I'm trying to understand why the empty set is a subset of every set and this is my reasoning (please correct me if I'm wrong):
By definition of a set S is a subset of a set A if all it’s elements are in A. ∅ has no elements if ∅ is not a subset of A then there is an element in ∅ that is not in A but ∅ as not elements. So ∅ is a subset of A by contradiction.
does it really follow that because the empty set has no elements it is a subset of every set? I mean imagine this: I have a box with nothing in it (the empty set). then I have a box with something in it (3 balls if you will). how is "nothingness" (if I may call the element of the empty set that) be in a box that has something in it already (the three balls).