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transitive closure (Definition)

The transitive closure of a set $X$ is the smallest transitive set $\operatorname{tc}(X)$ such that $X\subseteq \operatorname{tc}(X)$

The transitive closure of a set can be constructed as follows:

Define a function $f$ on $\omega$ by $f(0)=X$ and $f(n+1)=\bigcup f(n)$ $$\operatorname{tc}(X)=\bigcup_{n<\omega} f(n)$$




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

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Cross-references: function, transitive set
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This is version 1 of transitive closure, born on 2002-09-28.
Object id is 3486, canonical name is TransitiveClosure.
Accessed 6341 times total.

Classification:
AMS MSC03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )

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