Infinity, most often denoted as real number . The symbol 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, limit concept,
Similarly,
where the notation limit is taken from the positive
side of the real line .
In the Wolfram Language , 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. 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. Hardy, G. H.
Orders
of Infinity: The 'infinitarcalcul' of Paul Du Bois-Reymond, 2nd ed. Lavine, S. Understanding
the Infinite. Maor,
E. To
Infinity and Beyond: A Cultural History of the Infinite. Moore, A. W. The
Infinite. Morris, R. Achilles
in the Quantum Universe: The Definitive History of Infinity. 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. Rucker, R. Infinity
and the Mind: The Science and Philosophy of the Infinite. 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. Weisstein,
E. W. "Books about Infinity." http://www.ericweisstein.com/encyclopedias/books/Infinity.html . Wilson,
A. M. The
Infinite in the Finite. Zippin,
L. Uses
of Infinity. Referenced on Wolfram|Alpha Infinity
Cite this as:
Weisstein, Eric W. "Infinity." From MathWorld https://mathworld.wolfram.com/Infinity.html
Subject classifications
, 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.
,
a statement that can be made rigorous using the limit concept,
indicates that the limit is taken from the positive
side of the real line.
is represented using the symbol Infinity.
