Ad infinitum
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This article is about the Latin phrase, you may have been looking for: Ad infinitum, the short lived British musical group, AD Infinitum is also the name of a software product that assists in the management of Active Directory.
Ad infinitum is a Latin phrase meaning "to infinity."
In context, it usually means "continue forever," 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 series 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 ditty:
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- "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."
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- Which was itself parodied by the Victorian era mathematician Augustus De Morgan:
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- "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."
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