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Re: [ontolog-forum] What words mean

 To: "[ontolog-forum] " Christopher Menzel Sat, 23 Feb 2008 14:22:36 -0600
 ```On Feb 23, 2008, at 9:19 AM, Wacek Kusnierczyk wrote: > ... > By definition (one from graph theory, Azamat might have had other > definitions in mind), a tree is a connected acyclic graph. Undirected > trees have no roots. > > A rooted tree is a directed tree with exactly one distinguished vertex > chosen as the tree's root. Following the definition (in a rooted > tree, > there is exactly one path from the root to any other vertex in the > graph), if a tree were to have two roots, each of them would have to > be > accessible from the other, which implies a cycle in the graph; but > such > a graph is not a tree.    (01) Yes, though one can define trees so that multiple roots are allowed, though of course in those cases the trees would not be connected; you'd have what by other definitions would be called a forest, as Randall noted. This is the case for the general set theoretic definition of a tree as a partially ordered set such that the set S_n of predecessors of any node is well-ordered by the partial ordering restricted to S_n. Not surprisingly, one often subsequently finds the definition of a "normal" tree among the conditions for being which are that the tree has only one root.    (02) -chris    (03) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04) ```
 Current Thread Re: [ontolog-forum] What words mean, (continued) Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, paola . dimaio Re: [ontolog-forum] What words mean, Randall R Schulz Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Sharma, Ravi Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Azamat Re: [ontolog-forum] What words mean, paola . dimaio Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, paola . dimaio Re: [ontolog-forum] What words mean, Christopher Menzel <= Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, Wacek Kusnierczyk Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, Barker, Sean (UK) Re: [ontolog-forum] What words mean, Christopher Menzel Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, John F. Sowa Re: [ontolog-forum] What words mean, Azamat Re: [ontolog-forum] What words mean, John F. Sowa