Definition of Irrational number

1. Noun. A real number that cannot be expressed as a rational number.

Exact synonyms: Irrational
Generic synonyms: Real, Real Number
Specialized synonyms: Transcendental Number, Algebraic Number

Definition of Irrational number

1. Noun. (mathematics) Any real number that cannot be expressed as a ratio of two integers. ¹

¹ Source: wiktionary.com

Irrational Number Pictures

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Lexicographical Neighbors of Irrational Number

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Literary usage of Irrational number

Below you will find example usage of this term as found in modern and/or classical literature:

1. Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw (1921)
"An irrational number is never equal to a rational number. ... Next, in § 5, we have seen that the irrational number given by the section (A, ..."

2. Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw (1921)
"An irrational number is never equal to a rational number. ... Next, in § 5, we have seen that the irrational number given by the section (A, ..."

3. Proceedings of the London Mathematical Society by London Mathematical Society (1907)
"An irrational number in general is an object which has a definite ordinal relation ... This conception of the nature of an irrational number is perhaps most ..."

4. The Theory of Functions of a Real Variable and the Theory of Fourier's Series by Ernest William Hobson (1907)
"Before the recent development of the arithmetical theories of irrational number, and to a considerable extent even later, a number has been regarded as the ..."

5. Lectures on Fundamental Concepts of Algebra and Geometry by John Wesley Young (1911)
"As to order, an irrational number a defined by a cut (d, ... To define the sum of a rational number m and an irrational number a defined by the cut (d, ..."

6. Proceedings of the London Mathematical Society by London Mathematical Society (1907)
"An irrational number in general is an object which has a definite ordinal relation ... This conception of the nature of an irrational number is perhaps most ..."

7. The Theory of Functions of a Real Variable and the Theory of Fourier's Series by Ernest William Hobson (1907)
"Before the recent development of the arithmetical theories of irrational number, and to a considerable extent even later, a number has been regarded as the ..."

8. Lectures on Fundamental Concepts of Algebra and Geometry by John Wesley Young (1911)
"As to order, an irrational number a defined by a cut (d, ... To define the sum of a rational number m and an irrational number a defined by the cut (d, ..."

9. A College Algebra by Henry Burchard Fine (1904)
"Hence, using a to denote any irrational number, we have the following general definition of such a number: An irrational number, a, is defined whenever a ..."

10. A College Algebra by Henry Burchard Fine (1904)
"Hence, using a to denote any irrational number, we have the following general definition of such a number: An irrational number, a, is defined whenever a ..."

11. The Monist by Hegeler Institute (1921)
"We will sum up what Couturat says of Russell's results: "His definition consists in identifying the irrational number with the lower class which previously ..."

12. An Introduction to the Theory of Infinite Series by Thomas John I'Anson Bromwich (1908)
"Algebraic operations with irrational numbers. The negative of an irrational number a is defined by means of the lower class —A and the upper class — a•', ..."

13. Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II by Richard Dedekind (1901)
"From now on, therefore, to every definite cut there corresponds a definite rational or irrational number, and we regard two numbers as different or unequal ..."

14. The Monist by Hegeler Institute (1921)
"We will sum up what Couturat says of Russell's results: "His definition consists in identifying the irrational number with the lower class which previously ..."

15. An Introduction to the Theory of Infinite Series by Thomas John I'Anson Bromwich (1908)
"Algebraic operations with irrational numbers. The negative of an irrational number a is defined by means of the lower class —A and the upper class — a•', ..."

16. Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II by Richard Dedekind (1901)
"From now on, therefore, to every definite cut there corresponds a definite rational or irrational number, and we regard two numbers as different or unequal ..."