Talk:5

Wiki Education assignment: 4A Wikipedia Assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 12 February 2024 and 14 June 2024. Further details are available on the course page. Student editor(s): Not Fidel (article contribs). Peer reviewers: GiaTran21.

— Assignment last updated by Ahlluhn (talk) 00:57, 31 May 2024 (UTC)

Glyph development section

I removed material from the "Evolution of the Arabic digit" section yesterday for WP:OR concerns, but it was restored by User:Radlrb. First, thanks to Radlrb for providing the link to the source book at [1]; I can see from this that at least the basic graphic listing of the glyphs is sourced appropriately. However, I'm still concerned about the nature of the whole descriptive narrative made about them, which still strikes me as WP:OR, i.e. statements such as "The evolution of the modern Western digit for the numeral 5 cannot be traced back to the Indian system" (well, evidently it can, otherwise we wouldn't have this succession of glyphs). All the narrative about who "took" what from where and what were the defining graphical characteristics and innovations of each glyph at each stage is not taken from the source, but is some Wikipedian's highly speculative interpretation of Ifrah's graphics. The same goes for the similar passage in the 7 article I also removed, which is full of interpretative claims such as "to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear". Add to these problems, there's the embarrassing error of referring to things like "Nagari" or "Ghubar" as if they were peoples. They are not; they are writing styles – there's no such thing as "Ghubar Arabs", any more than there's "Cursive Italians" or "Minuscule Frenchmen" or "Gothic Germans". (As an aside, all these passages were first written by a highly problematic editor back in 2004, User:Numerao, who was banned shortly after for running a sockfarm, and they have sat here uncorrected ever since.) – Fut.Perf. ☼ 10:27, 29 May 2024 (UTC)

If you read into the narrative in the book, and other sources, it's basically how it is explained in the section, however with much more concise, and less casual language. There are those embarrassing errors that you mentioned, and that should be changed, however it's not too far off. Basically, the early Indian 5 looked more like a 4, and the Europeans eventually started using a 5 that looked like a 3 or 4 from the Arabs (mainly) rather than the 5 from the Indians (that looked like a 4 still, and might be the explanation for writing "cannot be traced back to the Indian system" directly, if we are talking about maintaining most of the same original form it had - * alas, yes, the root is Indian regardless. Radlrb (talk) 04:07, 31 May 2024 (UTC) *). Thank you for pointing out those very obvious errors, and yes, as it stands it does read somewhat like OR, however the underlying notions, I believe, were not intended to be OR, were rather just written very casually (and quickly, possibly). It should be re-written, still. Radlrb (talk) 17:16, 29 May 2024 (UTC)

I think, I was more interested in why this information was taken out of 5 and 7, when the sourced used is also used in other integer articles we have, for the evolution of the digit to the forms used today, so it seemed selective to me, but maybe you were not aware that this source was used for many of the first ten integer articles we have? (And zero too? I have not checked.) We should reference at least four good sources here, the WP articles mentioning the evolution of gliphs have sources we can refer to as well I believe, if need be. Recent sources on the matter would also be interesting to include (fresh). Radlrb (talk) 20:44, 29 May 2024 (UTC)

6

after 5 and before 7 (i should be at harvard) 185.85.57.38 (talk) 13:19, 5 June 2024 (UTC)

That information does not seem especially helpful, as I suggested in Wikipedia talk:WikiProject Numbers/Archive 8#Following and preceding Certes (talk) 13:49, 5 June 2024 (UTC)

Clean up this number

Forgot to provide a rationale in my revert due to a silly mistake, but here it is. Basically articles about numbers have been filled with pointless mathematically trivial WP:CRUFT for a while now (heck, there is even a case to say that things like its position in a mathematical sequence are effectively irrelevant) so that's my rationale. In addition, someone should probably look at the "Evolution of the Arabic digit" sections of these articles, as they also tend to have a lot of WP:OR Allan Nonymous (talk) 04:04, 7 August 2024 (UTC)

Going Through Number Facts Here

All right User:Radlrb let's talk about a few number facts here. The Collatz process is a deterministic process, which means that you can construct a directed graph of the orbits of those numbers, working backwards from 1. Naturally this means that all of the orbits, which all end at one, gradually must come together (i.e. branches must combine) until they all end up as part of one branch, otherwise, the orbits would not end at 1. Hence, the fact there is a point where there are 2 branches of the graph is, in fact, what you would expect, and not terribly special.

Your rationale for keeping the second fact (about Mersenne Primes) references perfect numbers? To my knowledge, they seem to have no connection to the fact removed, which is merely a series of tangential calculations that fall squarely under NOFFTOPIC. The actual fact removed was about Mersenne primes. Saying 31 is the 5th Mersenne prime is both NOFFTOPIC, and NROUTINE. Allan Nonymous (talk) 00:22, 15 August 2024 (UTC)

Regarding your first commentary on the Collatz sequence and the points I decided to keep at 5: I mentioned more or less clearly that what makes 5 special is that it is at the first branch-off, alongside 32; and as the OEIS:A006577 nice sequence states, one of only two numbers to require 5 steps (alongside 32). Secondly, not only is it of consequence in this sense, in the "3x - 1" version, it is one of only three known beginning/ending points (1, and 17 are the other two). That is worth mentioning, so much so that Guy wrote about it in Unsolved Problems in Number Theory (2004), as referenced. I also added a related property, that it is part of the set of natural numbers congruent 1 mod 4 that are proven to always return to one, using methods that rely on proving that these congruencies will always reduce to 1 under successive 3x+1 and n/2 operations on sets of the natural numbers (in the set for numbers congruent 1 mod 4, the first numbers with this congruency are 1, 5, 9, etc., where five is the first non-trivial member of this partial set of natural numbers proven to return to 1).

