Re: Paths

In article <1179997210.751451.76210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 23 Mai, 22:55, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1179952072.517432.276...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

define a set of paths p' =/
= p which are both sufficient and *necessary* to cover p.

I can. Easily.

A NASC for set of paths p', with p' =/= p, to have every node of p is
some node of p' in an infinite tree is:
for each node, k, in p there must be at least one path p'
which contains k, but which branches off from p at or after
node k, and, of course, no p' = p.

It transpires that any such set will be infinite.
Note that if any infinite set of paths suffices, so will every infinite
subset of it, so that there is no "minimal" such set covering p.

It is, perhaps, this absence of a minimal set which has so scrambled
WM's understanding.

There is, however, a maximal such set, the set of all paths except p.

So you are not able to define a necessary set.

Wrong! I have defined a necessary and sufficient set, what I have not
defined, because there isn't one, is a minimal set.

And you cannot show
that your set is sufficient either

WRONG AGAIN! Any such set as I described is clearly quite sufficient, at
least unless WM can find any (non-leaf) node in any path that is not in
infinitely many other paths.

: For every p' we can prove that it
is insufficient and by induction we find that no p' is sufficient.

That no one path , or even finite set of paths, is sufficient does not
prove that an infinite set is insufficient, and but the proof above,
some infinite sets are sufficient.

In particular, if P is the set of all paths in a CIBT, or even an AIBT,
then P\{p} is sufficient to cover p.

Unless WM can find some node in p that is not in ANY other path
whatsoever.

Well, can yuh, WM?



But
you remain claiming (Easily!) to have a NASC and you remain claiming
that in the infinite the finite sets will be sufficient.

I have NASC, but nowhere did I say that any such covering set could be
finite. In fact I made a point of saying quite the opposite.

That is a poor performance.

AS it is a misrepresentation, possible deliberate, of my actual
performance, and poorness devolves upon WM himself.

Regards, WM
.

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