illustration / mapping
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illustration
A visual representation such as an image, drawing, diagram, or photo that serves to illustrate something in a text.
Die Abbildung auf Seite 50 zeigt den detaillierten Aufbau der Zelle.
The illustration on page 50 shows the detailed structure of the cell.
mapping
In mathematics, a rule that assigns exactly one element of another set, or the same set, to each element of a set.
Eine Funktion ist eine eindeutige Abbildung von der Definitionsmenge in die Wertemenge.
A function is a unique mapping from the domain to the range.
'Abbildung' (illustration/mapping) is a noun derived from the verb 'abbilden' (to depict something visually). It is closely related to the word 'das Bild' (the picture/image). The ending '-ung' makes it a feminine noun.
Der Künstler wollte die Realität möglichst genau abbilden.
The artist wanted to depict reality as accurately as possible.
In books or academic texts, an illustration is often referred to directly. Typical phrases are 'siehe Abbildung 3' (see Figure 3) or 'Abbildung 1 zeigt ...' (Figure 1 shows ...).
Wie in Abbildung 2 zu sehen ist, hat sich der Markt stark verändert.
As can be seen in Figure 2, the market has changed significantly.
The mathematical meaning of 'Abbildung' (mapping) is purely technical language. Outside mathematical or logical contexts, you will practically never encounter this meaning.
In der Vorlesung haben wir heute lineare Abbildungen besprochen.
In the lecture today, we discussed linear mappings.
picture / image
Bild and Abbildung both refer to a visual representation. Bild is the general everyday term, while Abbildung is used especially in an explanatory text as a clearly assigned element. Use Bild when speaking generally; in a text or explanation, Abbildung is often more suitable.
Bitte sieh dir die Abbildung mit den drei Pflanzen im Text an.
Please look at the illustration with the three plants in the text.
Bitte schick mir das Bild mit den drei Pflanzen.
Please send me the picture with the three plants.
