Definition of Transcendental number

1. Noun. An irrational number that is not algebraic.

Generic synonyms: Irrational, Irrational Number
Specialized synonyms: Pi, E



Definition of Transcendental number

1. Noun. (mathematics) any irrational number that is not an algebraic number ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Transcendental Number

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transcended
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transcendental function
transcendental functions
transcendental idealism
transcendental meditation
transcendental number (current term)
transcendental numbers
transcendental philosophy
transcendental realism
transcendentalism
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transcendentalists
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transcendentalizing
transcendentally
transcendentals

Literary usage of Transcendental number

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

1. The Encyclopedia Americana: A Library of Universal Knowledge (1919)
"Lindemann provided that* is a transcendental number and, hence, since it is not the root of any algebraic equation, it cannot be constructed to an assumed ..."

2. The Encyclopedia Americana: A Library of Universal Knowledge (1919)
"... the root of any algebraic equation, with integral coefficients, it is a transcendental number. Lindemann provided that* is a transcendental number and, ..."

3. Historical Introduction to Mathematical Literature by George Abram Miller (1916)
"... of a circle to its diameter, is also a transcendental number. The great importance of these results led to a number of simplifications in their proofs. ..."

4. The Americana: A Universal Reference Library, Comprising the Arts and ...by Frederick Converse Beach, George Edwin Rines by Frederick Converse Beach, George Edwin Rines (1912)
"Lindemann proved that T is a transcendental number and, hence, since it is not the root of any algebraic equation, it can not be constructed to an assumed ..."

5. Dynamics & Stochastics: Festschrift in Honour of M.S. Keane by M. S. Keane, Dee Denteneer, F. den Hollander, Evgeny Verbitskiy (2006)
"Then x is a transcendental number. As a corollary they get the transcendence of Sturmian numbers: // there exists q such that the expansion of x to base q ..."

6. Famous Problems of Elementary Geometry: The Duplication of the Cube; the by Felix Klein (1897)
"... e is not only not an algebraic number and therefore a transcendental number simply, but it is also not an ..."

7. The Encyclopedia Americanaedited by Frederick Converse Beach, George Edwin Rines edited by Frederick Converse Beach, George Edwin Rines (1904)
"Lindemann proved that я- is a transcendental number and, hence, since it is not the root of any algebraic equation, it can not be constructed to an assumed ..."

8. Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field by Jacob William Albert Young, Oswald Veblen, Thomas Franklin Holgate, Frederick Shenstone Woods, Edward Vermilye Huntington, George Abram Miller, Gilbert Ames Bliss, Leonard Eugene Dickson, David Eugene Smith (1911)
"... it is nevertheless necessary, as a preliminary to considering the nature of n, to prove that e is a transcendental number. 3. The transcendence of e. ..."

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