Cauchy-Folge

∀ϵ>0∃n0∈N∀m,n⩾n0:∥xn−xm∥<ϵ\begin{equation} \forall \epsilon>0 \exists n_{0} \in \mathbb{N} \forall m, n \geqslant n_{0}:\left\|x_{n}-x_{m}\right\|<\epsilon \end{equation}