Transitive set

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

  • whenever x ∈ A, and y ∈ x, then y ∈ A, or, equivalently,
  • whenever x ∈ A, 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.

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