I'm not sure about this expression:$$\emptyset \subset \{\emptyset\}$$, I think it's false.

Question

anonymous · Answer

Its true, i think

anonymous · Answer

This is read: The empty set is a proper subset of the set containing only the empty set.

anonymous · Answer

The empty set is a subset of any set, regardless of whats in it.

anonymous · Answer

A is a subset of B if and only if for all elements x of A, x is in B.

This is vacuously true, since there are no elements x of the empty set. Hence, the empty set is a subset of the empty set

anonymous · Answer

Yeah, I know it's true for the subsets, but I mean the PROPER subset

anonymous · Answer

Proper just means the sets arent equal. So the fact that the empty set is a subset of every set, even though every set isnt empty, means its a proper subset of any non empty set.

anonymous · Answer

Ohh than you @joemath314159 now I got it clear.