remnant / leftover
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remnant
A remainder or small part of something that has been left after the disappearance, destruction, or consumption of the larger whole.
Die alte Ruine ist das letzte Überbleibsel der mittelalterlichen Burg.
The old ruin is the last remnant of the medieval castle.
'Das Überbleibsel' (the remnant/leftover) is derived from the separable verb 'überbleiben' (to be left over). It refers to what remains after a process or destruction.
Vom großen Festessen ist nur ein kleines Überbleibsel im Kühlschrank.
Only a small leftover from the big feast is in the refrigerator.
To say what something is a remnant of, the preposition 'von' (of/from) followed by the dative is usually used. You speak of an 'Überbleibsel von etwas' (a remnant of something).
Diese alte Tradition ist ein Überbleibsel aus einer längst vergangenen Zeit.
This old tradition is a remnant from a long-past era.
The word is often used for historical or old things that come from an earlier era. However, it can also refer to abstract things such as habits or ideas.
Die Ruine ist ein Überbleibsel einer römischen Villa.
The ruin is a remnant of a Roman villa.
rest / remainder
Rest is a neutral, general term for the part that remains of a whole. Überbleibsel often highlights a single surviving object or trace of something that has disappeared or been destroyed. “Rest” is appropriate for a mere remaining quantity; “Überbleibsel” is more suitable for something visible that bears witness to what was there.
Vom alten Haus blieb nur ein steinerner Türbogen als Überbleibsel stehen.
The only thing left standing from the old house was a stone doorway arch.
Vom alten Haus blieb nur ein Rest der Außenmauer stehen.
Only part of the outside wall of the old house was left standing.
