EDB — 0MT

[0MT] Given a sequence $(x_n{)}_n\subseteq X$ and $x\in X$,

• we will say that ”$(x_n{)}_n$ converges to $x$” if $\underset{n}{lim}d(x_n,x)=0$; we will also write $x_n{\to }_{n}x$ to indicate that the sequence converges to $x$.

• We will say that ”$(x_n{)}_n$ is a Cauchy sequence” if

  $$\forall \epsilon >0\exists N\in \mathbb{N},\forall n,m\ge Nd(x_n,x_m)<\epsilon .$$