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 ,

Countable
Set ,

Countably Infinite ,

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 Explore this topic in the
MathWorld classroom
Related Wolfram sites http://functions.wolfram.com/Constants/Infinity/
Explore with Wolfram|Alpha
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. https://mathworld.wolfram.com/Infinity.html

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