Talk:convergent sequence

RFD discussion: May–July 2022

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convergent sequence

SOP. —Svārtava (t/u) • 09:05, 21 May 2022 (UTC)

Note that we also have convergent series. It can be argued (and I would agree) that this is equally SOP, since in mathematical parlance one says that a series “is convergent”^[1] or “converges” (or not);^[2] however, this is not fully covered by the current definitions of the mathematical senses of convergent and converge, whose formulations only cover the convergence of sequences. Then, there is also the entry divergent series. (We do not have divergent sequence, although this is also used.^[3][4][5])  --Lambiam 07:26, 22 May 2022 (UTC)

Delete. I think I’ve filled all missing bits.  --Lambiam 12:33, 31 May 2022 (UTC)

Ehh, I don't know. There are many technically SOP adj.+noun maths terms out there on Wiktionary (conformal mapping, convex set, ...) but they may be worth keeping because, one, there is usually only a very limited set of terms that the adjective can apply to, and two, because the semantic relations correspond to mathematical relations: abelian group being a hyponym of group corresponds to Ab being a subcategory of Grp. — Fytcha〈 T | L | C 〉 23:21, 4 June 2022 (UTC)

Given the relative sparsity of such collocations of some term of art in some field plus one of a very limited number of terms from that field to which the term may be applied, their inclusion may seem rather harmless, and so one might consider allowing this as a sanctioned exception to the CFI as they stand. However, note that abelian group is perfectly covered by abelian (“having a commutative defining operation”) +‎ group (“a set with an associative binary operation ...”), and including this raises the issue why we then don’t have abelian subgroup, perfectly attestable,^[6][7][8] or abelian ring,^[9][10][11] and so on. Next to convergent sequences and convergent series, there are also convergent integral^[12][13][14], convergent summation,^[15][16][17] and so on. Furthermore, I’m wary of inclusion creep making the criteria more and more fuzzy. These technical collocations do not appear to pass any of the current survival tests, so, if accepted, they should be added as an exception in some form or another.  --Lambiam 12:50, 6 June 2022 (UTC)

Weak keep. I will need to think more about how to hammer out a clear-cut test in the future but the conjunction of 1) being a technical collocation, a technical term so to say, 2) having really useful nyms (as described above) and 3) being pretty restricted in terms of productiveness (i.e. allowing far fewer combinations than red + noun whose referent can have a color) does it for me. Pinging also @Pingku, Solomonfromfinland, Surjection as three contributors who I've seen work on mathematical articles in the past to also weigh in on this. — Fytcha〈 T | L | C 〉 12:38, 4 July 2022 (UTC)

Weak keep. Thanks Fytcha. Firstly, formally speaking, the concept of convergence only applies to sequences, so it's not obvious which of convergent and convergent sequence is the more basic concept. (A series, for example, is regarded as a sequence of partial sums.) That said, mathematicians like to generalise concepts, and the most natural path might be to use the term convergent for things whose connection to a sequence is not immediately obvious.

Secondly, another nym: convergent sequence is a synonym of Cauchy sequence. Note that the definition of Cauchy sequence deliberately avoids the concept of limit. This is because the limit is not necessarily a member of the set that the sequence elements are assumed to belong to. For example, the limit of a sequence of rational numbers is, in general, a real number. By eschewing limits, the definition reinforces the notion that convergence is a property of sequences.

As an aside, I note that our definition of converge currently refers to a limit, and thus is technically deficient.— Pingku^dimmi 08:56, 5 July 2022 (UTC)

• Keep as it is an idiom, a very common combination. It has a great deal more interest to mathematicians. Graeme Bartlett (talk) 08:03, 8 July 2022 (UTC)

RFD-kept. Maybe a section should be added to WT:IDIOM because other entries such as convex set, if somebody RFD'd them, would probably be kept for the same reasons I'd imagine. For me it comes down to: 1. being part of the technical jargon 2. the range of valid combinations being relatively restricted and 3. the entry being in some way insightful (for instance because its linguistic relations (nyms etc.) are reflective of its technical relations (subcategory-ness etc.) in some way). — Fytcha〈 T | L | C 〉 16:58, 20 July 2022 (UTC)