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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):
See also List of Ship of Theseus examples Sorites paradox (also known as the paradox of the heap ): If one removes a single grain of sand from a heap, they still have a heap. If they keep removing single grains, the heap will disappear.
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."
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
For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress.
Infinitism, the view, for example, of Peter D. Klein, challenges this consensus, referring back to work of Paul Moser (1984) ... and so on ad infinitum ...
The canonical example is the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the ...
Ad infinitum is a Latin phrase. Ad Infinitum may also refer to: Ad Infinitum (British band) Ad Infinitum (Swiss band) Argumentum ad infinitum, another Latin phrase ...