Sequences and Convergence

This chapter introduces a major concept in analysis: convergence. Loosely put, the concept allows for a set of objects (often the outputs of a function) to get “closer and closer” to a given object (usually a target point in the codomain of the function). The chapter uses this broad concept repeatedly throughout the text, but it introduces it in a natural way here: by exploring what it means for a sequence of real numbers to converge to real number. The chapter proves a collection of properties of limits, sequences, and convergence that will prove useful to us. The main results describe algebraic rules involving limits.