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1.8.8 Advanced Topic: Lists as Sets

Mathematica usually keeps the elements of a list in exactly the order you originally entered them. If you want to treat a Mathematica list like a mathematical set, however, you may want to ignore the order of elements in the list.

Set theoretical functions.

  • Union gives the elements that occur in any of the lists.
  • In[1]:= Union[{c, a, b}, {d, a, c}, {a, e}]


  • Intersection gives only elements that occur in all the lists.
  • In[2]:= Intersection[{a, c, b}, {b, a, d, a}]


  • Complement gives elements that occur in the first list, but not in any of the others.
  • In[3]:= Complement[{a, b, c, d}, {a, d}]