TITLE: "Abuse of notation" in German
QUESTION [8 upvotes]: How do you express the common phrases "by an abuse of notation", "abusing the notation", etc. in German without invoking negative connotations? (Without this addendum, I'd have asked at german.se.) "Durch/Unter Missbrauch der Schreibweise/Notation" looks horrible to me, in particular, due to sexual allegations of the word "Missbrauch". How do they (e.g., folks such as Harro Heuser, or, from the further past, Edmund Landau, David Hilbert, Emmy Noether, von Neumann, etc.) typically write it in German books on mathematical subjects?
An example of the original sentence:

Abusing the notation, we write $ℚ⊂ℝ$, viewing the rational numbers as particular real numbers.

Related: "By an abuse of terminology" in German

REPLY [8 votes]: The German language features the wonderful word zweckentfremden (literally: to purpose-estrange), which means to use something for another purpose than intended. For me as a native speaker, it has no connotation of sexual or drug abuse. Rather, in everyday language it is often used for lifehacks and similar.

Abusing the notation, we write ℚ⊂ℝ, viewing the rational numbers as particular real numbers.

could be translated to:


Unter Zweckentfremdung der Notation schreiben wir ℚ⊂ℝ, …


Die Notation zweckentfremdend schreiben wir ℚ⊂ℝ, …


It is naturally hard to find examples of this usage, but here is one from Jänich’s textbook Mathematik 2:

Das Symbol $\langle \, , \rangle$ haben wir oft für die Bezeichnung eines Skalarprodukts benutzt, es wird hier also ein wenig zweckentfremdet, aber in einer praktischen und berechtigten Weise.