Re: Review of Mueckenheims book.

On Mar 18, 1:06 pm, mueck...@xxxxxxxxxxxxxxxxx wrote:
On 18 Mrz., 17:28, "William Hughes" <wpihug...@xxxxxxxxxxx> 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.
And the definition does not give us enough information to tell if
the Waft Maximum of a sequence that does not take on its supremum
exists.





Now, to continue setting up a list of statements we can both
agree on. Do you agree with

7. The infinite tree T(oo), is the union of all
finite trees, U(T(n)).

We should distinguish between the COMPLETE TREE T(oo) which contains
infinite paths and the UNION OF ALL FINITE TREES U(T(n)).


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

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.

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

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

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

15. There is no last level in T_U

16. No element of P_U has an end

17. Every element of P_F has an end

18. Every element of P_U corresponds to an endless
sequence of 0's and 1's


- William Hughes


.

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