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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.

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  • 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
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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.

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  • Is there a way to use these without a pronoun while remaining formal? – Schroder Apr 23 '19 at 19:26
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    @Schroder Yes, by using the participle: Angenommen, p ist prim and Vorausgesetzt, p sei prim – jonathan.scholbach Apr 23 '19 at 20:18
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    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
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One common phrase in mathematics (I think, it is the standard phrase) is

Sei X ...

which is the translation of

Let X be ...

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    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
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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.

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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”.

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

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