Is the space $c_0$ of all infinitesimal numeric sequences $a = (a_1, a_2,...,a_n,...)$ complete? The norm is $||a|| = sup|a_i|$.
As i couldn't prove that every Cauchy sequence has a limit in $c_0$ (so it'd be complete), I've been trying to find such Cauchy sequence that does not have a limit in $c_0$ to prove its incompleteness. But I haven't succeeded.