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transitive (Definition)

Let $ A$ be a set. $ A$ is said to be transitive if whenever $ x\in A$ then $ x\subseteq A$.

Equivalently, $ A$ is transitive if whenever $ x\in A$ and $ y\in x$ then $ y\in A$.



"transitive" is owned by Evandar.
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See Also: transitive closure

Other names:  transitive set

Attachments:
criterion for a set to be transitive (Theorem) by Wkbj79
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This is version 2 of transitive, born on 2002-01-23, modified 2004-03-31.
Object id is 1565, canonical name is Transitive.
Accessed 4781 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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