An unbounded number greater than every Real Number, most often denoted as . The symbol had been used as an alternative to M (1,000) in Roman Numerals until 1655, when John Wallis suggested it be used instead for infinity.

Infinity is a very tricky concept to work with, as evidenced by some of the counterintuitive results which follow from
Georg Cantor's treatment of Infinite Sets. Informally, , a
statement which can be made rigorous using the Limit concept,

Similarly,

where the notation indicates that the Limit is taken from the Positive side of the Real Line.

**References**

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, p. 19, 1996.

Courant, R. and Robbins, H. ``The Mathematical Analysis of Infinity.'' §2.4 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 77-88, 1996.

Hardy, G. H. *Orders of Infinity, the `infinitarcalcul' of Paul Du Bois-Reymond, 2nd ed.*
Cambridge, England: Cambridge University Press, 1924.

Lavine, S. *Understanding the Infinite.* Cambridge, MA: Harvard University Press, 1994.

Maor, E. *To Infinity and Beyond: A Cultural History of the Infinite.* Boston, MA: Birkhäuser, 1987.

Moore, A. W. *The Infinite.* New York: Routledge, 1991.

Morris, R. *Achilles in the Quantum Universe: The Definitive History of Infinity.* New York: Henry Holt, 1997.

Péter, R. *Playing with Infinity.* New York: Dover, 1976.

Smail, L. L. *Elements of the Theory of Infinite Processes.* New York: McGraw-Hill, 1923.

Vilenskin, N. Ya. *In Search of Infinity.* Boston, MA: Birkhäuser, 1995.

Wilson, A. M. *The Infinite in the Finite.* New York: Oxford University Press, 1996.

Zippin, L. *Uses of Infinity.* New York: Random House, 1962.

© 1996-9

1999-05-26