Editing Mathematical analysis (section)

=== Real analysis ===
{{Main|Real analysis}}
Real analysis (traditionally, the "theory of functions of a real variable") is a branch of mathematical analysis dealing with the [[real number]]s and real-valued functions of a real variable.<ref>{{cite book |last=Rudin |first=Walter |author-link=Walter Rudin |title=Principles of Mathematical Analysis |url=https://archive.org/details/principlesofmath00rudi |url-access=registration |series=Walter Rudin Student Series in Advanced Mathematics |date=1976 |edition=3rd |publisher=McGraw–Hill |isbn=978-0070542358}}</ref><ref>{{cite book |last=Abbott |first=Stephen |title=Understanding Analysis |series=Undergraduate Texts in Mathematics |isbn=978-0387950600 |date=2001 |location=New York |publisher=Springer-Verlag}}</ref> In particular, it deals with the analytic properties of real [[function (mathematics)|functions]] and [[sequence]]s, including [[Limit of a sequence|convergence]] and [[limit of a function|limits]] of [[sequence]]s of real numbers, the [[calculus]] of the real numbers, and [[continuous function|continuity]], [[smooth function|smoothness]] and related properties of real-valued functions.