Editing Real analysis (section)

===Relation to complex analysis===
Real analysis is an area of [[mathematical analysis|analysis]] that studies concepts such as sequences and their limits, continuity, [[derivative|differentiation]], [[integral|integration]] and sequences of functions. By definition, real analysis focuses on the [[real number]]s, often including positive and negative [[infinity (mathematics)|infinity]] to form the [[extended real line]]. Real analysis is closely related to [[complex analysis]], which studies broadly the same properties of [[complex number]]s. In complex analysis, it is natural to define [[derivative|differentiation]] via [[holomorphic functions]], which have a number of useful properties, such as repeated differentiability, expressibility as [[power series]], and satisfying the [[Cauchy integral formula]].

In real analysis, it is usually more natural to consider [[Differentiable function|differentiable]], [[smooth functions|smooth]], or [[harmonic functions]], which are more widely applicable, but may lack some more powerful properties of holomorphic functions. However, results such as the [[fundamental theorem of algebra]] are simpler when expressed in terms of complex numbers.

Techniques from the [[theory of analytic functions]] of a complex variable are often used in real analysis – such as evaluation of real integrals by [[residue theorem|residue calculus]].