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Finite, Infinite , Countable and Uncountable Sets of Real Numbers
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Classroom Contents
A Basic Course in Real Analysis
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- 1 Limit Theorems for functions (CH_30)
- 2 Continuity of Functions (Ch-30)
- 3 Finite, Infinite , Countable and Uncountable Sets of Real Numbers
- 4 Types of Sets with Examples,Metric Space
- 5 Various properties of open set, closure of a set
- 6 Ordered set, Least upper bound, greatest lower bound of a set
- 7 Compact Sets and its properties
- 8 Weiersstrass Theorem, Heine Borel Theorem,Connected set
- 9 Tutorial II
- 10 Concept of limit of a sequence
- 11 Some Important limits, Ratio tests for sequences of Real Numbers
- 12 Cauchy theorems on limit of sequences with examples
- 13 Theorems on Convergent and Divergent sequences
- 14 Cauchy sequence and its properties
- 15 Infinite series of real numbers
- 16 Comparision tests for series, Absolutely convergent and Conditional Convergent series
- 17 Tests for absolutely convergent series
- 18 Raabe's test, limit of functions, Cluster point
- 19 Some results on limit of functions
- 20 Limit Theorems for Functions
- 21 Extension of limit concept (One sided limits)
- 22 Continuity of Functions
- 23 Properties of Continuous functions
- 24 Boundedness theorem, Max-Min Theorem and Bolzano's theorem
- 25 Uniform continuity and Absolute continuity
- 26 Types of Discontinuities, Continuity and Compactness
- 27 Continuity and Compactness (Contd.) Connectedness
- 28 Continuum and Exercises
- 29 Equivalence of Dedekind and Cantor's Theory
- 30 Irrational numbers, Dedekind's Theorem
- 31 Rational Numbers and Rational Cuts
- 32 Cantor's Theory of Irrational Numbers (Contd.)
- 33 Cantor's Theory of Irrational Numbers
- 34 Continuum and Exercises (Contind..)
