Re: Review of Mueckenheims book.

On 22 Apr., 19:05, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1177230618.152409.276...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
And since each path bunch contains an uncountable number of
paths, there are an uncountable number of paths.

May be. But they cannot be distinguished unless they have separated.
For each separation, however, a node is required. Therefore only
countably many paths can be distinguished from one another.

Everyone but WM can "distinguish" that there are more than countably
many paths in a CIBT.

That he cannot do so is a direct result of his willful blindness to such
proofs as the following:

Down to level L(n) with n e N 2^n path bunches have been separated
while there are 2^(n+1) - 1 nodes. The ratio of separated path to
nodes is 2^n/(2^(n+1) - 1). The limit for the infinite tree is
therefore
lim[n-->oo] 2^n/(2^(n+1) - 1) = 0 < 1.
Every path is simultaneously a path bunch, because down to level L(n)
every node belonging to path p is also a node of path p' =/= p. This
holds for every n in N - and others are not available. If we denote
the n-th node belonging to path p by K(p,n) then we have:
forall K(p,n) with n in N thereis p' such that forall m in N with m =<
n : K(p',m) = K(p,m).
Hence every path is a bunch of paths. Hence the limit shown above is
valid for every path.

Thus Card(set of paths) =< Card(set of nodes) = Card(N)

öper edei deixai.


Regards, WM

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