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About the Author. Robert Gardner Bartle was an American mathematician specializing in real analysis. He is known for writing various popular textbooks.The Elements Of Real Analysis Pdf presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in A revised definition might be: A function f from a set A into a set B is a rule of correspondence that assigns to each element x in A Home · Robert G. Bartle-The Elements of Real Analysis, Second Edition-Wiley (1976) (1) (1) (1).pdf The Elements of Real Analysis. Robert G. Bartle. Department of Mothematics, University of Illinois. John Wiley & Sons, Inc., New York • London • Sydney