Transcendental Numbers
By Sally Itani and Issam Mneimneh
Two types of numbers:
In mathematics, there are two types of numbers: Algebraic and transcendental.
An algebraic number is any number that can be written as a root of a polynomial with rational coefficients.
Where did transcendental Numbers come from?
Transcendence theory is concerned with the converse question of algebraic numbers:
if we are given a complex number "a", can we find a polynomial P with rational coefficients such that P(a) = 0?
If not, then the number is called transcendental.
Properties of Transcendental Numbers
1) A transcendental number cannot be written as a root of a polynomial equation with rational coefficients.
2) Every transcendental number is irrational, but the opposite is not true.
3) A transcendental number cannot be written as a sum of algebraic terms.
4) For any two transcendental numbers "a" and "b", at least one of "ab" or "a+b" is transcendental.
Examples of Transcendental Numbers
Where "a" is algebraic and not equal to 0 or 1
Where "a" is nonzero and algebraic