Re: Review of Mueckenheims book.

On 19 Mrz., 12:37, "William Hughes" <wpihug...@xxxxxxxxxxx> wrote:
On Mar 19, 3:37 am, mueck...@xxxxxxxxxxxxxxxxx wrote:


[However, as you have only told us how to determine
what a Waft Maximum is for sequences which have a maximum,
this is of limited use]

It is enough to know that for sets which do not take on their supremum
the WaftMaximum is less than the supremum.

Sequences, not sets. The definition says nothing about sets which are
not sequences.

Is the real interval [0, 1] a sequence, or can it be written as a
sequence in your opinion?

[0.1] is not a sequence, nor can it be written as a sequence. It has
a maximum,
however, your definition, which starts "Let F be a sequence",
does not say anything about the maximum of a set
that is not a sequence.

Let F be a sequence does not exclude that the WM can be defined for
sets too. I remember that some of the exercises correctly solved by
you concerned uncountable sets. However: Improve the definition by
"Let F be a set ..."

Back to deterimining statements that we can both agree on.

O.K.

New definiton

Let T_U be the union of all finite trees, U(T(n)).

Since

10. The union of a set of trees is a tree

T_U is a tree.

Let P_U be the set of paths in T_U

Map each path on the natural number which gives the length of that
path.

Can you agree with the following statements?
(As usual, please indicate the first statement you cannot agree
with)

11. A path in a tree corresponds to a sequence
of 0's and 1's.

I think that is true.

12. Each element of P_F corresponds to a sequence
of 0's and 1's with an end.

yes

13. An endless path corresponds to an endless sequence of 0's
and 1's

An endless path cannot be mapped on a natural number.

14. A path in a tree can only end at the last level

15. There is no last level in T_U

There is no last natural number. OK. That does not mean that there is
an end of natural numbers or that there is an unnatural natural
number.

16. No element of P_U has an end

You conclude from the fact I just stated above that there are infinite
finite numbers?

Regards, WM

.

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