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What is an empty family of subsets?

  1. Oct 10, 2012 #1
    At the beginning of a question my book is saying: "Let the universe of discourse be the set ℝ of real numbers, and let [itex]A[/itex] 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?
  2. jcsd
  3. Oct 10, 2012 #2


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    It doesn't. That's why it's an empty family.
  4. Oct 10, 2012 #3
    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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