# Real Analysis by sc malik and savita arora

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Real analysis is the area of mathematics dealing with real numbers and the analytic properties of real-valued functions and sequences. In this course we shall develop concepts such as convergence, continuity, completeness, compactness and convexity in the settings of real numbers, Euclidean spaces, and more general metric spaces.

Real analysis is part of the foundation for further study in mathematics as well as graduate studies in economics. A considerable part of economic theory is difficult to follow without a strong background in real analysis. For example, the concepts of compactness and convexity play an important role in optimisation theory and thus in microeconomics.

The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set R together with two binary operations denoted + and ⋅, and an order denoted <. The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique complete ordered field, in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness means that there are no 'gaps' in the real numbers. This property distinguishes the real numbers from other ordered fields (e.g., the rational numbers Q) and is critical to the proof of several key properties of functions of the real numbers

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RISING STAR BOOKLETS
BALWAN MUDGAL SIR BOOKLETS
PIAM ACADEMY TEST SERIES
BALWAN SIR TEST SERIES
DIPS ACADEMY TEST SERIES
DIPS ACADEMY HANDWRITTEN NOTES
PIAM ACADEMY HANDWRITTEN NOTES
AIM ACADEMY HANDWRITTEN NOTES
RK RATHORE SIR HANDWRITTEN NOTES
ARHIANT PUBLICATION BOOK
UNIQUE PUBLICATION BOOK
LINEAR ALGEBRA BOOKS
REAL ANALYSIS BOOKS
COMPLEX ANALYSIS BOOKS
ABSTRACT ALGEBRA BOOKS
DIFFERENTIAL EQUATION BOOKS
PDE BOOKS