= Supremum error
{title2=$E_n=\sup_{x\in X}|f_n(x)-f(x)|$}
For <functions> taking values in <real numbers> on a nonempty <domain of a function> $X$, the <supremum error> is the <supremum> of the <absolute value> of the approximation error over all inputs. It may be infinite and need not be attained. When finite, it is the <supremum norm> of $f_n-f$; <uniform convergence> is exactly $E_n\to0$. Bounding this one quantity gives an accuracy guarantee for every input, including inputs that change with $n$.
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