ABSTRACT
This chapter looks into the details of sequences of real numbers. To define sequences and subsequences of a sequence, one must have a way of stating precisely what kinds of subsets of the integers one wants to focus on. The chapter discusses the right increasing subsets of integers and right increasing infinite subset. The set of all values of the sequence and the subsequences is different from their range. The set of values is provided as a sequence and the range is provided as the distinct values seen in the set of all sequence values. The chapter also discusses the uniquness of limits and provides a set of proofs of convergence.
