Chris and Sean, (01)
I agree with Chris on the following point, but there could
be another way of thinking about the data structure. (02)
CM> Multi-root trees (when allowed) necessarily consist of multiple
> "independent" (i.e., pairwise disconnected) single-root trees. (03)
SB>> having multiple roots requires that at least one node has at least
>> two parents. (04)
CM> By any standard definition, no such structure is a tree. (05)
I'm not sure what Sean intended, but perhaps he was thinking in terms
of a computer implementation. For example, one might implement a tree
(as defined by the formalism) in a computer data structure that has more
than one pointer to various nodes on the tree. (06)
In that sense, you could say that the formal mathematical structure
was a tree (or a forest or whatever), but the implementer chose to add
auxiliary pointers to nodes on the tree for convenience in accessing
or processing the tree. (07)
If you do something like that, it's important to distinguish the
formal structure and the operations that are formally defined on it
from auxiliary operations that handle I/O or indexing. (08)
John (09)
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