Is it possible for a set to equal another set, yet the former set be an element in the latter set? I.e.:
$\mathcal{X} = \mathcal{Y}$, yet $\mathcal{X} \in \mathcal{Y}$
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1See this. – David Mitra Apr 16 '19 at 10:54
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Also see this. – drhab Apr 16 '19 at 11:38
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1It's much clearer to just ask, "Can a set be an element of itself?" – Noah Schweber Apr 16 '19 at 12:03
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Working along the lines of @Noah, this is really just asking if $X\in X$ is even possible. I've marked this as a duplicate of a handful of questions related to this. There might be more. – Asaf Karagila Apr 16 '19 at 13:00