# Definition talk:Transitive Closure (Set Theory)/Definition 1

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## Naming

Shouldn't we find *some* way, preferably consistent, to name (completely) non-equivalent but very similar definitions, so they can be grouped together? It would be very unfortunate for this page to grow and end up with proofs that definitions 1, 2, and 4 are equivalent, and definitions 3 and 5 are equivalent. I don't think what I did is optimal by any stretch of the imagination, but I think it's a lot better than sticking such definitions on the main def page with no way to link to them... --Dfeuer (talk) 22:35, 6 April 2013 (UTC)

- Shouldn't we just.

- If you were to go back through the many discussions we have had on this subject over the last few months, you would be aware that there are multiple cases of this matter cropping up all over the place. An attempt was made in the area of natural numbers (which you are indeed well aware of because you've started contributing there as well) where parallel paths of axiomatic definitions were developed, each one in its own subcategory of the main namespace.

- As I have said before in other contexts, rather than attempt to amend individual pages so as to bolt on "alternative" definitions for these things, my suggested approach would be to go back to square one for each of these axiom schemata and construct them from the ground up. --prime mover (talk) 09:18, 7 April 2013 (UTC)