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Unit 7: Convergent Sequence
Answers: Self Assessment Notes
1. converges/diverges 2. bounded
3. compact metric 4. convergent subsequence
5. Cauchy sequence converges
7.12 Further Readings
Books Walter Rudin: Principles of Mathematical Analysis (3rd edition), Ch. 2, Ch. 3.
(3.1-3.12), Ch. 6 (6.1 - 6.22), Ch.7(7.1 - 7.27), Ch. 8 (8.1- 8.5, 8.17 - 8.22).
G.F. Simmons: Introduction to Topology and Modern Analysis, Ch. 2(9-13),
Appendix 1, p. 337-338.
Shanti Narayan: A Course of Mathematical Analysis, 4.81-4.86, 9.1-9.9, Ch.10,Ch.14,
Ch.15(15.2, 15.3, 15.4)
T.M. Apostol: Mathematical Analysis, (2nd Edition) 7.30 and 7.31.
S.C. Malik: Mathematical Analysis.
H.L. Royden: Real Analysis, Ch. 3, 4.
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