# Tag Info

28

This is not related to writing about probabilities in particular. Most probably this is just a typo of someone who is used to writing in English. You are right, in general a comma is used as the decimal separator in German. However, in contexts where most relevant literature is in English (as in statistics / stochastics) and in documents written by people ...

26

There are two common ways of indicating restricting conditions. One way is to use a subordinate clause initiated with the pronomial adverb wobei: Definition: Sei P(A,B) = A - B, wobei A ⊂ U und A ⊄ B gelten soll. (Some language economists among the mathematicians might even drop gelten soll.) A more succinct way is to use the preposition mit followed by ...

26

The sentence is: Diese beyden letzten Dinge wollen wir indeß bey Seite setzen, um den Fall nicht zu sehr zu verwickeln. Aendert... Some of the words had a different spelling in that time. What you considered an "n" is a "y", there are several words that were spelled with "ey" where nowadays it is "ei". This is the case in your word 1) beyden - modern ...

24

In a context of mathematics "z. Bw." is probably zum Beweis which is "as proof".

21

I am teaching statistics too at an Austrian university1 together with a professor for statistics (I'm not a professor). And I noticed, that my colleague - although he is a German native speaker, born, grown up and living in Austria - uses his compete computer equipment in English language. And this makes sense, because the lingua franca of any modern science,...

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.

17

This stands for ohne Einschränkung, short for ohne Beschränkung der Allgemeinheit and would usually be abbreviated as “o.B.d.A.” The english equivalent is “WLOG”, which is short for without loss of generality and carries the exact same meaning: the assumption holds for all cases, not just the discussed special case.

17

Alt, aber noch brauchbar ist tatsächlich ...aufgrund der ihr innewohnenden Schönheit. (Obwohl sich das schon ein bisschen geschraubt anhört) Für Fremdwortliebhaber: ...wegen ihrer inhärenten Schönheit ...aufgrund ihrer substantiellen Schönheit ...aufgrund ihrer immanenten Schönheit oder ganz einfach ...aufgrund ihrer inneren Schönheit. oder ......

15

i.e. solutions that are bounded for all values of zeta under any initial conditions. Solutions to differential equations can be distinguished in bounded and unbounded cases. In case like these (also in the reverse case, where you need a technical term translated from English to German), it often helps looking for the term in the localized versions of ...

15

I think you are referring to the normal Cartesian coordinate system. In this case, the coordinates are usually separated by "|" (senkrechter Strich - vertical bar/Pipe) or ";" (Semikolon - semicolon). In your example, P (x, y) becomes P (x | y) P (x; y) and Q (x, y, z) becomes Q (x | y | z) Q (x; y; z) Note: It can also happen that a ...

13

In most cases in physics, act on sth. is translated by auf etw. wirken. So the phrase is: Der Impulsoperator p wirkt auf das Ket |ψ>. For example, in this Wikipedia article you can read: In der Impulsdarstellung wirkt der Impulsoperator multiplikativ auf Impulswellenfunktionen [...]. Another possible construction I can think of is auf etw. angewandt/...

13

Eine sprachlich weniger mathematisch klingende Alternative, die man erwägen kann, wäre: ≥ muss mindestens: Das Bild muss mindestens 500 px hoch sein. ≤ darf höchstens: Das Bild darf höchstens 500 px hoch sein. = muss genau: Das Bild muss genau 500 px hoch sein.

13

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 ...

13

Usually you will add the suffix -tel -stel if the number ends with 'g' or 'd' (zwanzig, dreißig, tausend, etc.) -el if the number ends with 't' (acht, dreihundertacht, etc.) but no rule without exceptions 1/1 ein Eintel / ein Ganzes1 (not ein einstel - for the sake of completeness) 1/2 ein Halb (not ein Zweitel) 1/3 ein Drittel (...

13

The formal statement ∃ x ∈ A : P(x) using the existential quantifier reads as Es existiert ein x ∈ A, so dass P(x) gilt or Es gibt ein x ∈ A, so dass P(x) gilt. It is unnecessary to say mindestens ein or something like that. You can also say P(x) für ein x ∈ A. or Es gilt P(x) für ein x ∈ A. Saying für irgendein would be highly unusual. If you really ...

