A set without the empty set By definition, the empty set is a subset of every set, right? Then how would you interpret this set: $A\setminus\{\}$? On one hand it looks like a set without the empty set, on the other hand, the empty set is in every set... Can you explain?

The notation $A-\{\}$ roughly translates to "the set $A$ without the elements of $\{\}$."  The difference is that the empty set is not an element of $A$ and this notation just means you're not removing any elements from your original set.
