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franky172



Posts: 158
Joined: Jan. 2007

(Permalink) Posted: July 23 2007,19:47   

Quote
You stop Franky. If it doesn't abide by the principles of hierarchy then it isn't a nested hierarchy.


I have asked you a simple question.  Do you think this is a nested hierarchy:

Code Sample

             D(sam)
            /           \
D(sam's first son) D(sam's second son)


This is a straightforward question.

 
Quote
What are the defintionS for each of your levels? Male descendant is one definition and it is also part of the definition of the whole.

I do not understand your statement.

 
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A correct rendition of a paternal family tree has the patriach at the top- alone.

Do you understand that?

It is true that in typical renditions of "family trees" we replace the notation D(sam) with simply "Sam", but this is merely shorthand - we understand that the lines connecting different people are shorthand for "descendent of" and we can interpret the names shown on the treee as belonging to the unique individual whose position is at each node.  I.e. the shorthand:

Code Sample

      Sam
     /   \
   Bill Steve

Means that Bill and Steve are descendents of Sam, and in terms of the "descendent" relationship, this structure forms a nested hierarchy since we are using an implicit shorthand for:

Code Sample

      D(Sam)
     /   \
   D(Bill) D(Steve)


 
Quote
A simple yes or no. We cannot continue until we agree on that point.

It depends what you mean by "patriarchal family tree", typically we use shorthand to represent the nested hierarchical structure that descent from a common ancestor leads to, and we simply write "X" at each node of a tree.  This is for many reasons, one of which is simplicity of notation.  That the relationship of "descended from" forms a nested hierarchical structure is not, I believe, in dispute, so what you appear to be arguing over is notation.  Do we agree that we can sort the descendents of a person into a nested hierarchy, and that with slight change of notation this structure is identical to the colloquial "family tree"?

 
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By including all male decendants into the top superset D(x) you no longer have a paternal family tree.

I believe that the notation D(x) explicitly shows that decent-based relationships form nested hierarchies, regardless of whatever definition of "paternal family tree" you want to use.  Do we agree?

Now that I have answered your questions, there are several questions that have been posed to you that remain unanswered.  Would you do us the favor of answering them?

  
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