As far as I know, "unendlich" is an adverb/adjective. And after bis should come a noun.

I found

integrieren bis Unendlich

while I expected

integrieren bis Unendlichkeit

How is the first citation ok? Can someone explain?

  • 1
    The infinity sign is labeled "Unendlich" in German.. which truly is a bit weird, you are right.
    – Annatar
    Aug 15 '17 at 12:02
  • 1
    How is that different from bis fünf or bis x, where x is any number? Aug 15 '17 at 12:49
  • 10
    Just consider "unendlich" a (somewhat special) number, and I think you'll be fine.
    – tofro
    Aug 15 '17 at 13:14
  • 1
    To infinity and beyond!
    – Lars Beck
    Aug 16 '17 at 6:18

Unendlich is used as a "number word" in mathematics like five or ninetynine

You also say Die Zahlen von eins bis fünf, so you can also say Die Summe von fünf bis unendlich.

The mathematical symbol ∞ is called Unendlich.

  • What? The symbol is called "Unendlichzeichen" de.wikipedia.org/wiki/Unendlichzeichen
    – adjan
    Aug 16 '17 at 9:42
  • There is no German word "Unendlich" (as a noun)
    – adjan
    Aug 16 '17 at 9:44
  • 4
    @Adrian: Man sagt auch "Der Pfeil zeigt nach links", nicht so oft "Das Pfeilzeichen zeigt nach links." Bei "Diese Schrift hat kein Euro- und kein Unendlichzeichen" würde man aber weit eher das ~zeichen benutzen. Mar 26 '20 at 16:49

Actually I see no reason for a substantive there. The word unendlich is the appropriate number word on the same level as zero, one, pi and four (which are no substantives either). In German Unendlichkeit is the term for philosophy and religion and I find it quite appropriate, to have that separated.

Finally: yes, integrieren von 0 bis unendlich is fine (no reason for uppercase).

  • 3
    It's also gleich and ungleich in math and not Gleichheit and Ungleichheit.
    – Janka
    Aug 15 '17 at 12:51
  • 3
    @Janka those are operators though, roughly corresponding to verbs in natural language, where unendlich is a number or an object. Aug 15 '17 at 14:58
  • 5
    @Janka Gleicheit and Ungleichheit are the substantive forms of gleich and ungleich. Example: "Vektor Ax ist ungleich x. Aufgrund der Ungleichheit von Ax und x kann A nicht die Einheitsmatrix sein." Aug 15 '17 at 15:01
  • 2
    @guidot The intuition leading to Unendlichkeit is probably that the number is called (positive/negative) infinity in English, and with prepositions as in bis unendlich the reason becomes clear. Aug 15 '17 at 15:03
  • Am Satzanfang schreibt man auch unendlich groß, man muss dann schon umformulieren, wenn man es partout nicht will. Mar 26 '20 at 16:51

And after bis should come a noun

... no, not at all:

Bis morgen, bis hierher, bis dann, bis fünf, bis unendlich

where do you see nouns used here?

Nouns are used with bis + prep., e.g.

bis zum Ende, bis an die Kante, ...

Correct German would be "bis unendlich" and "bis zur/an die Unendlichkeit". Only the former is used in mathematics, consistent with other numeral words like "bis fünf" (and not "bis zur Fünf")

  • bis + noun: ... bis Oberkante Unterlippe, ... bis die Wolken wieder lila sind
    – moooeeeep
    Aug 20 '17 at 13:37

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