Talk:Collatz conjecture

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 Field: Number theory

Pls look at it...[edit]

This forum is for discussion of the Wikipedia article.

The appropriate place to discuss this is the Usenet group sci.math and I've transferred it there. You can reach it via Google Groups with subject Collatz Conjecture proof?



if i wanna add alot of info about the Collatz conjecture that are not on the article what i need to do? do i first need to post in talk and then it will be posted in the article or what?

i have alot of stuff i was working on that are not showen in the article — Preceding unsigned comment added by Isaac.mor (talkcontribs) 10:19, 22 February 2015 (UTC)

If by "stuff I was working on" you mean things you have worked out yourself, then that should not be added to the article: see WP:No original research. Anything you add should be supported by reliable sources. AndrewWTaylor (talk) 18:31, 22 February 2015 (UTC)
Or, to put it more constructively: first get your work published in the usual way in a peer-reviewed mathematics journal, and then come back to this talk page with the publication information; we might or might not add it here but in any case it will be published in the journal for the world to see. —David Eppstein (talk) 19:44, 22 February 2015 (UTC)

What exactly IS "the real extension of the Collatz map optimized by replacing 3n+1 by (3n+1)/2" ?[edit]

Picture caption:

"Cobweb plot of the orbit 10-5-8-4-2-1-2-1-2-1-etc. in the real extension of the Collatz map (optimized by replacing "3n + 1" with "(3n + 1)/2")"

Since there is nothing in the article that refers to a "real extension" of the Collatz map (no less an "optimized" one) — and the caption doesn't go to any trouble to explain what it might be trying to say — can we please remove this picture and its unhelpful caption? (Sorry, but I have zero patience for nonsense posing as editing.)Daqu (talk) 01:41, 12 March 2015 (UTC)

I'm having difficulty understanding, the real extension is right next to the picture in the section "Iterating on real or complex numbers", and it says, right in the caption, what the optimization is (despite being a rather trivial one).Phoenixia1177 (talk) 15:00, 31 March 2015 (UTC)
Ok, but why this particular real function among so many others? Do we have a source for this? Does this offer any actual insight into the Collatz conjecture? As it is, it looks like unsourced original research and as such should be removed. —David Eppstein (talk) 17:31, 31 March 2015 (UTC)
I have no idea why this particulair one, I didn't put it there nor argue that it is the right one. That said, it is an obvious one and I've seen it more than once, but there are others that have been employed, and of equal to greater use - moreover, it is trivial to add terms to the one in the article to get something more general. I don't really see the point in removing it as it is, essentially, a really obvious extension of the parity function, but I would downplay any emphasis that makes it sound like it is the "standard" or "right" real version of the Collatz function (but does serve as a reasonably simple example of an extension, basic enough that I don't think it is OR).Phoenixia1177 (talk) 01:41, 26 May 2015 (UTC)

Histogram is misleading[edit]

The histogram on stopping times is very misleading.

While "valid" as stated, it is inappropriate for the distribution.

The underlying distribution has no mean (like an exponential distribution).

In fact, the actual distribution can be ( with difficulty) computed.

The essential point is the number of integers with stopping time n is a non-decreasing function of n (which is easily shown without the need to a difficult computation).

At the very least, the histogram should be complimented with the actual distribution (say though the same domain).

This would not only be illuminating, but would be a nice illustration of some subtle, yet key points about distributions (i.e. histograms are only useful with distributions with means and "small" tails). — Preceding unsigned comment added by (talk) 15:59, 6 September 2015 (UTC)

You are certainly right in saying that the number of integers with stopping time n is a non-decreasing function of n, and the histogram clearly gives a very different impression, so I shall remove it. If you or anyone else can do put more accurate information about the distribution into the article, that will be very helpful. The editor who uses the pseudonym "JamesBWatson" (talk) 12:40, 22 March 2016 (UTC)
The number of all integers with stopping time n is equal to the number of nodes at the n-th level of the Collatz graph, which is approximately an, where 1 < a < 2, as expected from an "average" infinite tree whose nodes have one or two children.
Although this result may be interesting, it does not say anything about the expected stopping time of an integer chosen at random from a fixed interval. And that is the purpose of the removed histogram, which illustrates an important aspect of the Collatz sequence behavior. Petr Matas 19:01, 25 March 2016 (UTC)

Artistic visualizations[edit]

Note that on are some beautiful pictures generated from 3n+1 sequences, maybe some of them should be included in the article? — Preceding unsigned comment added by (talk) 10:26, 27 September 2015 (UTC)

Not clear[edit]

It is not clear to me why anyone wants to study this conjecture. Any other recursion could be used. — Preceding unsigned comment added by (talk) 14:42, 30 December 2015 (UTC)

Well, this is mathematics. We study it because it is there, and curious. Much of today's computing is based on mathematical research from the 50s that made no business sense whatsoever. --WiseWoman (talk) 12:30, 21 March 2016 (UTC)

This isn't a discussion forum about the Collatz conjecture or why people might or might not be interested. The topic of the talk page is to discuss the state of the article. From WP:TALK#USE:

Stay on topic: Talk pages are for discussing the article, not for general conversation about the article's subject (much less other subjects). Keep discussions focused on how to improve the article. If you want to discuss the subject of an article, you can do so at Wikipedia:Reference desk instead. Comments that are plainly irrelevant are subject to archival or removal. (talk) 21:15, 24 March 2016 (UTC)