Transitive Set

Transitive Set

In set theory, a set A is transitive, if and only if

  • whenever xA, and yx, then yA, or, equivalently,
  • whenever xA, and x is not an urelement, then x is a subset of A.

Similarly, a class M is transitive if every element of M is a subset of M.

Read more about Transitive Set:  Examples, Properties, Transitive Closure, Transitive Models of Set Theory, See Also

Famous quotes containing the word set:

    Euclid alone
    Has looked on Beauty bare. Fortunate they
    Who, though once only and then but far away,
    Have heard her massive sandal set on stone.
    Edna St. Vincent Millay (1892–1950)