
grundlos
without reason
Without an apparent reason, cause, or justification.
Er hat sich grundlos über eine Kleinigkeit aufgeregt.
He got upset over a little thing for no reason.
groundless
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without reason
Without an apparent reason, cause, or justification.
Er hat sich grundlos über eine Kleinigkeit aufgeregt.
He got upset over a little thing for no reason.

bottomless
Literally: without a bottom, very deep or bottomless. This meaning is rare and more literary.
Der Held stürzte in eine scheinbar grundlose Tiefe.
The hero plunged into a seemingly bottomless depth.
The word is built very logically: it consists of 'Grund' (reason, cause) and the ending '-los' (-less), which means 'without'. So 'grundlos' literally means 'ohne Grund' (without reason).
Deine Angst ist völlig grundlos, es wird nichts passieren.
Your fear is completely groundless; nothing is going to happen.
'Grundlos' (without reason) is very often used as an adverb to modify a verb or an entire sentence. It describes that an action happens without any apparent cause.
Sie fing grundlos an zu lachen.
She started laughing for no reason.
Common combinations describe emotional reactions or negative actions. Typical phrases are: 'sich grundlos Sorgen machen' (to worry for no reason), 'grundlos wütend werden' (to get angry for no reason), or 'jemanden grundlos beschuldigen' (to accuse someone without reason).
Mach dir keine grundlosen Sorgen, es ist alles in Ordnung.
Don't worry for no reason; everything is fine.
The literal meaning 'ohne Boden' (without a bottom) is very rare and is used almost only in literary or poetic texts. In normal usage, you should always assume the meaning 'ohne Grund' (without reason).
Er fiel in einen grundlosen Abgrund seiner Träume.
He fell into a bottomless abyss of his dreams.
arbitrary
Grundlos only says that there is no apparent reason or justification. Willkürlich additionally indicates a personal, random, or rule-free decision. Use grundlos when the reason is missing, and willkürlich when the way the decision was made is also being criticized.

Der Chef strich ihren freien Tag grundlos.
The boss canceled her day off for no reason.
Der Chef verteilte die freien Tage willkürlich nach seiner eigenen Laune.
The boss assigned the days off arbitrarily, according to his own whim.