real analysis, sequence of sequences convergence proof

1. The problem statement, all variables and given/known data

[itex]\ell[/itex] is the set of sequences of real numbers where only a finite number of terms is non-zero, and the distance metric is [itex]d(x,y) = sup|x_n - y_n|[/itex], for all n in naural-numbers

then the sequence [tex]u_k =...



real analysis, sequence of sequences convergence proof

real analysis, sequence of sequences convergence proof