reversal / inversion
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reversal
The act of putting something in the opposite direction, order, or position; the state of being reversed.
Die Umkehrung der Fahrtrichtung in dieser Einbahnstraße führte zu großem Chaos.
The reversal of the driving direction on this one-way street led to major chaos.
'Die Umkehrung' (the reversal/inversion) is the noun corresponding to the separable verb 'umkehren' (to turn around/reverse). The ending '-ung' forms nouns from verbs that describe an action or its result. Someone who reverses something carries out an 'Umkehrung' (reversal).
Wegen des Staus mussten die Autofahrer umkehren.
Because of the traffic jam, the drivers had to turn around.
The noun 'Umkehrung' (reversal/inversion) is very often used with a genitive object to specify what is being reversed. Examples are 'die Umkehrung der Tatsachen' (the reversal of the facts) or 'die Umkehrung eines Prinzips' (the reversal of a principle).
Seine Aussage war eine reine Umkehrung der Wahrheit.
His statement was a pure reversal of the truth.
To emphasize that a change is complete, 'Umkehrung' (reversal) is often combined with adjectives such as 'völlige' (complete), 'komplette' (complete), or 'radikale' (radical).
Nach der Wahl gab es eine völlige Umkehrung der politischen Strategie.
After the election, there was a complete reversal of political strategy.
This meaning of 'Umkehrung' (inversion/inverse) is typical of specialized language such as mathematics, logic, or music theory. For example, people speak of the 'Umkehrung einer Funktion' (inverse of a function) or the 'Umkehrung eines Akkords' (inversion of a chord).
In der Musik ist die Umkehrung eines Intervalls eine grundlegende Technik.
In music, the inversion of an interval is a basic technique.
opposite
'das Gegenteil' and 'die Umkehrung' can both mean that something goes in the opposite direction. However, 'Gegenteil' usually names the opposite itself, for example a quality or meaning. 'Umkehrung' emphasizes the change or process more strongly: something is turned around, swapped, or brought into the opposite state. Learners may confuse the words because both have to do with 'opposite'. If you mean the opposite term or concept, 'Gegenteil' fits. If you mean that something is reversed or changed, 'Umkehrung' fits.
Nach der Umkehrung der Reihenfolge steht der wichtigste Punkt jetzt am Anfang.
After the order was reversed, the most important point is now at the beginning.
Sparen ist in diesem Fall das Gegenteil von Geld ausgeben.
In this case, saving is the opposite of spending money.