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I'm taking Discrete Mathematics and am a little confused on the "empty set" or "null set" defined by ∅.

I understand that ∅ is not a member of {∅} but is ∅ a member of {∅, {∅}} given that there is a null set inside this set?

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marked as duplicate by Kevin Carlson, William, Sujaan Kunalan, Moishe Kohan, user147263 Sep 14 '14 at 2:59

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    $\begingroup$ $\phi$ infact is a member of $\{\phi \}$ $\endgroup$ – voldemort Sep 14 '14 at 2:20
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    $\begingroup$ $\emptyset$ has no elements. $\{ \emptyset \}$ has an element, namely $\emptyset$. $\{ \emptyset, \{ \emptyset \} \}$ has two elements, namely $\emptyset$ and $\{ \emptyset \}$. $\endgroup$ – Ian Sep 14 '14 at 2:20
  • $\begingroup$ math.stackexchange.com/questions/302064/… $\endgroup$ – Vikram Sep 14 '14 at 2:20