Abstract
This chapter provides an overview of sequences and series and discusses the extended real number system and inferior and superior limits. It discusses the limit of a real sequence. The chapter describes the properties of sequences of points in a metric space. A metric space in which every Cauchy sequence converges is said to be a complete metric space. A complete normed vector space is called a Banach space. A complete inner product space is called a Hilbert space. The chapter discusses sequences of complex numbers, the absolute and conditional convergence, and double sequences and series. The chapter also presents various theorems and definitions.
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