Ad infinitum

Ad infinitum

"Ad infinitum" is a Latin phrase meaning "to infinity"."

In context, it usually means "continue forever, without limit" and thus can be used to describe a non-terminating process, a non-terminating "repeating" process, or a set of instructions to be repeated "forever", among other uses. It may also be used in a manner similar to the Latin phrase "et cetera" to denote written words or a concept that continues for a lengthy period beyond what is shown. Examples include:

*"The sequence 2, 4, 6, 8, 10 ... continues "ad infinitum"."
*"The perimeter of a fractal may be iteratively drawn "ad infinitum"."
*The 17th century writer Jonathan Swift mocked the idea of self-similarity in natural philosophy with the following lines in his poem 'On Poetry: A Rhapsody' [Jonathon Swift, "On Poetry: A Rhapsody", pub. 1733] :quotation
:...:"So nat'ralists observe, a flea:Hath smaller fleas that on him prey,:And these have smaller fleas that bite 'em,:And so proceed "ad infinitum".":...
*The Victorian era mathematician Augustus De Morgan expanded on this with a similar verse [Augustus de Moran, "A Budget of Paradoxes", pub. 1872, p. 377] quotation
:"Great fleas have little fleas upon their backs to bite 'em,:And little fleas have lesser fleas, and so "ad infinitum".:And the great fleas themselves, in turn, have greater fleas to go on,:While these again have greater still, and greater still, and so on."

ee also

* The song that never ends
* Turtles all the way down
* Recursion
* Self-reference
* Induction

References


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  • Infinītum — (lat.), das Unendliche …   Pierer's Universal-Lexikon

  • Infinītum — (lat.), das Unbegrenzte, Unendliche …   Meyers Großes Konversations-Lexikon

  • Infinitum — Este artículo o sección necesita referencias que aparezcan en una publicación acreditada, como revistas especializadas, monografías, prensa diaria o páginas de Internet fidedignas. Puedes añadirlas así o avisar …   Wikipedia Español

  • Infinitum — In|fi|ni|tum 〈n.; s, ni|ta〉 Unendlichkeit, das Unendliche; →a. ad infinitum [lat., „unbegrenzt“; zu in... „nicht“ + finire „begrenzen“] …   Universal-Lexikon

  • Infinitum — In|fi|ni|tum 〈n.; Gen.: s, Pl.: ni|ta〉 Unendlichkeit, das Unendliche; →a. s. ad infinitum [Etym.: lat., »unbegrenzt« <in… »nicht« + finire »begrenzen«] …   Lexikalische Deutsches Wörterbuch

  • Infinitum — In|fi|ni|tum das; s, ...ta <aus gleichbed. lat. infinitum zu infinitus »unbegrenzt«>: 1. Unendlichkeit, das Unendliche. 2. svw. ↑infinite Form …   Das große Fremdwörterbuch

  • infinitum — [[t]ɪ̱nfɪna͟ɪtəm[/t]] see ad infinitum …   English dictionary

  • infinitum — n. part of the phrase ad infinitum (without end) …   English contemporary dictionary

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