Odd and Even equation

cshum00

I am sorry about it. I mean it like it loops with always repeat the same values.

For example:

1 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> 4 -> 2 -> 1 -> ......

matt grime

There are no known non-trivial (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?).

cshum00

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.

matt grime

no. google it. approximately it means 'a proposition cannot be deduced from the axioms of arithmetic, and nor can its negation'



I have no idea what you mean by that.

I didn't say that it (the 3n+1 conjecture) was undecidable, I said Conway (I think) found similar iterations that were undecidable. And bear in mind what 'undecidable' really means.



It is impossible to write out 'every' possible series of iterations since there are infintely many of them.

you should at least decide what it is you're trying to do - i presumed it was to answer the 3n+1 conjecture. Then do some examples to give an idea of what is going on as necessary. Proofs tend not to be done by example though. (Though some may be reduced to checking finitely many cases).

cshum00

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 re-read 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.

You said that 1 is 'non-trivial' which that is why i said that it is true that 1 doesn't decide everything but it is one clue that i have.

matt grime

I am not shutting you down, but as this thread has progressed, it has become clear that you are not familiar with the 3n+1 conjecture. The conjecture has turned out to be satsified for every starting value that people have tried (and thus it is unlikely that you will ever find any starting value that does anything other than eventually reach 1 and enter the trivial loop).

It is a conjecture that it alway hits 1. No one has been able to prove it or disprove it, but many have spent years trying. I am trying to make you aware of that.

again, I am not telling you not to do this. If you want, go ahead. My belief is that you would learn more if you investigated other things. Possibly including things that others have not thought of. As it is all you seem to be doing is just iterating things and either hitting 1 or going beyond the capability of your computer to do integer arithmetic. This is precisely what you could have predicted without doing any work by meta-reasoning.

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.

this has nothing to do with randomness. If you attempt to prove a problem in a model that is undecidable you will never succeed. Nor can you succeed in showing its negation. If tou could show that the 3n+1 conjecture is undecidable that would be important.


I said that non-trivial intermediate loops should be those that do not contain 1 in them. The existence, or non-existence of them, is what the conjecture is about.

cshum00

I already explained some time ago that it is new to me and i wanted to play with it until i get bored about it. As i said then why don't you tell me what you know so that i don't have to make redundant or meaningless search and so that i can progress faster and so that i know when to give up.

Well that's good thing to know that it always hist 1 but then check it with negative numbers then you will see that it never hit 1.

I am thankful for your concerns but once in a while everyone have a hobby. Some watch tv others read books, i am just making a research and learning new things on the way.

Ok, rather that just telling me that it is wrong, why don't you explain the word to me with simple words and examples so that i can understand it better? It is not that i didn't ask you to explain it.

Well, then negative numbers would be example of it. And from wikipedia: "n mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic." So like you said, 1 is likely to be true but since it is a value from the infinite sets. I can't prove with with 1 but like i said that your statement of it being trivial is 'True'. I didn't deny it.

matt grime

The 3n+1 conjecture is about strictly *positive* integers - the (non-zero, 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.

cshum00

Right then it means that my research haven't been pointless at all because i learned about how the conjecture might works in negative numbers.

matt grime

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

cshum00

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.

matt grime

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?

cshum00

Thanks for the info.