empty set

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empty set (plural empty sets)

  1. (set theory) The unique set that contains no elements, denoted or {}.
    • 1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257:
      Start with the empty set. We define it as “the set of all objects not equal to themselves,” since there are no such objects. All empty sets have the same members—no members at all! Therefore, as sets they're identical, by definition of identity of sets. In other words, there's only one empty set. This unique empty set is our building block. Next comes the set whose only member is—the empty set. This set is not empty.
    • 2004, Michael Potter, Set Theory and its Philosophy, Oxford University Press, page 58:
      The existence of the empty set is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever.
    • 2007, A. K. Sharma, Measure Theory, Discovery Publishing House, page 1:
      A topological space may be very sparsely endowed with open sets. As we know, some spaces have only two, the empty set and the full space.
    • 2008, Sam Gillespie, The Mathematics of Novelty: Badiou's Minimalist Metaphysics, re.press, page 57:
      Their existence can be generated on the basis of the empty set, since one is simply the set of the empty set, two is simply that set plus the empty set and so forth.



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