Ad infinitum

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, and thus its length will approach infinity."
• And this humorous 18th century poem by Jonathan Swift:

Great fleas have little fleas

upon their backs to bite 'em,

And little fleas have lesser fleas,

and so on ad infinitum.

Ad infinitum is also a short-lived British musical group. "AD Infinitum" is also the name of a software product that assists in the management of Active Directory.