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German Language/Etymology of Abbildung


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"?

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:

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

German Language

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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.


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