at least
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at least
Expresses that something is the minimum that applies, is expected, or has been achieved. It is often used to make a limitation or to highlight a positive aspect in an otherwise negative situation.
Ich habe den Zug verpasst, aber zumindest habe ich mein Buch dabei.
I missed the train, but at least I have my book with me.
The word is made up of 'zu' and 'mindest'. 'Mindest' is a superlative form of 'wenig' (little) and means 'the least'. So 'zumindest' (at least) literally means 'up to the smallest degree'.
Die Reise war teuer, aber zumindest war das Wetter gut.
The trip was expensive, but at least the weather was good.
'Zumindest' (at least) can stand in position 1; then the verb follows directly after it (inversion). But it can also stand in the sentence like a normal adverb, often after the verb and the subject.
Zumindest hat er sich entschuldigt.
At least he apologized.
'Zumindest' (at least) is often used to limit a negative statement or to highlight a positive aspect. It signals that the situation is not ideal, but that a minimum has been fulfilled.
Ich habe die Prüfung nicht bestanden, aber zumindest habe ich viel gelernt.
I didn't pass the exam, but at least I learned a lot.
at least
'zumindest' and 'mindestens' both talk about a minimum. 'mindestens' is used especially with numbers, quantities, or measurements: not less than a certain number. 'zumindest' fits better when you are making a limitation or mentioning something positive in a situation that is not ideal. You can sometimes use 'mindestens' like 'zumindest', but with exact numbers, 'mindestens' sounds more natural. Learners can easily confuse the words because both express a lower limit. As a helpful guide: with numbers, usually use 'mindestens'; for a small consolation or a limitation, often use 'zumindest'.
Der Bus kommt spät, aber zumindest müssen wir nicht im Regen warten.
The bus is coming late, but at least we don't have to wait in the rain.
Für den Kuchen brauchen wir mindestens drei Eier.
For the cake, we need at least three eggs.