Solution
= Solution
{c}
\b[True.] Write $s=\sup A$ and $u=\sup\{\sup R_m:m\geq1\}$. All these <suprema> exist in $[0,1]$. Since $R_m\subseteq A$, we have $\sup R_m\leq s$ for every $m$, hence $u\leq s$. Conversely, every $x_{m,n}\leq\sup R_m\leq u$, so $u$ is an <upper bound> of $A$ and $s\leq u$. Thus the <iterated extrema of an array> satisfy
$$
\boxed{\sup A=\sup_{m\geq1}\sup_{n\geq1}x_{m,n}.}
$$