# Is it a Transitive Set?

Is $\{\{0\},\{\{0\}\}\}$ a transitive set? Or only $\{0,\{0\},\{\{0\}\}\}$ is transitive?

if the first isnt a transitive set, can someone give me an example of a transitive set which does not contain urelements?

Thanks!

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@vadim123: That would be a set that DOES contain urelements. (Whether such a set can be transitive depends on the exact definition of "transitive" you're working with). –  Henning Makholm Oct 18 '13 at 19:52
$\{\varnothing,\{\varnothing\},\{\{\varnothing\}\}\}$ is a transitive set that does NOT contain urelements. –  Henning Makholm Oct 18 '13 at 19:53

We have $0\in\{0\}$ and $\{0\}\in\{\{0\},\{\{0\}\}\}$, but $0\notin\{\{0\},\{\{0\}\}\}$, so no, it is not transitive.
$\{\}$ is transitive and has no urelements.