once / someday
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once
Formerly, a long time ago. Used to refer to a past state or an event in the past.
Wo heute hohe Bürogebäude stehen, war einst ein lebendiges Künstlerviertel.
Where tall office buildings stand today, there was once a lively artists' district.
'Einst' (once) is mainly used in written language, in stories, or in a formal, slightly poetic style to talk about the past. It often sounds like 'Once upon a time ...'.
Dieses Schloss war einst die Residenz eines mächtigen Königs.
This castle was once the residence of a powerful king.
As an adverb, 'einst' (once / someday) can stand in different positions in the sentence. If it stands at the beginning of the sentence (position 1), the verb follows directly after it in position 2.
Einst lebte hier ein berühmter Dichter.
Once, a famous poet lived here.
The meaning of 'einst' (once / someday) depends on the tense of the verb. If the verb is in the past tense (e.g. preterite), it means 'formerly'. If it is in the future tense or subjunctive, it can mean 'one day in the future', but this is very rare and literary.
Hier stand einst eine alte Mühle am Fluss.
An old mill once stood here by the river.
day
'eines Tages' and 'einst' can both mean an unspecified point in the future. For this meaning, 'eines Tages' is clear and natural in everyday language. 'einst' can also mean 'früher' (earlier / in the past), and in its future meaning it is more likely to be used in elevated or literary language. That is why the words are similar only in certain sentences. If you are speaking normally about a future wish, 'eines Tages' is usually more suitable. 'einst' sounds more solemn or narrative.
Einst wird diese kleine Idee vielleicht vielen Menschen helfen.
Someday, this small idea may help many people.
Eines Tages will Mara ihre eigene Firma gründen.
One day, Mara wants to start her own company.