Family of Sets - Examples

Examples

  • The power set P(S) is a family of sets over S.
  • The k-subsets S(k) of a set S with n elements form a family of sets.
  • Let S = {a,b,c,1,2}, an example of a family of sets over S (in the multiset sense) is given by F = {A1, A2, A3, A4} where A1 = {a,b,c}, A2 = {1,2}, A3 = {1,2} and A4 = {a,b,1}.
  • The class Ord of all ordinal numbers is a large family of sets; that is, it is not itself a set but instead a proper class.

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