Real numbers/Constant sequence/Example

A constant sequence ${}x_{n}:=c$ converges to the limit ${}c$. This follows immediately, since for every ${}\epsilon >0$, we can take ${}n_{0}=0$. Then we have

${}\vert {x_{n}-c}\vert =\vert {c-c}\vert =\vert {0}\vert =0<\epsilon \,$

for all ${}n$.