Sum theorem of Cauchy
= Sum theorem of Cauchy
{c}
The continuity assertion for sums of continuous <functions> in the <Cours d'analyse by Augustin-Louis Cauchy>, Chapter VI, §I. Under a modern pointwise reading the assertion needs stronger control: $x^n$ on $[0,1]$ has a discontinuous <pointwise limit>. <Uniform convergence> supplies a sufficient hypothesis through the <uniform limit theorem>.