"By an abuse of terminology" in German

Question

How to translate the standard mathematical mantra "By an abuse of terminology, …" into German?

E.g.

An environment is a family of partial maps $\eta_M\colon X_M\dashrightarrow\dots$ for $M\in S$ such that …

By an abuse of terminology, if the sets $X_M$ for $M\in S$ are pairwise disjoint, an environment is a partial map $\eta\colon\bigcup_{M\in S}X_M\dashrightarrow\dots$ such that …

I'm sure German has a standard phrase for that, but it simply won't occur to me now!

Google Translate does "Durch einen Missbrauch der Notation..." It's probably not idiomatic German, but it might get you by. — Adrian Keister, Apr 12 '18 at 15:28
I'm not sure that German has a standard phrase. My professors used to say "par abus de notation" if it was specifically about notation, "par abus de langage" otherwise. Sounds like a loaned phrase. — Daniel Fischer, Apr 12 '18 at 15:30

score 4 · Answer 1 · answered Apr 12 '18 at 15:30

4

Here is a citation: "Man beachte, dass die Benutzung des Gleichheitszeichens in der Landau-Notation in gewisser Weise einen Missbrauch darstellt".

answered Apr 12 '18 at 15:30

Dietrich Burde

140,055

Fair enough, Anush Taraz is a reference good enough to me. – Apr 12 '18 at 16:00

"By an abuse of terminology" in German

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