# irrational number

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Related to Irrational numbers: Imaginary numbers

## irrational number

any real number that cannot be expressed as the ratio of two integers, such as π
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Irrational Number

a number that is not rational (that is, not an integer or fraction). Real irrational numbers can be represented by an infinite non repeating decimal; for example, √2 = 1.41 …, π = 3.14 …. The existence of irrational ratios (for example, the irrationality of the ratio of the diagonal of a square to its side) was known in antiquity. The irrationality of the number π was established by the German mathematician J. Lambert (1766). However, a rigorous theory of irrational numbers was constructed only in the second half of the 19th century. Irrational numbers are divided into nonrational algebraic numbers and transcendental numbers.

## irrational number

[i′rash·ən·əl ′nəm·bər]
(mathematics)
A number which is not the quotient of two integers.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## irrational number

(mathematics)
A real number which is not a rational number, i.e. it is not the ratio of two integers.

The decimal expansion of an irrational is infinite but does not end in an infinite repeating sequence of digits.

Examples of irrational numbers are pi, e and the square root of two.
References in periodicals archive ?
Considering the existence of two complementary fractals on the sets of rational and irrational numbers accordingly , the probability that small variations (fluctuations) lead to coincidences between irrational and rational numbers of small quotients is minimum.
Now choose an irrational number [[omega].sub.0] [member of] [0,1) and a compatible partition as in (43) of the last section.
(25) The Greeks also found the notion of irrational numbers totally abhorrent.
(The understanding that this is an irrational number was less secure, and would generally need some more explicit teaching in relation to sets of numbers and their properties).
(1) Regardless of the fact that the determined bit of the test data is 0 or 1, it has a little effect on compression ratio in the process of finding the irrational number. (2) Do not-care bit can accelerate the search speed of irrational number, reduce the value of irrational number used to store the test data, and improve the compression ratio.
Let p and q [member of] [R.sup.+]\{1} such that [log.sub.q]p be an irrational number. We now prove the case of q > 1.
The Hindus also developed correct procedures for operating with irrational numbers.
It then explores the use of symbols and algebra, the concepts of rational and irrational numbers, and how numbers are represented geometrically.
(Hagit Sela and Orit Zaslavsky); (23) Explicit Linking in the Sequence of Consecutive Lessons in Mathematics Classrooms in Japan (Yoshinori Shimizu); (24) On the Teaching Situation of Conceptual Change: Epistemological Considerations of Irrational Numbers (Yusuke Shinno); (25) Posing Problems with Use the "What If Not?" Strategy in NIM Game (SangHun Song, JaeHoon Yim, EunJu Shin, and HyangHoon Lee); (26) Embodied, Symbolic and Formal Aspects of Basic Linear Algebra Concepts (Sepideh Stewart and Michael O.
Mathematical achievements such as concepts of irrational numbers, imaginary numbers, the infinitesimal, the fourth dimension, periodic space, and more are explored in terms accessible to lay readers, and their intersection with art, literature, philosophy, and physics among other disciplines is laid bare.
It is usually simply stated the real numbers are comprised of rational and irrational numbers. It is very common to start from such a generality.

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