= Universal planar set for countable real sections
{title2=$A=\{(c(s),s_n):s\in\mathbb R^{\mathbb N},\ n\geq1\}$}
Use <coding of real sequences by ternary digits> to give each real sequence a distinct column coordinate $c(s)\in[0,1/2]$. Put every term of that sequence in its column. The vertical <affine section of a planar set> at $c(s)$ is exactly the sequence range. Every nonempty <countable set> has such an enumeration, with repetitions allowed, while any column outside the code interval gives the empty set. This realizes every countable real subset; the other sections are unrestricted.
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