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When explaining that something (a fact, for example) follows from (is a deduction thereof) something else (another fact, for example), which preposition is used? I would guess "aus" but these things are better to know and not to guess. If I wish to say that "This fact follows from the previous argument" could I write:

Dieser Fakt folgt aus das bisherige Argument

If I wish to clarify how it follows, I need another preposition. Could I write

Dieser Fakt folgt aus das bisherige Argument bei Picard iterierung

for "This fact follows from the previous argument combined with Picard iteration"?

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up vote 5 down vote accepted

"Aus" is correct, and it goes with the Dativ. So you say

Diese Tatsache folgt aus dem bisher Gezeigten.

(Fakt is a German word, but Tatsache is a better translation of fact here. Similary, I replaced your use of Argument, which is somehow different than the English argument.)

As for how it follows, you can't say

Diese Tatsache folgt aus dem bisher Gezeigten bei Picard-Iteration.

In English you'd say by Picard iteration, but bei is a false friend here. You could say mittels Picard-Iteration or durch Picard-Iteration; but maybe I'd use a different formulation altogether.

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Thanks for the answer Hendrik. I'll leave the mistakes in my original post since it perhaps gives better context to learners. It would be great if you could think of a 'standard' reformulation for the second part of the question. – Glen Wheeler Jun 23 '11 at 11:14
In mathematical or technical context it's probably the best to say Diese Tatsachte folgt aus dem bisher Gezeigten durch Anwendung der Fixpunktiteration. The way how the fact follows from the argument may almost always be appended with durch, and it's good style to use durch Anwendung/Verwendung eines/r Verfahrens/Methode. In other context it can be omitted: Dies folgt aus dem Gesagten durch reifliche Überlegung. – Deve Jun 23 '11 at 11:54
@Glen: It's so difficult to think about one's own mother tongue! If it doesn't come out of your mouth naturally, it's virtually impossible to force it. But I tend more and more to the formulation with mittels. Maybe you can give me a bit of context? – Hendrik Vogt Jun 23 '11 at 11:55
I'm just (re)writing an informal Skript for a Vorlesung. The original has a multi-line series of equations, and before them has "Using the divergence theorem we compute" and at the end has "Note that the last equation follows from the argument of Lemma XX combined with standard estimates, as can be for example found in [XX,Lemma XX]." I don't know if this really helps however :). – Glen Wheeler Jun 23 '11 at 12:36
@Glen: Then I'd probably say something like "Im letzten Schritt haben wir blablabla und blubb benutzt." – Hendrik Vogt Jun 23 '11 at 12:43

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