On the second commentary for Mersenne primes: This is a grave misunderstanding, Mersenne primes will have a form $2^{n}-1$ with prime exponents </math> only for a select $n$: 2,3,5,7,13,17,19,31,61,89107,127,... to name a few, meaning that this is not, whatsoever, ROUTINE. I did not see that this was what was removed, I had believed it was about perfect numbers, so my apologies for that! Radlrb (talk) 00:44, 15 August 2024 (UTC)

OEIS:A006577 is pretty clearly ROUTINE, NOTOEIS SEQUENCE. The mention in Unsolved Problems in Number Theory (2004), seems to be a rote listing of the whole sequence, which, need I not remind you, is very different from coverage of the specific number in question. Granted, I can't read the source, right no (will get to ut when I can), but there is no evidence here of the specific coverage needed.

Yes, Mersenne primes are non-routine, the n's for which Mersenne numbers are prime, is an edge case, but I feel it wold best be covered on the article on the prime itself, hence NOFFTOPIC for an article about the index. We shouldn't repeat a number fact on two separate articles, if at all possible. Allan Nonymous (talk) 00:57, 15 August 2024 (UTC)

Please read the sourcing accurately, where Guy includes the only possible cycles that return to 5 in 3x-1, where 5 is clearly mentioned (alongside 1, and 17). (Nothing else needs to be stated about it because that is all that is relevant about it. They do not need to say also explicitly, necessarily, "5 is the first member"; it goes without saying.) 5 was also shown as belonging to a partial set of natural numbers that will always return to 1 (those that are congruent 1 mod 4, with 5 the first such number greater than 1).

About Mersenne primes it is not NOFFTOPIC, it is clearly on topic because 5 is of consequence in generating the set of double Mersenne primes, and hence it is ONTOPIC, as a prime property arising from 5 as a prime number itself. It's as much on topic as it is for 5 being the second super-prime, where here we are talking about the family of "super-Mersenne primes", if you will. They are analogous in wording.

Opinions from other editors are welcomed. Radlrb (talk) 01:28, 15 August 2024 (UTC)

It took me a while to find the sourcing here, but I found it. No, the book does not provide nearly the kind of WP:DEPTH needed here. In fact, 5 is mentioned twice in this section, once as part of a tree including loads of numbers and once as an arbitrary example. So, no, this is not sufficient sourcing.

I am changing my mind as to whether Mersenne exponents are WP:NUM/ROUTINE. It's an edge case so, it could go both ways, so include is fine. Fortunately, this has been covered in other sections of the article, so we can remove the section in question, which does little more than cover it again and then go into WP:NUM/OFFTOPIC info. Allan Nonymous (talk) 19:04, 16 August 2024 (UTC)

I am sorry, you must not have looked at the right passage in the book by Richard K. Guy. See, on page 332, where it explicitly says:

If $3a_{n}+1$ is replaced by $3a_{n}-1$ (or if we allow negative integers then it seems likely that any sequence concludes with one of the cycles $\{1,2\}$, $\{5,14,7,20,10\}$ or $\{17,50,25,74,37,110,55,164,82,41,122,61,182,91,272,136,68,34\}$. This is true for all $a_{1}\leq 10^{8}.$

Here as is evident in the quote, the tree is actually small, of only four other numbers before returning to 5, and the other is larger with 18 numbers before returning to 17, and then there is the trivial example {1,2}.

As far as the Mersenne prime affirmation, thank you, I thought it was indeed reasonable to include. However, it has not been covered in other sections of the article, maybe you mean peripherally by mention of perfect numbers? Both should be merged, really. I will return the Collatz points in the article since I believe you did not adequately see, and therefore read, the passage I referenced; so maybe have another look. You also did not discuss the merits of the other sourcing which mentions 5 as part of the family of natural numbers congruent 1 mod 4, making it in so far as the first number greater than 0 in the set of the natural numbers {1, 5, 9, 13, ...} which have been shown to return back to 1, so I am unsure as to what you referred to in your edit history when you said "a fact that's not really backed up by its source", since I provided the source. Thank you for engaging. Radlrb (talk) 02:57, 17 August 2024 (UTC)

If you still disagree, and no one else joins in the discussion, then I will agree with removing it in good-faith, since there would be no consensus either way. Radlrb (talk) 04:45, 17 August 2024 (UTC)

That is, again, one, rather small mention of 5, bringing it up to 3. Not really enough to show depth, given the paragraph mentions several other numbers. If the paragraph does not include an in-prose mention of 5 in 6 whole pages, I doubt it has the sufficient WP:DEPTH Allan Nonymous (talk) 14:17, 17 August 2024 (UTC)

Disagree, that was enough coverage since there is nothing else that is known and can be said about it, which is why it is worth including on its own. But, we disagree and there is no one else chiming in, so it needs to be removed (to my sadness, because there is clearly something going on with 5 and 3x+-1), but I guess we're not interested in relaying that. Radlrb (talk) 15:05, 17 August 2024 (UTC)

No, if there is nothing else that is known and can be said about it, that means that we shouldn't be covering it. XOR'easter (talk) 21:16, 17 August 2024 (UTC)