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Examples include: "The sequence 1, 2, 3, ... continues ad infinitum." "The perimeter of a fractal may be iteratively drawn ad infinitum." The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody (1733):
And there is a vicious regress because invoking tense to explain how different tenses are exemplified successively, gives rise to second-order tenses that again are incompatible unless we again invoke tense to show how they are exemplified successively, etcetera ad infinitum. It bears mentioning that in the mature version of the argument ...
Challenging the concept of eternal recurrence (the idea that the universe and its events have already occurred and will recur ad infinitum), the story's thematic meditations posit the alternative: that each person has only one life to live and that which occurs in life occurs only once and never again – thus the "lightness" of being. Moreover ...
A man walks a mile from a point α. But there is an infinity of gods each of whom, unknown to the others, intends to obstruct him. One of them will raise a barrier to stop his further advance if he reaches the half-mile point, a second if he reaches the quarter-mile point, a third if he goes one-eighth of a mile, and so on ad infinitum.
ad idem: to the same thing In agreement. / ˌ æ d ˈ aɪ d ə m / ad infinitum: to infinity To continue forever. / ˌ æ d ɪ n f ɪ ˈ n aɪ t ə m / ad litem: for the case Describes those designated to represent parties deemed incapable of representing themselves, such as a child or incapacitated adult. / ˌ æ d ˈ l aɪ t ɛ m / ad quod ...
i.e., "to the point of disgust". Sometimes used as a humorous alternative to ad infinitum. An argumentum ad nauseam is a logical fallacy in which erroneous proof is proffered by prolonged repetition of the argument, i. e., the argument is repeated so many times that persons are "sick of it". ad oculos: to the eyes
The regressive argument, in which each proof requires a further proof, ad infinitum; The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended; The trilemma, then, is the decision among the three equally unsatisfying options.
Argument from repetition (argumentum ad nauseam or argumentum ad infinitum) – repeating an argument until nobody cares to discuss it any more and referencing that lack of objection as evidence of support for the truth of the conclusion; [66] [67] sometimes confused with proof by assertion.