informal gesprochen vs. informell gesprochen

Question

Let's consider the following passages:

Informal gesprochen nennen wir A und B unabhängig, wenn die Kenntnis des Eintretens von B die Prognose für A nicht ändert. Formal (für P(B) > 0):

A, B unabhängig ⇔ P(A|B) = P(A)

(cf. http://mathe.weissi.net/pdf/sto_0708_v1.pdf)

and

Informell gesprochen ist eine Verknüpfung auf einer Menge M eine Vorschrift, die je zwei Elementen x und y aus M (unter Beachtung der Reihenfolge) ein weiteres Element z von M zuordnet. Die präzise Definition ist wie folgt. ...

(cf. http://www.mathematik.uni-dortmund.de/~shoeppne/Algebra%20%28SS2010%29/Skript/alg1-3.pdf).

Given that the mathematicians are not necessarily strong in German even when German is their mother language, is "informal gesprochen" or "informell gesprochen" correct in the above contexts? Clearly, in both passages the authors mean "informally speaking" and provide a plain-language definition followed by formulas, but which phrase is correct in the above contexts:

• informal gesprochen or

• informell gesprochen ?

Duden is of no help here: "informally speaking" is in both cases both "nicht auf vorgegebenen Regeln, Richtlinien beruhend, sondern spontan [sich ergebend]" (since the plain-language description doesn't contain rules or formulas) and "dem Zweck der [ersten] Information dienend" (since the plain-language description introduces a term (a piece of information) for the first time).

References to established sources supporting your answer are welcome.

Answer 1

In the given context (and only in it), I am very much in favor of informal. The reason is that "informell" has a strong social connotation, f. ex.

Vor dem EU-Gipfel gab es ein kurzes informelles Treffen.

whereas here we are bound to a purely scientific context.

This seems also be backed by the Duden as the meanings given for "informell" do not fit well here:

ohne [formalen] Auftrag -> does not fit at all

ohne Formalitäten, nicht offiziell -> does not fit well

On the other hand, the meaning for "informal"

nicht auf vorgegebenen Regeln, Richtlinien beruhend, sondern spontan [sich ergebend]

fits quite well. The author does not keep to the standard rulings for expression here, but uses plain language, as you already mentioned correctly.

Having all said this I still do not want to be understood in the sense that "informell" is incorrect, but it does not fit as well as "informal".