TRANSCENDENTAL NUMBER Meaning and
Definition
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A transcendental number is a real number that is not a solution to any non-zero polynomial equation with integer coefficients. In other words, it is a number that cannot be expressed as a root of any polynomial equation with integer coefficients, irrespective of the degree of the polynomial. Transcendental numbers are not algebraic, meaning they are not the solution to any algebraic equation.
The concept of transcendental numbers was first introduced by Joseph Liouville in 1844, and later proved to exist by Carl Gustav Jacob Jacobi and Charles Hermite. The existence of transcendental numbers was a groundbreaking discovery in the realm of mathematics.
Transcendental numbers are inherently irrational and possess infinite decimal expansions with no repeating pattern or periodicity. Familiar examples of transcendental numbers include the mathematical constants π (pi) and e (the base of the natural logarithm), which have been proven to be transcendental.
The properties of transcendental numbers make them highly significant in various mathematical branches, such as number theory, algebraic geometry, and mathematical analysis. They carry a certain level of mystery and fascination due to their uncountable nature and inability to be expressed as a solution to a polynomial equation. Transcendental numbers play a crucial role in challenging and expanding the boundaries of mathematical knowledge and research.
Common Misspellings for TRANSCENDENTAL NUMBER
- rranscendental number
- franscendental number
- granscendental number
- yranscendental number
- 6ranscendental number
- 5ranscendental number
- teanscendental number
- tdanscendental number
- tfanscendental number
- ttanscendental number
- t5anscendental number
- t4anscendental number
- trznscendental number
- trsnscendental number
- trwnscendental number
- trqnscendental number
- trabscendental number
- tramscendental number
- trajscendental number
Etymology of TRANSCENDENTAL NUMBER
The word transcendental comes from the Latin word transcendere, which means to climb over or to go beyond. It refers to something that goes beyond or surpasses the limits of ordinary experience or understanding. The term transcendental number was introduced by the German mathematician Carl Friedrich Gauss in the early 19th century. It was used to describe a type of number that is not a root of any non-zero polynomial equation with integer coefficients. These numbers transcend algebraic methods and cannot be expressed as a fraction or a root of an algebraic equation, hence the term transcendental.
