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Odd and Even equationby cshum00
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#19
Mar1607, 03:03 PM

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There are no known nontrivial (i.e. without a 1 in them) intermediate loops. That's the whole point of the problem.
You have found out what the proper statement of the 'hard' conjecture is, right? Given the operation above, it is conjectured that every possible starting (positive at least) integer reaches 1 eventually. This is a *very hard* conjecture, and has been extensively investigated, and verified for many many starting values. There are similar problems which are known to be undecidable (do you know what the formal definition of undecidable is?). 


#20
Mar1607, 03:21 PM

P: 213

It is somehow related with randomness. I know that 1 as part of the intermediate loop because i picked the number but if it where random, there is not a general rule that can make it work the way it does, right? Is that what you mean by undecidable?
You can always tell me your definition of undecidable so that i make sure i understand. True that 1 won't define everything but this is a clue for the many possible patterns in the infinite set of numbers. Besides, even though the problem is undecidable, this one is bound to a few restrictions which is odd, even and the two equations (3x+1) and (x/2). By detailing out every possible pattern is one way to begin a research. Unless you are telling me that i should tackle it without any aims or i should be a genius that is able to see through it instantly. Edit: Although the statements are hard conjectures they are the ones that i can use at the moment so that i can progress. I am putting them in here in case anyone is interested in doing the problem too. Anything else, If the statements are wrong then tell me so that i can correct it. 


#21
Mar1607, 03:34 PM

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#22
Mar1607, 03:51 PM

P: 213

I know that i am doing proof by exhaustion which is not a smart way to do so because it will take me a infinite time to be able to deal with the infinite set of numbers. But as i said it is the beginning.
Rather than shutting me down, why don't you share what you know about it since you seem to know, so that it helps. I feel like i am being in a court defending my rights to start a research. If you say that there is no answer then prove it. Not all the problems are solved as they come, mathematicians always tackled their problem because there wasn't a known solution by that time. If you are telling me that it is a waste of time, the time i have i am the one to decide what to do with it. You might not be shutting me down intentionally but that is how it looks like if you don't believe me reread all your previous posts. I googled the word 'undecidable' and i wrote what i understood, that is why i asked you to explain it to me in case i am wrong. Or is it that my interpretation is not clear or i am using a different mentality since i am applying to the problem. Edit: from wikipedia: " * A decision problem is called (recursively) undecidable if no algorithm can decide it, such as for Turing's halting problem; see also under Decidable. * "Undecidable" is sometimes used as a synonym of "independent", where a formula in mathematical logic is independent of a logical theory if neither that formula nor its negation can be proved within the theory." I can't prove a theory with values or that there is no rule that can decide the values that i am assigning to it. But why is there such term? Isn't like i said that the numbers in reality are random and not assigned by me so that it has to do with randomness. 


#23
Mar1607, 04:03 PM

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You are completely free to spend as much time on this as you wish just iterating things. However, you should be aware of what has preceded you. 


#24
Mar1607, 04:15 PM

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#25
Mar1607, 04:20 PM

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The 3n+1 conjecture is about strictly *positive* integers  the (nonzero, just in case) natural numbers. One of the first things you do in research is search for what has been done.
There is plenty of writing out there about this conjecture, related conjectures, and undecidability. All written by experts, and my field does not overlap any of the areas involved. You're better off with them. I'm not sure what more I can do other than say 'undecidability is not about randomness'. It is sort of like saying 'the colour green has nothing to do with the smell of bread'. I don't know that I have any simple examples. 


#26
Mar1607, 04:22 PM

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#27
Mar1607, 04:26 PM

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The conjecture isn't about negative numbers.....



#28
Mar1607, 04:28 PM

P: 213

It is not but it does not harm to play with negative numbers too. I might learn some patterns form the negative numbers which can or cannot be applied to positive numbers. And so i might learn why it does and why it does not.



#29
Mar1607, 04:29 PM

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http://en.wikipedia.org/wiki/Collatz_conjecture
there are some things you'll find interesting perhaps you'll find a 6th loop for all integers? 


#30
Mar1607, 04:31 PM

P: 213

Thanks for the info.



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