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

Posted in Notes | Tagged , , , , , , , | Leave a comment

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 , , , , , | Leave a comment