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A follow-up question to the use of "sei" in mathematics.

Compare the two following sentences, which are both common:

  • Es sei f eine stetige Funktion.
  • Sei f eine stetige Funktion.

Would you regard one version more correct than the other, at least historically?

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I am more interested in the grammatical correctness than in the frequency. I do agree that "Sei" is much more frequent, but I had a heated dispute with one of the non-mathematical lectors of one of my math papers on the grammatical correctness. –  Phira Aug 10 '11 at 11:23

3 Answers 3

I've studied mathematics for a long time and in my experience the second form (i.e. without the "es" at the beginning) is used more often or almost exclusively. So I would use the second version although the first one seems perfectly correct and understandable.

EDIT: Since there seems to be some disagreement here, I picked 4 random books about mathematics and computer science from my bookshelf:

  1. "Sei G eine endliche Gruppe von Automorphismen eines Körpers L, und sei K ihr Fixkörper." (M. Artin, "Algebra", Birkhäuser Verlag, 1998, S. 633)
  2. "Sei v ein Multiplikatorsystem vom Gewicht r/2 bezüglich einer Kongruenzgruppe \Theta" (E. Freitag / R. Busam, "Funktionentheorie", Springer, 2000, S. 363)
  3. "Sei G ein Graph mit den Cliquen C_1, ... , C_m" (C. Beierle, "Methoden Wissensbasierter Systeme", Vieweg, 2003, S. 341)
  4. "Es sei K ein Körper, p(x) ein separables Polynom in K und E ein Zerfällungskörper für p(x)." (E. Artin, "Galoissche Theorie", Verlag Harry Deutsch, 1988, S. 67)

So, only in one out of four books the "es" at the beginning was used. Although this selection is by no means representative, it suggests a certain trend, which I also observed in all the mathematics classes i had to take in the past.

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As a German who had some math lectures - both are correct. I assume that most people skip the "Es" just because it's shorter. Mathematicians are lazy. –  Tobias Langner Jul 12 '11 at 8:43
As a German who had Math in school (a while back) I would tend to use the first version with "Sei" because it feels more natural to me. However, by no means can I remember what version was used way back when I was in school. Looking at the publishing dates of the books mentioned here and the one mentioned by @GeorgesElencwajg, the books using "Es sei" are older then the "Sei" books. So may be there is a trend from one to the other. –  Peter Schuetze May 14 '14 at 18:21

I consider both of them equally correct and I don't feel that one of them is used more frequently than the other.

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Im ersten deutschen Buch dass ich aufschlage, Leutbechers Zahlentheorie, wird ausschliesslich "es sei" benutzt. Willkürliches Beispiel Seite 222: "Es sei L/K eine galoissche Zahlkörpererweiterung...".
Im Plural scheint mir, dass "Es seien" häufiger vorkommt als "seien": Leutbecher schreibt (Seite 233) "Es seien K_1,K_2 zwei endliche Erweiterungen des Zahlkörpers...".
Ich habe aber keine Statistik (hard numbers!) um diesen Eindruck zu bestätigen.

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