# Correctly translating “Assume” and “Suppose” to German in Mathematics

It is common in mathematics in English to use the words assume and suppose differently, that is, to use the word assume when dealing with a reduction or case, while using the word suppose when looking for a contradiction. For example, one may use the phrases "Thus, it can be assumed that..." and "For the sake of contradiction, suppose that... ."

I have seen the word angenommen used in mathematics in German, but I am not sure whether it encompasses what both assume and suppose mean in English or not. Does it? Or is there another word that is also used?

I am aware of the words annehmen and ausgegangen, but I have not seen them in mathematical texts before.

• As a German who has published mathematics in English, I was not consciously aware of that distinction. That may be just me, but also maybe the distinction is less strict in German. – Carsten S May 9 at 12:02

## 4 Answers

Let's assume p is a prime.

Setzen wir voraus, p sei prim.

Let's suppose p is a prime.

Nehmen wir an, p sei prim.

Voraussetzen is much stronger than annehmen.

Nehmen Sie etwa an, wir hätten viel Geld? — Das setze ich voraus, sonst wären Sie doch gar nicht hier.

• Is there a way to use these without a pronoun while remaining formal? – Schroder Apr 23 '19 at 19:26
• @Schroder Yes, by using the participle: Angenommen, p ist prim and Vorausgesetzt, p sei prim – jonathan.scholbach Apr 23 '19 at 20:18
• In addition: There's also "davon ausgehen", as mentioned in the question ("Gehen wir davon aus, dass p prim ist"), which also means to assume. – HalvarF May 1 at 18:56
• Without a pronoun that would be "Davon ausgehend" – infinitezero May 9 at 12:36

One common phrase in mathematics (I think, it is the standard phrase) is

Sei X ...

which is the translation of

Let X be ...

• You are right, there is also a third common phrase. How does `assume` and `suppose` fit in with their translation? – Shegit Brahm Apr 24 '19 at 13:02

The use in German is identical to the use in English.

• angenommen is a typical beginning of a proof by contradiction. Look at the section Indirekter Beweis in the wikipedia-article Beweis (Mathematik).

• vorausgesetzt means that you make an assumption for a theorem. Other ways to express it are "Unter der Voraussetzung, dass ..." or simply "Sei ... erfüllt." See jonathan.scholbach's answer.

Oft benutzt: “Ohne Beschränkung der Allgemeinheit”. Zum Beispiel x >= y und y <= x sind möglich. Der Beweis für den zweiten Fall ist genau umgekehrt vom ersten Fall. Also beweise ich den Fall x>= y und den anderen Fall kannst du selber machen wenn Du Langeweile hast. “Ohne Beschränkung der Allgemeinheit sei x>= Y”.

• Wlog is not what the question asked for. – Carsten S May 9 at 12:00