12

Both is correct. The "Vereinigungsmenge" is read as: A vereinigt mit B or Die Vereinigung(or Vereinigungsmenge) von A und B Consequently, the "Schnittmenge" is read as: A geschnitten mit B or Die Schnittmenge von A und B Wikipedia is indeed a great place to start, but I also suggest – in case you're interested in maths – to watch lectures on Youtube. I ...

12

Here is a picture from my schoolbook from 2006 using the vertical line as a separator to avoid a clash with decimal separators: Nein, er hat nicht recht. Der untere Graph gehört zu einer anderen Funktion. Er schneidet zwar ebenso wie der obere Graph die y-Achse beim Wert 2,5. Jedoch verläuft der untere Graph im weiteren [sic] durch den Punkt (2,5 | 5), ...

11

Der französische Mathematiker C. Kramp führte um 1798 den Begriff faculty bzw. faculté (dt. „Fähigkeit“) ein.(1) Bei der Eindeutschung wurde dafür die im wissenschaftlichen Bereich übliche Endung -ät verwendet (wie z.B. in Universität). Es könnte einen Zusammenhang geben zwischen der Wahl des Begriffs Fähigkeit und der mathematisch dahinterstehenden ...

10

Both algebraical constructs can be expressed using modulo. Factorized constructs like $F/\sigma_n$ are read F durch die symmetrische Gruppe or F (faktorisiert) nach der symmetrischen Gruppe or F modulo symmetrische Gruppe or F modulo der symmetrischen Gruppe (I haven't heard anybody say F modulo die symmetrische Gruppe but I wouldn't even bother if I did.) ...

10

Good observation. In fact, the expression 5 - 4 = 1 should be read as Fünf minus vier ist (gleich) eins. Five minus four is (equal to) one. The equality sign within an expression A = B puts the entire left term A, here 5 - 4, into an equivalence relation with the entire right term B, here 1. No matter how complicated the compositions of A and B are — ...

9

There seems to be no equally used German counterpart as I have often heard (and used) the English “hand waving” while conversing about mathematics in German.

9

Yes, that is the verb, texen or TeXen. Ich texe meine Doktorarbeit. Note that pronunciation may vary. Bavarians sometimes lean towards /x/ for the x. Those who are proud of their knowledge of classical Greek will use /k/. But /ç/ is most common across Germany. Since the pronunciation of the x is taken from what Knuth et al. originally wanted for TeX, it ...

9

Yes, "derart, dass" means the same as "so dass", namely "such that". "So, dass" is more common, though. There is also "dergestalt, dass", which means the same, but is even rarer.

9

I think it would be referred to either generally as Polynomdivision / Partialdivision, which is the general term for polynomial division, or alternatively as das Horner-Schema. We have that name in English too; Horner's Scheme/Rule/Method, and in both languages as far as I understand it's not exactly the same as saying "synthetic division" in English, but it'...

9

Ich hätte hier 5 minus 4 ist gleich 1 gesagt, und ich denke, das ist die gängigere Praxis. Die Logik dahinter ist (5 minus 4) ist gleich 1 Jedoch lässt es nach meiner Beobachtung das deutsche Sprachgefühl zur Not auch zu, 5 minus 4 sind gleich 1 zu sagen, nämlich wenn man es interpretiert als 5 (minus 4) sind gleich 1, oder anders gesagt: ...

9

Yes and no. Taking a look at wikipedia, you will find the same sign: a comma. Thus these examples live without any real numbers, this is sufficient and does not help in your question. In education this is especially common for explantations as long as I write with variables (x,y) or I'm in a system with integers only (good for beginners): (2,3) Other given ...

8

When I was studying maths at university, "Beweis durch Händewedeln" was in use, but that describes a very very vague "proof" in the sense of "it can be easily seen that theorem 1.2 applies together with lemma 2.3, and the details are left as an exercise for the reader". For "proofs" the appeal to intuition or common sense, I'd use "Beweis durch Anschauung" ...

8

My recommendation is to try the soon-to-be-published book Wie man mathematisch schreibt by Burkhard Kümmerer, ISBN 978-3-658-01576-3. This should get the job done for you.

8

Ausgeschrieben heißt es "größer oder gleich". Umgangssprächlich wird es auch oft zu "größer gleich" verkürzt.

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