Empty Set

An Empty Set is a set with Zero Set Members.

• AKA: Ø, Λ, Null Set.
• Context:
  • For any set A:
    • ⊆(Ø, A) ⇒ True.
    • ∪(A, Ø) ⇒ A
    • ∩(A, Ø) ⇒ Ø.
    • ×(A, Ø) ⇒ Ø.
  • It must have Set Cardinality Function = 0.
  • It can be detected by an Empty Set Relation.
  • …
• Example(s):
  • an Empty Sequence.
  • an Empty Interval.
  • an Empty String.
  • …
• Counter-Example(s):
  • an Non-Empty Set, such as a single member set.
• See: Set System.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/empty_set Retrieved:2015-6-1.
  • In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.

    Null set was once a common synonym for "empty set", but is now a technical term in measure theory. The empty set may also be called the void set.

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