 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The <sequence of functions> $(f_n)$ <converges uniformly> to $f$ on $E$ if
$$
\forall\varepsilon>0\ \exists N\ \forall n\geq N\ \forall x\in E:\quad |f_n(x)-f(x)|<\varepsilon.
$$
The same $N$ must work for every $x$. Equivalently, the <supremum norm> of $f_n-f$ tends to zero. This is stronger than <pointwise convergence>, where $N$ may depend on $x$.

 Back to article page