Identifying Irrationals

R. Sivaraman

Abstract: Irrational numbers have always been a fascination to mathematicians for several millennia. This is because Irrational numbers neither terminate nor repeat in their decimal expansion. Hence exploring the next set of digits after a given decimal place has kept many mathematicians and computer scientists busy in past few decades. A classic example is exploration of digits of the most famous and important real number. In this paper, I shall present a novel method with proof using analysis to find the rational numbers which are very good approximations to the given Irrational Number and present a more general method of finding approximations to all Algebraic numbers.

Keywords: Irrational Numbers, Sequence and Sub-sequence, Cauchy Sequence, Convergence, Algebraic Numbers, Approximations