Infinity
Infinity, most often denoted as 
, is an unbounded
quantity that is greater than every real number. The
symbol 
had been used as an alternative to M (
) 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 that follow from Georg Cantor's treatment of infinite
sets.
Informally, 
, a statement that 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.
In the Wolfram Language, 
is represented
using the symbol Infinity.
SEE ALSO: Aleph,
Aleph-0,
Aleph-1,
Cardinal Number,
Complex Infinity,
Continuum,
Continuum Hypothesis,
Directed
Infinity,
Division by Zero,
Hilbert
Hotel,
Infinite,
Infinite
Set,
Infinitesimal,
Limit,
Line at Infinity,
L'Hospital's
Rule,
Point at Infinity,
Transfinite
Number,
Uncountably Infinite,
Zero
RELATED WOLFRAM SITES: http://functions.wolfram.com/Constants/Infinity/
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.
Owen, H. P. "Infinity in Theology and Metaphysics." In The Encyclopedia
of Philosophy, Vol. 4. New York: Crowell Collier, pp. 190-193, 1967.
Péter, R. Playing
with Infinity. New York: Dover, 1976.
Rucker, R. Infinity and the Mind: The Science and Philosophy of the Infinite. Princeton, NJ:
Princeton University Press, 1995.
Smail, L. L. Elements of the Theory of Infinite Processes. New York:
McGraw-Hill, 1923.
Thomson, J. "Infinity in Mathematics and Logic." In The Encyclopedia
of Philosophy, Vol. 4. New York: Crowell Collier, pp. 183-190, 1967.
Vilenskin, N. Ya. In
Search of Infinity. Boston, MA: Birkhäuser, 1995.
Weisstein, E. W. "Books about Infinity." http://www.ericweisstein.com/encyclopedias/books/Infinity.html.
Wilson, A. M. The
Infinite in the Finite. New York: Oxford University Press, 1996.
Zippin, L. Uses
of Infinity. New York: Random House, 1962.
Referenced on Wolfram|Alpha:
Infinity
CITE THIS AS:
Weisstein, Eric W. "Infinity." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Infinity.html
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