Definition:Infinity/Ad Infinitum

Definition

The term ad infinitum means:

endlessly

repeating indefinitely

generating an infinite sequence of terms

and so on.

Sometimes it has the suggestion of an endless loop.

Also, ad infinitum can be used when an infinite sequence is defined merely by showing some initial terms but without explicitly specifying either with a formula or recursively.

Linguistic Note

The phrase ad infinitum comes from the Latin, and literally means to Infinity.

It is one of those phrases which has entered natural language as rhetorical hyperbole, in this case meaning going on for a long time.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): ad infinitum
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ad infinitum
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ad infinitum
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): ad infinitum