Question

what is the difference with an empty set and the zero with a line in it?

Answer 1

they are basically the same thing, the only difference is that one of them is just two curly braces, and the other is a zero with a line in it :P because they both mean empty or null set.

Answer 2

{ } is an empty set and
∅ is the symbol used to denote an empty set
but they both mean empty set

read this http://en.wikipedia.org/wiki/Empty_set