Re: Review of Mueckenheims book.

In article <1174141114.644013.135130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 16 Mrz., 15:40, "William Hughes" <wpihug...@xxxxxxxxxxx> wrote:
On Mar 16, 8:30 am, mueck...@xxxxxxxxxxxxxxxxx wrote:

On 15 Mrz., 15:21, "William Hughes" <wpihug...@xxxxxxxxxxx> wrote:
You appear to have changed the meaning of "projection" beyond
all recognition. Please define projection.

A projection is the process of gaining information about the Waft
Maximum (WM) of a set or about "what the projection does".

In other words the term "projection" is essentially meaningless.

It denotes the process, like multiplying or integrating.

WM, in merely stating what he thinks a projection does, rather than
saying how it achieves that alleged end, does not define anything.

It has become clear that we cannot agree on the meaning
of projection, we cannot even agree on what we are
discussing! Lets go back a bit and see if there
are things we can agree on.

Let P_F be the set of all finite paths.
Let P_I be the set of all infinite paths.

Please indicate the first statement you disagree with.

1. The question we are discussing is: Is the set P_I countable?

This question will be discussed later, namely when the question about
P_F will have been settled.

The set of all finite paths in any one finite tree is finite, and the
set of finite paths in any countably infinite collection of finite trees
is countably infinite, but the set of infinite paths in a CIBT is
equinumerous with the set of all subsets of a countably infinite set,
which makes it larger in cardinality that any countable set..

2. The elements of P_F can be put in a list

3. There is no last element in the list of
the elements of P_F

4. Each element of P_I corresponds to a infinite sequence of
elements of P_F

That is in question. Therefore I devised the projection.

That "projection" is merely the union, which contains as many elements
as there are lines, and is, therefore, not finite.

5. Any set that can be put in a list is
countable

6. If X is countable, and a list of the elements of X
has no end, then the infinite subsets of X form
an uncountable set.

That's all fine but out of interest. The set {1, 1, 1, ...} is
infinite.

On the contrary, that set, which equals {1}, has cardinality 1.

If WM is trying, but failing, to talk about the infinite-tuple
(1,1,1,...), or, more properly, the function f:N --> {1}:n |--> 1,
he should learn enough mathematics to express himself correctly.
.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... Maximum of a set or about "what the projection does". ... Let P_I be the set of all infinite paths. ... its Waft Maximum is 1. ... Waft Maximum of the set of all finite paths. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... projection of all finite lines is infinite. ... F be a sequence. ... Why then do you think the projection leads to WM = oo in example 7? ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... there is a projection of all finite lines. ... projection of all finite lines is infinite. ... The projection of a sequence has a Waft Maximum abbreviated by WM. ... know, an infinite finite number is not possible, even in set theory ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... The triangle contains an infinite number of lines and, ... that the projection surpasses all the lines projected. ... The projection is not a union of lines but a projection. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... The projection of the EIT contains an infinite number of elements. ... Because the Waft Maximum of R is the same as the Waft Maximum of the ...
    (sci.math)