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Tag Archives: completeness of reals
Basic Analysis: Sequence Convergence (2)
Monotone Convergence We start with a useful theorem. Monotone Convergence Theorem (MCT). A sequence is monotonically increasing (or just increasing) if for all n. Now the theorem says: an increasing sequence with an upper bound is convergent. Proof. Let L = sup{a1, a2, … }, … Continue reading
Basic Analysis: Sequence Convergence (1)
Much of analysis deals with the study of R, the set of real numbers. It provides a rigourous foundation of concepts which we usually take for granted, e.g. continuity, differentiation, sequence convergence etc. One should have a mental picture of the … Continue reading
Posted in Notes
Tagged analysis, completeness of reals, convergence, infimum, sequences, supremum
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