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Classification of Irrational Numbers


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An irrational number expressed in decimal form / infinite continued fractions or sum of infinite series of rational numbers, can only evaluate its approximate magnitude, but cannot represent it. There are different kinds of irrational numbers. One of the kinds is generated by extraction of ischolar_mains of the positive rational numbers. The deliberation shows that all irrational numbers of this kind are not of similar category, which has been defined as the ‘order of irrational numbers’.
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  • R. Courant & H. Robbins, (edited by Stewart, I.): What is Mathematics? An Elementary
  • Approach to Ideas and Methods, 1996, 2nd Edition, New York/Oxford: Oxford University Press.
  • G. F. Simmons, ‘Introduction to Topology and Modern Analysis’, Tata McGraw Hills Edition (2004).
  • David M. Burton, ‘Elementary Number Theory’, 1995, 2nd Edition, Universal Book Stall, New Delhi.

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  • Classification of Irrational Numbers

Abstract Views: 423  |  PDF Views: 3

Authors

Nirendra Mohan Ganguli
234A N. S. C. Bose Road, Kolkata 700040, India

Abstract


An irrational number expressed in decimal form / infinite continued fractions or sum of infinite series of rational numbers, can only evaluate its approximate magnitude, but cannot represent it. There are different kinds of irrational numbers. One of the kinds is generated by extraction of ischolar_mains of the positive rational numbers. The deliberation shows that all irrational numbers of this kind are not of similar category, which has been defined as the ‘order of irrational numbers’.

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DOI: https://doi.org/10.24906/isc%2F2018%2Fv33%2Fi1%2F181784