
die Bedingung
requirement
A prerequisite that must be fulfilled so that something else can happen or be valid.
Pünktlichkeit ist eine wichtige Bedingung für diese Arbeitsstelle.
Punctuality is an important requirement for this job.
condition / requirement
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requirement
A prerequisite that must be fulfilled so that something else can happen or be valid.
Pünktlichkeit ist eine wichtige Bedingung für diese Arbeitsstelle.
Punctuality is an important requirement for this job.

conditions
Usually used in the plural to describe the external circumstances or conditions under which something takes place or someone lives or works.
Die Mitarbeiter protestieren gegen die schlechten Arbeitsbedingungen.
The employees are protesting against the poor working conditions.

on the condition that
A fixed expression that introduces a clause that must be fulfilled. It means 'only if' or 'provided that'.
Du darfst am Wochenende ausgehen, unter der Bedingung, dass deine Hausaufgaben fertig sind.
You may go out on the weekend on the condition that your homework is finished.

unconditionally
Means that something happens without restrictions, reservations, or demands.
Er liebte sie ohne Bedingung.
He loved her unconditionally.
'Die Bedingung' means 'prerequisite' or 'requirement'. It is often confused with the English word 'condition', which can also describe the physical state of something. For physical state, German uses 'der Zustand' (condition/state).
Das Auto ist in einem sehr guten Zustand.
The car is in very good condition.
'Die Bedingung' (condition/requirement) is related to the adverb 'unbedingt' (absolutely, definitely). 'Unbedingt' literally means 'without condition' and expresses that something is absolutely necessary.
Du musst dir diesen Film unbedingt ansehen!
You absolutely have to watch this film!
In the sense of a prerequisite, 'Bedingung' (requirement/condition) is often used with the verbs 'stellen' (to set/make) and 'erfüllen' (to fulfill/meet). Someone can 'eine Bedingung stellen' (set a condition), and the other side must 'diese Bedingung erfüllen' (meet this condition).
Der Verkäufer stellte die Bedingung, dass der Preis sofort bezahlt wird.
The seller set the condition that the price be paid immediately.
When general circumstances or conditions are being discussed, the plural form 'die Bedingungen' is almost always used. Typical examples are 'Arbeitsbedingungen' (working conditions), 'Lebensbedingungen' (living conditions), or 'Wetterbedingungen' (weather conditions).
Die Sportler klagten über die extremen Wetterbedingungen.
The athletes complained about the extreme weather conditions.
The fixed expression 'unter der Bedingung, dass' (on the condition that) introduces a conditional clause. The following part of the sentence is a subordinate clause, in which the conjugated verb stands at the end.
Ich leihe dir mein Auto, unter der Bedingung, dass du es volltankst.
I'll lend you my car on the condition that you fill up the tank.
edition / condition
A Bedingung must be fulfilled for a decision or agreement to be valid or for something to happen. An Auflage, by contrast, is an additional obligation imposed by an authority, a court, or a contract. So, when dealing with a permit, ask whether something determines its validity or is an additional requirement.

Die Genehmigung gilt unter der Bedingung, dass alle Unterlagen vollständig sind.
The permit is valid on the condition that all the documents are complete.
Die Genehmigung enthält die Auflage, dass der Veranstalter die Besucherzahl begrenzt.
The permit includes the stipulation that the organizer must limit the number of visitors.