Is this true or false?
$$\emptyset \subset \emptyset $$

Question

Is this true or false?
$$\emptyset \subset \emptyset $$

anonymous · Answer

I know that the empty set is a subset of every set but I'm not sure if its a subset of itself.

anonymous · Answer

It is a subset of itself because a subset of finite set also contains that set.

anonymous · Answer

It depends if you mean just subset and proper subset.  One allows the set to be a subset of itself, and the other doesn't.

anonymous · Answer

This is really a matter of semantics, since there are notational inconsistencies regarding $ \subset$ and $ \subseteq $

anonymous · Answer

I mean proper subset. I think its false.

anonymous · Answer

but considering just a subset is TRUE.

anonymous · Answer

It is false for a proper subset, but it is a subset.

anonymous · Answer

ya its not a proper subset of itself, but it sure is a subset of itself