Transcendental numbers

In mathematics, a transcendental numbers are real or complex numbers that are not algebraic—that is, they are not a root of a non-zero polynomial equation with rational coefficients. The best-known transcendental numbers are π and e. 


Though only a few classes of transcendental numbers are known (in part because it can be extremely difficult to show that a given number is transcendental), transcendental numbers are not rare. 

Countability

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.


Source: Transcendental number. (2015, October 12). In Wikipedia, The Free Encyclopedia. Retrieved 05:47, October 14, 2015, from https://en.wikipedia.org/w/index.php?title=Transcendental_number&oldid=685372749