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On page 77 in Topologische Differentialalgebra by U. Gebhardt et al. which I found on MathOverflow, there is this exercise that asks the reader to find sequences of consecutive singular/plural pairs:

Aufgabe 4 (Hyperpluralfolgen)
Eine Folge von Substantiven (S1, ..., Sn) heißt Hyperpluralfolge der Ordnung n (kurz: Hn-Folge), wenn folgende Bedingungen erfüllt sind:
a) Die Si sind paarweise verschieden
b) Für i < n gilt: Si+1 ist der Plural von Si.
Beispiel: (Herd, Herde, Herden) ist eine H3-Folge.
Geben Sie drei weitere H3-Folgen und eine Hn-Folge (n > 3) an!

Additionally to Herd, Herde, Herden there is Kohl, Kohle, Kohlen as well as Term, Terme, Termen (note that Terme references a border stone) and Spalt, Spalte, Spalten. Does someone know a hyper plural sequence of order 4 (or higher)?

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2 Answers 2

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bakunin's argument makes us look for different forms of plural endings. The first candidate is a stem that forms the plural with -s followed by a plural with -e:

If we accept the brand name Rei as a German word, then the following fits into that Schema:

Rei [in der Tube] → Reis [multiple cans of Rei in der Tube, but also the plant, rice] → Reise [different kinds of rice, but also the journey] → Reisen

Same schema:

Wie [the question word] → Wies [multiple question words Wie, but also a town, for instance in Austria or Bavaria] → Wiese [the collection of all those towns with the name Wies, but also the meadow] → Wiesen

In a comment below, Wolfgang Spindeler gave the sequence

Mu [see Wikipedia] → Mus [multiple words Mu, but also a mush like applesauce for instance] → Muse [a muse] → Musen

[That is Community Wiki answer. Just append solutions by editing.]

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  • Vielleicht gibt es auch noch andere Lösungen, wenn man fremdsprachige Pluralbildung hinzuzieht. Gute Chancen hat man vielleicht bei Lateinischen Fremdworten. Ich denke an so etwas wi JusJura als Anfang. Oder etwas nach dem Endungsschema -us-is-ise-isen. Hat man erstmal ein solches Endungsschema, kann man ein Reimwörterbuch daraufhin befragen.
    – Jonathan Herrera
    Commented Feb 4, 2022 at 16:25
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    OK, if we take made up names (trademarks) like "rei" into account we can make up as long sequences as we want. We just have to claim that in i.e.: "xy", "xye", "xyen", "xyene", "xyenes", "xyeneses", etc., are trademarks. The task was "eine Folge von Substantiven", though, and "rei" is not a Substantiv - nor is "xy".
    – bakunin
    Commented Feb 5, 2022 at 13:19
  • Furthermore i wonder if "Substantiv" doesn't imply a german word. i.e. an english equivalent of a "Substantiv" would be called "noun".
    – bakunin
    Commented Feb 5, 2022 at 13:26
  • @bakunin Why would "Rei" not be a German "Substantiv"? It is not a trade mark I invented, but it does exist in German.
    – Jonathan Herrera
    Commented Feb 6, 2022 at 10:53
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    Added Mu as first answer to the list because it might very well be possible that the authors of the source (who are mathematicians and are probably aware of the book “Gödel, Escher, Bach” by Douglas R. Hofstadter as well as the MU-puzzle, see Wikipedia) thought of this themselves and hence came up with that exercise. (Only a hypothesis.)
    – Bixxli
    Commented Feb 8, 2022 at 0:01
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Ich glaube nicht, daß es eine Folge mit n > 3 geben kann. Der Grund ist, daß H3-Folgen als drittes Element ein Wort mit der Endung -en haben ("Kohl", "Kohle", "Kohlen") und bei Wörtern, die auf -en enden, der Plural gleich dem Singular ist, sofern sie überhaupt einen Plural haben (zB. "das Leben", "der Pfosten"), was bei substantivierten Verben ("das Gehen", etc.), die vermutlich den größten Teil dieser Wortgruppe ausmachen, nicht der Fall ist.

Dieser Umstand aber verletzt die Forderung, daß die Wörter "paarweise verschieden" sein sollen.

Ich frage mich aber, was das mit Topologie oder Funktionenanalysis zu tun hat.

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    I think in principle sequences for n = 4 are possible, though I don't have an example. As a probably wrong example, however illustrating the possibility of existence consider the word "Mu". Looking up it's meaning there are some, like a mythical continent or a Chinese measure of area. Assume there is a meaning having plural "Mus" (which I don't know there is) then we can go on like: Mu, Mus, Muse, Musen. (Der oder Das Mus, as in "Apfelmus", Die Muse as in "die Muse hat mich geküsst") Commented Feb 3, 2022 at 11:05
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    Please write answers always in the same language as the question. See german.meta.stackexchange.com/a/1050/1487 and german.meta.stackexchange.com/a/830/1487 Commented Feb 4, 2022 at 12:25
  • The questions title was in german, the text of the question too.
    – bakunin
    Commented Feb 5, 2022 at 13:13
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    @WolfgangSpindeler Whether the name of the continent is correct may be debatable and I think the plural form of the area unit is again Mu if am not mistaken. But to me, the title of de.m.wikipedia.org/wiki/Mu_(Philosophie) seems to be a noun with plural „Mus“ and then your solution should work out.
    – Bixxli
    Commented Feb 5, 2022 at 16:14

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