Re: Paths

In article <1179997972.837565.198880@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 24 Mai, 06:31, William Hughes <wpihug...@xxxxxxxxxxx> wrote:
On May 23, 4:42 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:


True or false

An infinite set of paths can be replaced by
a fixed single path belonging to the set.

True (if infinite paths and sets of paths do exist).

Note: if infinite paths and sets of paths do exist!

Please resolve the following contradiction.

Consider the set R.

You claim that R can be replaced by a single
fixed path in R, call this path R_D.

The set R contains an infinite number of zero
nodes.

R_D contains a finite number of zero nodes.

(Note: The question is not whether
there is a path in R that cannot be replaced,
the question is whether R can be replaced
by a single fixed path.)

You claim that the set R can be replaced by an infinite set P of
finite paths p.

Misrepresenting what others say is the fallacy called the straw man.

For any path p in an infinite binary tree, the set
Q(p) = {p': p' is a path and p' =/= p} 'covers' every node of p

Please resolve the following contradiction: From the finiteness of
each p we know that it is insufficient. How can you claim that this
situation changes for infinitely many paths p?

By showing that every node of p is in some path other than p.

Hint: In the finite sequence 1,2,3,..., n every element is less than
oo. Why do you believe that in the infinite sequence 1,2,3,... there
is at least one element as large as oo?

Another straw man. Irrelevant, as usual.

WM has a penchant for focusing on irrelevancies while ignoring
essentials.

Or a bit more suggestive:

In the finite sequence 1,1,1,...,1 every element is less than 2. Why
do you believe that in the infinite sequence 1,1,1,... there is at
least one element as large as 2?

Another straw man!

Regards, WM
.

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