Thriving Towards Transcendental

Abstract

In this paper, I had attempted to find a novel method to determine the approximations to transcendental numbers, which are integral part of real number system with an elegant approach, which in turn can be very effectively used in various applications to different branches of Sciences.

Real numbers are basic entities of the mathematical world. It took quite a long time for humanity to fully understand about the nature of Real Numbers. In fact, after Cantor’s description of the countable and uncountable versions, the world came to know clearly about the true structure of real numbers. Real numbers are classified broadly in to Rational and Irrational numbers. But for mathematicians, real numbers can be divided in to Algebraic numbers and Transcendental numbers.

Algebraic numbers are those real numbers which are roots of a polynomial with integer coefficients. For example, the number  is Algebraic, since it is a root of the equation . Similarly, the number is Algebraic, for the fact that it is a root of the polynomial equation . Now there are certain numbers which are not roots of any polynomial equations with integer coefficients. For example, the numbers and the logarithmic base, e are not roots of any polynomial with integer coefficients. Such numbers are called “Transcendental Numbers”. This paper provides an easy way of determining such wonderful and useful numbers