Talk:Transitive set
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[edit] Transitive set vs. transitive relation
A set A in not transitive iff ∈ is transitive on A. Example 1: A={0,{0},{{0}}} is a transitive set, but ∈ is not transitive on A. Example 2: ∈ is transitive on A={{0}}, but A is not a transitive set. -- EJ 13:18, 17 August 2005 (UTC)
- My mistake. I was trying to find justification for using the same word -- possibly historical justification. -- Arthur Rubin 14:06, 17 August 2005 (UTC)
- Well, the conditions look similar, at least if you strip all quantifiers and not bother much what letter denotes what. I am not sure if there is a more coherent justification of the name. -- EJ 14:24, 17 August 2005 (UTC)
[edit] Urelements and subsets
Explaining my revert: A urelement cannot be a subset of anything because it is not a set. -- Arthur Rubin 19:17, 24 September 2005 (UTC)
[edit] Transitive closure
Could this be a good place to elaborate on transitive closure rather than creating a separate article for it and have to repeat most of the context? If so a redirect will be needed to this page from Transitive closure. Vonkje 16:15, 8 September 2006 (UTC)
- You are welcome to elaborate on transitive closure here, especially because the current article is just a short stub. However, a redirect would be problematic, as transitive closure already exists, and describes a different but presumably more common usage of the term. -- EJ 17:05, 8 September 2006 (UTC)
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- I added a disambiguation link from transitive closure to this article back in April 2006. JRSpriggs 07:05, 9 September 2006 (UTC)
[edit] Category Theory and Transitive Sets?
It would be quite interesting were transitive closure a universal object or other category construction. Does anyone know?Rich 01:34, 9 September 2006 (UTC)
- I doubt it is possible. Transitive sets and transitive closures are hopelessly non-invariant under isomorphism in any category I can think of. -- EJ 23:43, 9 September 2006 (UTC)
