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German Language/Etymology of Abbildung

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Question
The word "abbildung" (synonymous with "funktion") is sometimes used in German to refer to functions, a mapping in mathematics. "Abbildung," I believe, comes from the nominalization of the word "bild," meaning image. Why is this word used in German to describe the concept of a function? What does a function have to do with "bild," or images? Why are functions, the idea in math, relevant to the literal meaning of "abbildung"?

Answer
Hello Anthony,

thank you for your question.

I must admit that Maths isn't really my strong point, and before I read your question I didn't know that "Abbildung" was used synonymously with "Funktion" in German.
When I see the word "Abbildung" I think of a depiction, an illustration, an image.

However, I found an explanation on the German Wikipedia page for mathematical functions, and I am going to translate what it says for you.
Here's a link to the Wikipedia page: http://de.wikipedia.org/wiki/Funktion_%28Mathematik%29#Begriffsgeschichte

It says:
[...] the Group Theory was introduced in the 19th century and it is used to systematically examine how algebraic equations change under the influence of consecutive transformations. When this theory was applied to geometrical problems, the terms "Bewegung" (movement) and "Abbildung" (image) were used synonymously with transformation.
When the basics of mathematics were consistently phrased in the language of the set theory at the beginning of the 20th century, it became clear that the terms "Funktion" and "Abbildung" had the same meaning. However, the different traditions still have an effect on the linguistic usage. In mathematical analysis it is still common to use "Funktion", while "Abbildung" is used in algebra and geometry. Some mathematicians still strictly differentiate between a "Funktion" and an "Abbildung". For them a "Funktion" is an "Abbildung" in the real or complex number field.


I hope that this makes sense, because as I said I am not very knowledgeable in this area.

Hope this helps.

Best wishes
Janina  

German Language

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Janina

Expertise

As a native German speaker working professionally with languages, I can answer questions concerning German grammar, spelling and punctuation. I can also help with understanding and short German-English translations. As I also speak French, I might also be helpful concerning German-French translations. Translation only refers to short texts here.

Experience

I am a German native speaker working as a translator for English and French. I am concerned with language issues as grammar and spelling on a daily basis. I am very interested in these kind of topics, as any good translator should be. I also have a very good insight in the differences between English and German (and also French), so I might be able to give helpful explanations why specific things are the way they are in a specific language.

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I am a member of the German Translator Association BDÜ.

Publications
My translations are published in form of manuals, company and product presentations, and websites, but you won't find my name there, as translators of technical texts are only rarely featured.

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I studied translation at the University of Applied Sciences in Cologne (FH Köln), and have been working as a freelance translator for five years now.

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I haven't received any awards, but receiving awards is really quite rare for translators.

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Mostly translation agencies in many different countries.

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