Definition talk:Rooted Tree

Do we really want to enforce countability? Intuitively, $\N^\N$, the set of all sequences of natural numbers, can be represented as a rooted tree as well (though every node has countably many direct descendants, but that shouldn't be a problem). --Lord_Farin 06:37, 5 June 2012 (EDT)

The source work 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability I was using defined it as having a "finite or countable" set of nodes. Maybe they deliberately restricted the concept for their own purposes, that of providing a proof model for zeroth order logic. Shrug. --prime mover 09:33, 5 June 2012 (EDT)

No more shrugging. We should get a more general definition and an "also defined as" and all that fun stuff. --Dfeuer (talk) 20:54, 27 May 2013 (UTC)

Shrug. --prime mover (talk) 21:53, 27 May 2013 (UTC)

Why the refactor template? Looks to me like the refactoring has already been done. --prime mover (talk) 00:35, 10 December 2013 (UTC)

The header levels are off -- fixing this requires using the extension transclusion. Also, some definitions (like parent mapping) are hidden on the subpages of other definitions. The page as a whole would benefit from a reconsideration of its presentation. — Lord_Farin (talk) 09:35, 10 December 2013 (UTC)

Circular definition

In the current state of the website, the definition of the root node is dependent on the concept of an ancestor node and vice versa.

I have no access to proper literature at the moment, though, so I'm not sure what's the best way to resolve the problem.

Well not really, because we have already implicitly defined the root node as being the (unique) distinguished node. At that point the ancestry is incidental, and probably does not need to be included in the definition of root node as such, and the fact that it is an ancestor of all other nodes could be expressed as a result.

But your point is valid, and it could do with being rewritten. --prime mover (talk) 15:12, 27 December 2023 (UTC)