Definitions for transcendental number
tran·scen·den·tal num·ber

Princeton's WordNetRate this definition:0.0 / 0 votes

1. transcendental numbernoun

   an irrational number that is not algebraic

WiktionaryRate this definition:0.0 / 0 votes

1. transcendental numbernoun

   any irrational number that is not an algebraic number

WikipediaRate this definition:0.0 / 0 votes

1. Transcendental number

   In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are π and e.Though only a few classes of transcendental numbers are known—partly because it can be extremely difficult to show that a given number is transcendental—transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers comprise a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental. Hence, the set of real numbers consists of non-overlapping rational, algebraic non-rational and transcendental real numbers. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x2 − x − 1 = 0. The quality of a number being transcendental is called transcendence.

ChatGPTRate this definition:0.0 / 0 votes

1. transcendental number

   A transcendental number is a number that is not a root of any non-zero polynomial equation with integer coefficients. In other words, they are not algebraic and cannot be expressed as the solution to any algebraic equations of finite degree. This means they cannot be expressed in terms of simple operations such as addition, subtraction, multiplication, division, and root extractions from integers or other algebraic numbers. Examples include Pi and Euler's number e.

WikidataRate this definition:0.0 / 0 votes

1. Transcendental number

   In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-zero polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e. Though only a few classes of transcendental numbers are known, transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable while the sets of real and complex numbers are both uncountable. All real transcendental numbers are irrational, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental; e.g., the square root of 2 is irrational but not a transcendental number, since it is a solution of the polynomial equation x² − 2 = 0.

Matched Categories

1. • Irrational Number

How to pronounce transcendental number?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say transcendental number in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of transcendental number in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of transcendental number in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=transcendental number
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Transcendental_Number
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Transcendental_Number
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=transcendental number