= Solution
Take
$$
A_2=\{(1/n,0):n\geq1\}.
$$
Its only <accumulation point> is $(0,0)$, which is absent from $A_2$. Every listed point is isolated, so none belongs to $A_2'$. Consequently
$$
\boxed{A_2'=\{(0,0)\},\qquad A_2'\not\subseteq A_2,\quad A_2\not\subseteq A_2'.}
$$
For completeness, away from the origin a sufficiently small disk meets only finitely many of the listed points and can be shrunk to exclude all but its <centre>, proving there are no further <accumulation points>.
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