can not be proven true or false due to infinite possibilities and variables. We assume that anything that can happen will happen in an infinite environment.
So, perhaps your proof is the infinite environment in which your algorithm takes place?

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Message 13588 - Posted: 3 Mar 2012, 21:16:43 UTC

We work with what we have got,
And if someone comes along later and says `you got that bit wrong and can prove it, and why`
Then `we` will just have to do it all again,
If a problem is not investigated, we learn nothing,
Any research is improved with time and experience, its part of the fun.

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Message 13591 - Posted: 4 Mar 2012, 11:55:06 UTC - in response to Message 13586.

So, has anyone stopped to consider that, with infinite numbers fueling the algorithm, the algorithm has no choice but to reach 1 at some point? Even if you flipped a coin an infinite number of times, the percentage of heads vs. tails would most likely reach 1% of one or the other eventually. Bearing that in mind, it becomes quantum mathematics because it can not be proven true or false due to infinite possibilities and variables. We assume that anything that can happen will happen in an infinite environment.
So, perhaps your proof is the infinite environment in which your algorithm takes place?


Being 'logical' has never been accepted as Scientific Proof, in the early ages the World was flat and you would fall off of it if you sailed too far, the 'proof' was all the ships that never came back, therefore it was 'logical'. After a few people said BS and went out and came back with stuff nobody had ever seen or even heard of before it was 'proven' to be round. There was MUCH more to it than that OF COURSE, but you get the idea.

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Message 13699 - Posted: 30 Mar 2012, 7:58:13 UTC - in response to Message 13591.

So the question is, how do we prove something true or false when there are infinite numbers to test? In this way, the flat world was "good enough." Are we taking that approach to this algorithm as well?

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Message 13704 - Posted: 30 Mar 2012, 16:56:34 UTC - in response to Message 13591.
Last modified: 30 Mar 2012, 17:33:56 UTC

Look, here's the simple proof.
2=4/2
4=8/2
8=16/2
16=32/2
32=64/2
64=128/2
128=256/2
256=512/2
512=1024/2
1024=2048/2
etc. to infinity
Now, taking that into account, all that is required is a point where an odd number*3+1 intersects with the above statements of 2^x. Given that there are infinite chances for this to occur and that only whole numbers are used, intersection is eventual.
Understand how my infinity theory works now? When you multiply by infinity, the statement becomes both true and false at the same time depending upon the precise point that you're at. For example, if this equation were multiplied by pi, it would be false. However, multiplying it by a simple 1 makes it true.
Knowing that infinity is both a whole number and a partial number as well as an imaginary number, our goal is defined to not show that any whole number can be used to reach 1 at infinity, but that any whole number can be used to reach 1 period. And it's a simple equation as well. Just look for where the points intersect and plot them. Think more along the lines of x and y.
2^x and odd(y)*3+1 You'll find that these intersects can be found at various points approaching infinity.
Cool?

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Message 13706 - Posted: 31 Mar 2012, 10:28:36 UTC - in response to Message 13704.

Look, here's the simple proof.
2=4/2
4=8/2
8=16/2
16=32/2
32=64/2
64=128/2
128=256/2
256=512/2
512=1024/2
1024=2048/2
etc. to infinity
Now, taking that into account, all that is required is a point where an odd number*3+1 intersects with the above statements of 2^x. Given that there are infinite chances for this to occur and that only whole numbers are used, intersection is eventual.
Understand how my infinity theory works now? When you multiply by infinity, the statement becomes both true and false at the same time depending upon the precise point that you're at. For example, if this equation were multiplied by pi, it would be false. However, multiplying it by a simple 1 makes it true.
Knowing that infinity is both a whole number and a partial number as well as an imaginary number, our goal is defined to not show that any whole number can be used to reach 1 at infinity, but that any whole number can be used to reach 1 period. And it's a simple equation as well. Just look for where the points intersect and plot them. Think more along the lines of x and y.
2^x and odd(y)*3+1 You'll find that these intersects can be found at various points approaching infinity.
Cool?


Maybe you should email Dr. Opfer.

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Message 13724 - Posted: 2 Apr 2012, 17:49:53 UTC - in response to Message 13699.

So the question is, how do we prove something true or false when there are infinite numbers to test? In this way, the flat world was "good enough." Are we taking that approach to this algorithm as well?


Proving it true would require checking numbers to infinity. However, proving it false requires finding only one number that becomes a loop that repeats every N cycles.

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Message 13818 - Posted: 20 Apr 2012, 9:59:48 UTC

The Polya conjecture was true until 906,150,257, Mertens conjecture still has no known counter proof value, but it is known that there is some massive number that does disproove it, Skewes number is not proven but lies between 1.53x10^1,165 and 1.65×10^1,165.

Big numbers like that may disprove Collatz eventually, but it will take time.
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