Transitive Set
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.
Read more about Transitive Set: Examples, Properties, Transitive Closure, Transitive Models of Set Theory, See Also
Famous quotes containing the word set:
“I have heard, in such a way as to believe it, of your recently saying that both the Army and the Government needed a Dictator. Of course it was not for this, but in spite of it, that I have given you the command. Only those generals who gain success, can set up dictators.”
—Abraham Lincoln (1809–1865)