Ad infinitum is a Latin phrase meaning "to infinity. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. This page lists direct English Translations of common Latin phrases, such as veni vidi vici and Et cetera. Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness "

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. Et cetera (in English contexts pronounced) is a Latin expression that means "and other things" or "and so forth" Examples include:

• "The sequence 2, 4, 6, 8, 10 . In Mathematics, a sequence is an ordered list of objects (or events . . continues ad infinitum. "
• "The perimeter of a fractal may be iteratively drawn ad infinitum. A fractal is generally "a rough or fragmented geometric shape that can be split into parts each of which is (at least approximately a reduced-size copy of the whole" "
• 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. Jonathan Swift (30 November 1667 In Mathematics, a self-similar object is exactly or approximately similar to a part of itself (i "

• 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. Culture The Victorian fascination with novelty resulted in a deep interest in the relationship between modernity and cultural continuities Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician.

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
• Induction