$\varnothing \subseteq A, \forall A$ What if $A = \varnothing$? I was just wondering, we know that $\varnothing \subseteq A$ for all $A$ but what if $A = \varnothing$? 
Then how does it make sense that $\varnothing \subseteq \varnothing$?
Thanks
 A: It does make sense, because for every set $A$ it is true that $A\subseteq A$.
A: Every element of the empty set is an element of the empty set. Is there a particular element of the empty set that is not an element of the empty set? Answer: no. Therefore, $\emptyset \subseteq \emptyset$
A: Do it using Venn diagrams.  Draw a circle with nothing in it.  This represents the empty set.  Now draw another circle inside the circle you just drew.  This will show you that the empty set is a subset of the empty set.
A: An alternative way to think about it: could is be that $\varnothing$ is not a subset of $\varnothing$?
Well, to show that $A$ is not a subset of $B$, we would find a suitable element $x$, then confirm that it is in $A$ and not in $B$.
In the case we are looking at we do it as follows: take an element $x$; confirm that $x\in\varnothing$. . . oops. . . we don't even get started since $x$ can't be an element of $\varnothing$.
Therefore it is impossible that $\varnothing$ is not a subset of $\varnothing$, which means that $\varnothing$ is a subset of $\varnothing$.
