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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:
- "So nat'ralists observe, a flea
- Hath smaller fleas that on him prey;
- And these have smaller fleas to bite 'em.
- And so proceeds Ad infinitum."
- "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."
This text is part of the nursery rhyme "The Siphonaptera".