Ad infinitum is a Latin phrase meaning "to infinity" or "forevermore".
Description In context, it usually means "continue forever, without limit" and this 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 incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody (1733):
The mathematician Augustus De Morgan included similar lines in his rhyme Siphonaptera.
See also
Mathematical induction Recursion Self-reference "The Song That Never Ends" Turtles all the way down
References