What is an empty family of subsets?

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An empty family of subsets refers to a collection that contains no sets, meaning it cannot have any subsets of the universe of discourse, in this case, the set of real numbers ℝ. The confusion arises from the terminology; an empty family is still defined in relation to a larger set, but it contains no elements. The phrase "empty family of subsets" emphasizes that while the family is empty, it is conceptually tied to subsets of ℝ. The book's wording is intended to clarify the context, even though it may seem redundant. Understanding this distinction helps clarify the concept of empty families in set theory.
Aziza
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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?
 
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Aziza said:
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.
 
Hurkyl said:
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 ??
 

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