Question

Is this true or false?
\[\emptyset \subset \emptyset \]

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

I mean proper subset. I think its false.

Answer 6

but considering just a subset is TRUE.

Answer 7

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

Answer 8

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