What Does Transcendental Mean In Math?


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Yooti Bhansali Profile
Yooti Bhansali answered
In the area of mathematics, a transcendental number is that number which is either real or complex, but is not algebraic. In other words, a transcendental number is that which is not the answer to a non zero polynomial equation having integer coefficients.

The most widely known instance of a transcendental number is pi. Only limited sets of transcendental numbers are identified by man, as establishing that a particular number is transcendental in nature is very complicated.

The possible credit for identifying and describing transcendental numbers in the modern context goes to Euler. The word 'transcendentals' derives from Leibniz in a paper he wrote in 1682; proving sin (x) was not an algebraic function of x (2). The presence of transcendental numbers was first identified by Joseph Liouville in the year 1844.
Thomas Gallagher Profile
In mathematics, a transcendental number is a number (possibly a complex number) which is not algebraic—that is, it is not a solution of a non-constant polynomial equation with rationalcoefficients.The most prominent examples of transcendental numbers are π and e. Only a few classes of transcendental numbers are known. This is partly because it can be extremely difficult to show that a given number is transcendental.However, transcendental numbers are not rare: Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable, but the sets of real and complex numbers are uncountable. All real transcendental numbers are irrational, since all rational numbers are algebraic. The converse is not true: Not all irrational numbers are transcendental (however, most are).

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