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.

Read more about this topic:  Family Of Sets

Famous quotes containing the word examples:

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)