Definition of ad infinitum adverb from the Oxford Advanced Learner's Dictionary

 

ad infinitum

 adverb
adverb
BrE BrE//ˌæd ˌɪnfɪˈnaɪtəm//
 
; NAmE NAmE//ˌæd ˌɪnfɪˈnaɪtəm//
 
(from Latin)
 
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without ever coming to an end; again and again You cannot stay here ad infinitum without paying rent. The problem would be repeated ad infinitum. Word OriginLatin, literally ‘to infinity’.
See the Oxford Advanced American Dictionary entry: ad infinitum