$\displaystyle {Let \ x _n \ be \ a \ sequence \ of \ integers \ ; \ x_n \in Z \ , \ \forall n \in N } $ $\displaystyle { . If \ x_n \ is \ cauchy \ , \ prove \ that \ x_n \ is \ eventually \ constant \ }$

$\displaystyle {(i.e , \exists c\in Z , \exists k \in N \ s.t \ x_n =c , \forall n \geq k )} $