My answers.    m.a.

    Bruno,
              Can you provide definitions of  "belongs-to"  and  "included-in" 
that distinguish them from "union" and "intersection"?









      Here we met a set of sets.
      The set of subsets of a set, can only be, of course, a set of sets. The 
set {2, 21, 14} is a set of numbers. The set { { }, {4, 78, 56} } is a set of 
sets. It has two elements: the empty set {}, and the set of numbers {4, 78, 
56}. Do not confuse a number, like 24, and a set, like {24}, which is a set 
having a number has elements. In particular it is the case that  {4, 78, 56} 
belongs to { { }, {4, 78, 56} }. Take it easy, and meditate on the following 
exercise:


      Which of the following are true


      {3, 5} included-in {3, 5} True

      {3, 5} belongs-to {3, 5} True 
      {3, 5} included-in { {3, 5} } False
      {3, 5} belongs-to { {3, 5} } True


      Take your time, 


      Bruno






      http://iridia.ulb.ac.be/~marchal/





      

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