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 sequence '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:
::::::::"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''."

★ Which was itself parodied by the Victorian era mathematician Augustus De Morgan:
::::::::"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."

Contents

See also

See also

★ Turtles all the way down

★ Möbius strip

★ Recursion

★ Self-reference

★ Induction