hope
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hope
The confident wish or expectation that something positive will happen in the future.
Trotz der schwierigen Lage haben wir die Hoffnung auf eine Besserung nicht verloren.
Despite the difficult situation, we have not lost hope for an improvement.
'Hoffnung' (hope) is the noun that belongs to the verb 'hoffen' (to hope). If you hope for something, then you have hope.
Ich hoffe auf gutes Wetter und habe die Hoffnung, dass die Sonne scheint.
I’m hoping for good weather and have the hope that the sun will shine.
When you want to express hope for something specific, you use the preposition 'auf' followed by the accusative.
Viele Menschen haben die Hoffnung auf eine friedliche Zukunft.
Many people have hope for a peaceful future.
'Hoffnung' (hope) is often combined with certain verbs. Typical phrases are 'Hoffnung haben' (to have hope), 'die Hoffnung aufgeben' (to give up hope), or 'Hoffnung schöpfen' (to find new hope).
Nach dem Gespräch schöpfte er neue Hoffnung.
After the conversation, he found new hope.
The phrase 'sich Hoffnung machen' (to get one's hopes up) is reflexive. The person who is hoping appears with a dative pronoun: 'Ich mache mir Hoffnung' (I'm getting my hopes up).
Er macht sich Hoffnung, die Prüfung zu bestehen.
He is getting his hopes up about passing the exam.
wish
'die Hoffnung' and 'der Wunsch' both show that you want something positive. 'Wunsch' puts more emphasis on what you would like to have or what you are asking for. 'Hoffnung' puts more emphasis on believing, or very much wishing, that it will really happen, even though it is uncertain. So you can have a wish without having much hope. The words can be confused because both look ahead to the future. As a simple guide: 'der Wunsch' says what I want; 'die Hoffnung' says that I still believe in it.
Nach dem guten Gespräch hat Maria wieder Hoffnung auf die Stelle.
After the good conversation, Maria has hope again about getting the position.
Mein Nachbar hat am Telefon den Wunsch nach einem späteren Termin geäußert.
My neighbor expressed a request for a later appointment on the phone.