Ad infinitum
Ad infinitum is a Latin phrase meaning "to infinity" or "forevermore".
Description
In context, it usually means "continue forever, without limit" and this 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 1, 2, 3, ... continues ad infinitum."
- "The perimeter of a fractal may be iteratively drawn ad infinitum."
The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody (1733):
The vermin only teaze and pinch
Their foes superior by an inch.
So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em,
And so proceed ad infinitum.
Thus every poet, in his kind,
Is bit by him that comes behind[1]
The mathematician Augustus De Morgan included similar lines in his rhyme Siphonaptera.[2]
See also
- Mathematical induction
- Recursion
- Self-reference
- "The Song That Never Ends"
- Turtles all the way down
References
- v
- t
- e
- Ananta (infinite)
- Apeiron
- Controversy over Cantor's theory
- Galileo's paradox
- Hilbert's paradox of the Grand Hotel
- Infinity (philosophy)
- Paradoxes of infinity
- Paradoxes of set theory
- 0.999...
- Absolute infinite
- Actual infinity
- Aleph number
- Beth number
- Cardinal numbers
- Cardinality of the continuum
- Dedekind-infinite set
- Directed infinity
- Division by zero (Complex infinity)
- Epsilon number
- Gimel function
- Hilbert space
- Hyperreal numbers
- Infinite set
- Infinitesimal
- Ordinal numbers
- Point at infinity
- Regular cardinal
- Sphere at infinity (Kleinian group)
- Supertask
- Surreal numbers
- Transfinite numbers