Real analysis is an area of mathematics that deals with sets and sequences of real numbers , as well as functions of one or more real variables . As one of the main branches of analysis , it can be seen as a subset of complex analysis , many results of the former being special cases of results in the latter . Real analysis is also used as a starting point for other areas of analysis , such as complex analysis , functional analysis , and harmonic analysis , as well as motivating the development of topology , and as a tool in other areas , such as applied mathematics .