infinity
infinity, in mathematics, that which is not finite; it is often indicated by the symbol ∞art/infinity.gif. A sequence of numbers, a _{1}, a 2, a 3, … , is said to "approach infinity" if the numbers eventually become arbitrarily large, i.e., are larger than some number, N, that may be chosen at will to be a million, a billion, or any other large number (see limit). The term infinity is used in a somewhat different sense to refer to a collection of objects that does not contain a finite number of objects. For example, there are infinitely many points on a line, and Euclid demonstrated that there are infinitely many prime numbers. The German mathematician Georg Cantor showed that there are different orders of infinity, the infinity of points on a line being of a greater order than that of prime numbers (see transfinite number). In geometry one may define a point at infinity, or ideal point, as the point of intersection of two parallel lines, and similarly the line at infinity is the locus of all such points; if homogeneous coordinates ( x 1, x 2, x 3) are used, the line at infinity is the locus of all points ( x 1, x 2, 0), where x 1 and x 2 are not both zero. (Homogeneous coordinates are related to Cartesian coordinates by x = x 1/ x 3 and y = x 2/ x 3.) See A. D. Aczel, The Mystery of the Aleph (2000); D. F. Wallace, Everything and More (2003).
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved. More on infinity from Fact Monster:
 electric potential  potential, electric potential, electric, work per unit of electric charge expended in moving a ...
 Howard Stern  Howard Stern television and radio personality, author Born: 1/12/1954 Birthplace: New York City ...
 John Wallis  Wallis, John Wallis, John , 1616–1703, English mathematician. He was Savilian professor of ...
 Srinivasa Ramanujan  Ramanujan, Srinivasa Ramanujan, Srinivasa , 1889–1920, Indian mathematician. He was a ...
 Jonathan Pryce  Jonathan Pryce actor Born: 6/1/1947 Birthplace: Holywell, Wales The blackclad man who graced the ...
See more Encyclopedia articles on: Mathematics

24 X 7
Private Tutor

24 x 7 Tutor Availability 

Unlimited Online Tutoring 

1on1 Tutoring 
