Talk:198 (number)

Draft for number 198

Hello. I realized 198 does not have a wikipedia page yet. I knew it was a brazilian phone number, and I found some interesting mathematical properties of it after some researching. This is my first wikipedia article, and I want to submit it for review. However, I was wondering if my draft is correctly formatted according to the WikiProject guidelines. Natureader (talk) 06:53, 4 June 2023 (UTC)

Reviewer Note

I am attempting to accept the draft via a round-robin move. Robert McClenon (talk) 19:55, 5 June 2023 (UTC) @Theroadislong, Whpq, David Eppstein, and Natureader: - I think that I have completed the round-robin move and only left one accidental redirect and one redirect as the reslt of a race condition. Robert McClenon (talk) 20:14, 5 June 2023 (UTC)

What happened to the page that previously occupied the spot? That page was not just a simple redirect, the page history is required for attribution as material from it was merged into 190 (number). -- Whpq (talk) 00:27, 6 June 2023 (UTC)

Apparently McClenon buried its history at Draft:198 (number) (the history) after some confusing page moves. —David Eppstein (talk) 00:37, 6 June 2023 (UTC)

The draft of a title is a place where the history is sometimes buried. If you dig there, you may find things that should be left buried. Robert McClenon (talk) 06:04, 6 June 2023 (UTC)

AFC Comments from Draft

• Comment: I have never, in my life, heard of the property "being the sum of its digits concatenated twice" being called interesting, or seen a paper discussing that property. Anything tied to a particular base is almost always less interesting to the mathematical community overall, and this typifies that. In the absence of actual references, it's trivia. If people want to search the OEIS for all appearances of the number 198, well, the OEIS is right there to search. Like I said, I'm generally happier when articles can be saved instead of deleted, but this still doesn't seem like it actually informs anyone about, say, Diophantine equations. One should come away from a mathematics article feeling at least a little edified, rather than going, "Yeah, so, and what of it?" Does gathering together a few examples of a number appearing six or nine entries down an OEIS entry actually make an encyclopedia article? I'm yet to be convinced. XOR'easter (talk) 04:45, 5 June 2023 (UTC)

• Comment: Okay, I finally managed to learn how to make a comment. Obviously, I would like the article to be included, so I will try to address the questions brought up earlier. My apologies for the length.
  Before that, I would like to make it clear that I understand the previous article about 198 was deleted, and I understand we want to abide by notability guidelines. I also understand that having number articles that are "less notable" than this one (such as 195 and 203, in my honest opinion) is not basis for allowing the inclusion of 198. However, I think the properties I listed are interesting enough, and I justify their inclusion at the end of this comment.
  If these arguments don't suffice, I added a few other properties (2nd, 3rd, 6th, and last bullet points) that perhaps relate more to what David Eppstein has in mind. They are all "nice" sequences in OEIS, and 198 is among the first few terms.
  Here's why I think three of the listed properties are interesting:
  1) Not only is 198 = 11 + 99 + 88, but it's the only number with this property (being the sum of its digits concatenated twice). It's simple to verify, it's interesting, and it's the only number with this property. I honestly think this is more interesting than being a prime number very far down the list (sorry, XOR'easter). I don't think anyone would cite 197 as an example of a prime number. Still, I think it's a property that deserves to be in the 197 article. On the other hand, 198 is the only example that satisfies this concatenation property.
  2) I also believe the representation property is interesting enough. It is a neat example of Jacobi's four-square theorem and Lagrange's four-square theorem. There is depth to this property. Beyond that, the fact that it's the first one to have 10 representation is nice. I believe people get excited and think it's interesting when the number 10 is involved. Finally, although it's not one of the first elements in the sequence, the coordination sequence for hexagonal lattices is a "nice" OEIS sequence.
  3) Companion pell numbers are equal to half of the denominators in the sequence of rational approximations to sqrt(2). In this sequence, 198 is the 6th element. They are closely related to many interesting number sequences, such as Fibonacci and Lucas.
  Natureader (talk) 03:42, 5 June 2023 (UTC)

• Comment: As a headstrong inclusionist, I will not admit that you have me convinced and instead cite WP:IAR on the grounds that I find such a beautiful number as 198 not meeting notability guidelines deeply unsatisfying. Nonetheless, thank you both very much for having patience with regards to explaining policy to a less-experienced editor. :) Bass77_talkcontribs 00:00, 5 June 2023 (UTC)

• Comment: I !voted to delete in Wikipedia:Articles for deletion/198 (number), and while I'd be happier to see an article, I don't think the material presented here justifies one. Going from "197 is a prime number" to "198 is the only number equal to the sum of its digits concatenated twice" is like going off a cliff edge of significance. While we might not be able to say what numbers are "interesting" in a universal, objective sense, we can certainly outsource the question to our sources: what does the written documentation in reliable sources indicate about what mathematicians find interesting? (For example, we can look to whether the OEIS labels a sequence as "nice".) I don't see how that standard is met here. Moreover, I don't see why Wikipedia:WikiProject Numbers should force our hands here. The business about integers "Continuous [?] from −1 to 200" is just something that some guy said some day, based on a conversation where one other person agreed with them (and another disagreed). The AfD was pretty quiet, but it was better attended than that. XOR'easter (talk) 23:37, 4 June 2023 (UTC)

