= Pointwise limit
{title2=$f(x)=\lim_{n\to\infty}f_n(x)$}
A <pointwise limit> assigns to each input the <limit of a sequence> of <function> values there, on the specified <domain of a function>. It is unique wherever it exists, by uniqueness of the numerical <limit of a sequence>. Its existence supplies no common approximation rate over the <domain of a function>. For $f_n(x)=x^n$ on $[0,1]$, it equals zero below one and one at one; restricting to $[0,a]$ with $a<1$ gives the zero <function>.
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