"Abuse of notation" in German

Question

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

Answer 1

I would say "Durch Missbrauch der Notation" but "Notationsmissbrauch" is also quite common as far as I am aware so "Durch einen Notationsmissbrauch wird es als ℚ⊂ℝ geschrieben, damit die rationale Zahlen als bestimmte reelle Zahlen darzustellen." Or something like that.

Answer 2

The English "abuse" is adequately translated by the German "Missbrauch". In both languages it may have a sexual connotation, but if you read it in a mathematical text you would never interpret it like that. It often occurs as a compound with other nouns, for example "Alkoholmissbrauch" or "Machtmissbrauch".

An example of a mathematical text containing the phrase is https://www.math.uni-hamburg.de/home/riemenschneider/anvorl3.pdf p.568 (the spelling is old orthography). It seems to me that the following variants are not bad:

• Unter Missbrauch der Notation schreiben wir $\mathbb{Q} \subset \mathbb{R}$

• Wir schreiben missbräuchlich $\mathbb{Q} \subset \mathbb{R}$

• Wir verwenden die missbräuchliche Schreibweise $\mathbb{Q} \subset \mathbb{R}$

Note that the following does not sound nice:

• Unter Missbrauch der Schreibweise schreiben wir $\mathbb{Q} \subset \mathbb{R}$

However, perhaps you should also ask a question in https://german.stackexchange.com/

Edited:

The phrase does not occur that frequently in German. I cannot remember that I have ever seen it in older literature, but I admittedly I am not sure. This indicates that it might be an Anglicism. Another hint is this:

A Google search with "Missbrauch der Schreibweise" produces only a few results, but if you do it with "Missbrauch der Notation" you will get a lot more. And the latter is the most literal translation of "abuse of notation".

Answer 3

You could also use "missbräuchliche Notation". This does not sound as clunky and does not have any connotations related to sexual/ drug-related abuse.

Answer 4

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.

Answer 5

i) If I had to write an article (mathematics of physics) in German I'd definitely use Mißbrauch at that place. The only disadvantage is that it's not very specific in how far the (local) use in the article deviates from the standard. That means in a math paper one would be more precise and write "Unter Erweiterung der Notation..." or "Unter Einengung der Schreibweise..." "Durch Entleien der Schreibweise aus der Mengenlehre....", "als einfache Mnemonic schreiben wir...", "Wir schreiben dies als ..., obwohl diese Nomenclatur normalerweise ... assoziiert..."

ii) The association of "abuse" with sexual abuse is an Americanism, a bias not found on the old continent. The German or European readers in natural sciences would obviously not misinterpret the terminoloy. There are attempts in science to introduce sexuality at p laces like cryptography (Bob and Alice the example here) which are just irrational, non sequitur.

iii) Nowadays German has obviously lost it's status as a lingua franca in Math papers. So on a statistical basis searching for "abuse" in the papers gets many more hits than searching for "Mißbrauch".