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empty set is an subset of any sets maybe any collection of sets.

I wonder what about the case of the empty set being a member,not subset, of any collection (family) of sets.

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    $\begingroup$ No, there is no reason why it should be an element. $\endgroup$
    – Tobias Kildetoft
    Mar 11, 2015 at 10:29
  • $\begingroup$ The empty set is an element of every power set. $\endgroup$
    – Dan Christensen
    Mar 11, 2015 at 17:04

3 Answers 3

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This not true in general. For example, the empty set is a collection of sets that does not contain the empty set (because it does not contain any members).

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  • $\begingroup$ Nice seeing familiar names. $\endgroup$
    – Asaf Karagila ♦
    Mar 11, 2015 at 11:02
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Counterexample: the only element of $\{\{\emptyset\}\}$ is $\{\emptyset\}\ne\emptyset$.

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$\varnothing\in\mathcal{P}(\varnothing)$ but $\varnothing\notin \varnothing$.

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