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


  Take your time, 


  Bruno






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






  

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