Realanalysisisabranchofmathematicalanalysisthatdealswiththerealnumbersandreal-valuedfunctionsofarealvariable.Itrigorouslystudiesconceptssuchaslimits,continuity,differentiation,integration,andsequencesoffunctions.Thefieldprovidesthetheoreticalfoundationforcalculusandexploresthepropertiesofrealnumbers,includingcompleteness,compactness,andconnectedness.Realanalysisisessentialforunderstandingconvergence,measuretheory,andthebehavioroffunctionsinboththeoreticalandappliedmathematics,includingphysics,engineering,andeconomics.Thesubjectoftenbeginswiththeconstructionoftherealnumbersystemanddevelopstoolsforanalyzingfunctionsandtheirpropertiesinapreciseandformalmanner.