• Comment: 198 is the only integer that lies between 197 and 199. That doesn't make that an interesting property. The usual criterion I use is that it appears very early in the list of an OEIS property labeled as "nice", not true of your examples. An alternative criterion I have seen proposed is that it is one of the numbers mentioned as examples in an actual bluelinked Wikipedia article about the property. I think only the companion Pell numbers have a claim to that, and even they are dubious (not the main subject of the redirect for that title). We need multiple properties. "I do not know why" is an inadequate justification for something to be reasonable. If you want to initiate more AfDs on more number articles, go ahead. Most of our number articles are jammed full of unencyclopedic cruft, like bus lines in specific cities that happen to have a bus with that number. —David Eppstein (talk) 23:17, 4 June 2023 (UTC)

• Comment: User:David Eppstein: I think the trouble here is that there is no non-circular definition for "interesting" anywhere in the notability guidelines for numbers. Even if we ignore the inconsistency between the main page of WP:NUM and the project's notability guidelines WP:NNUM on -1 to 200, it doesn't change the fact that the first three statements under the mathematics section in this draft are true for only 198 or 198 is the smallest number for which they are true. I do not know why these are not sufficiently interesting when several other numbers in the range from 100 to 200 rely on statements which, in my subjective opinion, are similar in nature to and no more interesting than that of 198. Take 197 as an example; it has a very similar structure to this article, and one, not knowing which article was already in the mainspace, would have a great deal of trouble trying to guess which met the notability guidelines and which did not. Either 198 ought to be included or these other numbers should be deleted as well for sake of consistency. Bass77_talkcontribs 23:00, 4 June 2023 (UTC)

• Comment: That was added prior to the AfD for 198, so cannot take priority over that outcome. Also it's a bad blanket rule. If it's not notable, declaring it to be notable (even though really it isn't) doesn't help. —David Eppstein (talk) 21:42, 4 June 2023 (UTC)

• Comment: User:David Eppstein: The main page of WP:WikiProject Numbers explicitly states that all integers from -1 to 200 are notable enough to have their own articles, unconditionally of other guidelines. To my recollection this range holds 198, and the fact that this fact was completely overlooked at the previous AFD floors me. Best, Bass77_talkcontribs 20:39, 4 June 2023 (UTC)

• Comment: OK I am not an admin so can’t see the deleted version I understand it was a borderline case before. It appears to have at least three unrelated interesting mathematical properties but I have no strong feelings about it,I have no expertise in this area so happy for you to decline if you feel it correct to do so. Theroadislong (talk) 19:57, 4 June 2023 (UTC)

• Comment: User:Theroadislong: Have you compared Wikipedia:Articles for deletion/198 (number) and identified specific items that demonstrate notability above and beyond the items that were considered and rejected in that AfD? I see no such content in this draft. It is basically a duplicate of the bad crufty version that was deleted. It is packed with sourced claims, but none of them are interesting or unusual, of a type that would pass our criteria for notability of numbers. None of the sourced properties have any depth of coverage of the specific number 198, as would be required for WP:GNG notability. As such, it should not be accepted. —David Eppstein (talk) 19:26, 4 June 2023 (UTC)

• Comment: happy to accept, just waiting for the redirect to be deleted. Theroadislong (talk) 10:36, 4 June 2023 (UTC)

Does it matter whether it is true?

I removed this claim: "198 is the only number equal to the sum of its digits concatenated twice (198 = 11 + 99 + 88)." Never mind whether the "W-source" is "W-reliable", or who Erich Friedman is, he only claims that 198 = 11 + 99 + 88 which is True (not "W-true") by elementary arithmetic. There is no evidence for the stunningly insignificant claim that this is the only such number. Imaginatorium (talk) 06:38, 26 July 2023 (UTC)

Erich Friedman's GitHub is listed on the number notability guidelines as a good source (Wikipedia:Notability (numbers)). Also, the fact that it is the only such number is easily verifiable with a pocket calculator, which the WikiProject page says doesn't need a proof (Wikipedia:WikiProject Numbers). Any number with less than 3 digits is too small to have a chance at satisfying the property, any number with more than 3 digits is too large. You can use your calculator and simply check that 198 is the only one with such property. Natureader (talk) 02:27, 15 August 2023 (UTC)

The precise text from Github is: "198 = 11 + 99 + 88." This is true, and verifiable (immediately, in an obvious way) without a calculator. So the Github source is not even required. But the source does not even state the claimed property of being the only such number, and is thus of no use anyway. Verifying by exhaustive search is not really "elementary calculation", and anyway a simpler proof is easy... the claim is that for a, b, c, integers in the range [1, 9], then 100a+10b+c = 11a+11b+11c. (Though I question whether the wording in the article is really clear enough to make the meaning obvious...)

Rearrange both sides: 89a = b + 10c

Range for LHS is 89, 178, ...; range for RHS is 11..99

Only possible value is therefore 89, so a=1.

If b+10c = 89, only values are b=9, c=8. QED

For the claim to remain it needs valid support: either your arm-waving appeal to exhaustive search, or my four-line proof.

The Github article is plainly scraping the bucket, since its aim is to list "a distinctive fact" about every one of the natural numbers, and only gives up at 391. David Wells' "Dictionary of Curious and Interesting numbers" (Penguin) on the other hand gives up at 43 (if you count his entry for 39 as the "first uninteresting number". This seems to me a much better basis for deciding what might be W-notable.

I will remove the item again; please do not put it back without a *much* better argument. Imaginatorium (talk) 05:56, 15 August 2023 (UTC)