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

How to Cite?: R. Sivaraman, "Identifying Irrationals", Volume 6 Issue 3, March 2017, International Journal of Science and Research (IJSR), Pages: 1849-1851, https://www.ijsr.net/getabstract.php?paperid=ART20171822, DOI: https://dx.doi.org/10.21275/ART20171822