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 1, 2, 3, ... 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':
| “ | ...
"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
| “ | "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." | ” |
See also
The song that never ends
Turtles all the way down
Recursion
Self-reference
Mathematical induction
Translation
The phrase "Ad infinitum" occurs as such in the following languages: English, Breton, Dutch, Norwegian (Bokmål), Portuguese, Serbian.
Translation in Hebrew: אד אינפיניטום.
|
