to instruct / lecture
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to prove wrong
To show or prove to someone that their previous assumption or opinion was wrong.
Ich dachte, die Aufgabe sei unmöglich, aber er hat mich eines Besseren belehrt.
I thought the task was impossible, but he proved me wrong.
to lecture
To teach or explain something to someone, often in a reproachful or condescending way.
Er versucht ständig, seine Kollegen über ihre Arbeit zu belehren.
He is constantly trying to lecture his colleagues about their work.
The prefix 'be-' is inseparable. It remains firmly attached to the verb stem 'lehren' (to teach) in all tenses and sentence constructions.
Er hat mich darüber belehrt, wie man die Maschine richtig bedient.
He instructed me on how to operate the machine correctly.
The expression 'jemanden eines Besseren belehren' (to prove someone wrong) requires the genitive 'eines Besseren'. The structure is fixed and cannot be changed.
Sie glaubte nicht, dass ich es schaffe, aber ich habe sie eines Besseren belehrt.
She didn't believe that I could do it, but I proved her wrong.
When 'belehren' (to lecture/instruct) is used without the addition 'eines Besseren', it often has a negative, slightly arrogant meaning. It implies that someone is giving advice in a pushy or condescending way.
Bitte hör auf, mich ständig zu belehren; ich weiß, was ich tue.
Please stop constantly lecturing me; I know what I'm doing.
The expression 'eines Besseren' signals the neutral meaning of showing someone that they were wrong. Without this addition, the negative, admonishing meaning is usually intended.
Er belehrte mich eines Besseren und zeigte mir meinen Fehler.
He proved me wrong and showed me my mistake.
to explain / declare
Erklären is usually a neutral way of making something understandable to someone. Belehren can also convey knowledge, but it often sounds reproachful or condescending. If you want to help objectively, you explain something; if you are criticizing someone’s behavior or lack of knowledge, you are more likely to lecture them.
Der Kollege belehrt mich herablassend darüber, wie das neue Programm funktioniert.
The colleague lectures me condescendingly about how the new program works.
Der Kollege erklärt mir freundlich, wie das neue Programm funktioniert.
The colleague kindly explains to me how the new program works.
