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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):
The light grey font indicates the elided constituent, i.e. the ellipsis, and the underline marks the antecedent constituent to the ellipsis. Since the antecedent constituent contains the ellipsis itself, resolution of the ellipsis necessitates an infinite regress as the antecedent is substituted ad infinitum into the ellipsis site.
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
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.
The book appeared the year after the publication of his essay The Literature of Exhaustion, in which Barth said that the traditional modes of realistic fiction had been used up, but that this exhaustion itself could be used to inspire a new generation of writers, citing Nabokov, Beckett, and especially Borges as exemplars of this new approach.
The advent of artificial intelligence (AI) is seen by many as one of the modern era's most incredible developments. And to be fair, it is a game changer.
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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