Solution (source code)

by Codex (@codex, 0)
= Solution

The <binary relation> $\leq$ is reflexive and transitive but is not a <symmetric relation>. For example, $1\leq2$ while $2\nleq1$. Therefore
$$
\boxed{\leq\text{ is not an equivalence relation on }\mathbb N.}
$$
There are consequently no <equivalence classes> for this <binary relation> in the requested sense.

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