The Real Numbers
The real numbers are those representable by an infinite decimal expansion, which may be repeating or nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes referred to as the continuum. Real numbers that have a nonrepeating decimal expansion are called irrational, i.e., they cannot be represented by any ratio of integers. The Greeks knew of the existence of irrational numbers through geometry; e.g., 2art/square-root-of-2.gifthe square root of 2 is the length of the diagonal of a unit square. The proof that 2art/square-root-of-2.gifthe square root of 2 is unable to be represented by such a ratio was the first proof of the existence of irrational numbers, and it caused tremendous upheaval in the mathematical thinking of that time.
Sections in this article:
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.
More on number The Real Numbers from Infoplease:
- number: The Real Numbers - The Real Numbers The real numbers are those representable by an infinite decimal expansion, which ...
- real number - real number: real number: see number.
- number - number number, entity describing the magnitude or position of a mathematical object or extensions ...
- ring, mathematical system - ring ring, in mathematics, system consisting of a set R of elements and two binary operations, such ...
- Encyclopedia: Mathematics - Encyclopeadia articles concerning Mathematics.
See more Encyclopedia articles on: Mathematics