What is an empty family of subsets?

[Aziza]

At the beginning of a question my book is saying: "Let the universe of discourse be the set ℝ of real numbers, and let $A$ be the empty family of subsets of ℝ.."

How on Earth can an empty family contain sets which are subsets of something? A family is a set whose elements are sets. If the family is empty, it cannot contain any elements. Thus it cannot contain sets which are subsets of ℝ! Am I right?

 

[Hurkyl]

How on Earth can an empty family contain sets which are subsets of something?

It doesn't. That's why it's an empty family.

 

[Aziza]

It doesn't. That's why it's an empty family.

Then why can't my book just say, Let A be an empty family. Why is it saying, Let A be an empty family of subsets ??