# Definition(s) > [!NOTE] Definition 1 (Complete Metric Space) > Let $(X,d)$ be a [[Metric Space|metric space]]. Then $(X,d)$ is complete iff every [[Cauchy Sequence|Cauchy sequence]] is [[Convergence|convergent]], i.e. its limit lies in $X.$ > [!Example] Example > See [[The Space of Continuous & Bounded Real Functions is Complete wrt Supremum Norm]] # Properties(s) # Application(s) **More examples**: # Bibliography