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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 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 ...
Examples for such models are an exponential-power model or an exponential-exponential-power model (see explicit models expounded further on). Since the final form of the model is determined by the values of RMM parameters, this implies that the data, used to estimate the parameters, determine the final form of the estimated RMM model (as with ...
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 damnum: according to the harm Used in tort law. Implies that the ...
Lost in the Funhouse was Barth's first book after the 1967 "The Literature of Exhaustion", [4] an essay in which Barth claimed that the traditional modes of realistic writing had been exhausted and no longer served the contemporary writer, but that the exhaustion of these techniques could be turned into a new source of inspiration.
Turn-of-the-century American architect John Drinkwater begins to suspect that within this world there lies another (and within that, another and another ad infinitum, each larger than the world that contains it). Towards the center is the realm of the fairies, which his wife, the Englishwoman Violet Bramble, can see and talk with.
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.
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.