Re: Review of Mueckenheims book.

On Mar 7, 4:11 pm, mueck...@xxxxxxxxxxxxxxxxx wrote:
On 7 Mrz., 20:41, "William Hughes" <wpihug...@xxxxxxxxxxx> wrote:

On Mar 7, 2:04 pm, mueck...@xxxxxxxxxxxxxxxxx wrote:
The Waft Maximum is defined as that what the projection does

No. You gave a detailed definition of the Waft Maximum

M: Let F be a sequence. WM(F) is the supremum S(F) of the range of the
M: sequence F = (a_n), if and only if this supremum is taken by the
M: sequence, i.e., if and only if S(F) is n the range of F, ran F =
{a_n
M: | n in N, a_n in R}. In all other cases WM(F) < S(F).

No mention of "that what the projection does".

No mention because this is the definition of "what the projection
does". But if you prefer to say "what the projection does" I will
agree.


What the projection does not does not do is tell you whether
or not there are an infinite number of nodes in the union
of all finite trees. So "what the projection does" is irrelevant.
Changing the name from "Waft Maximum" to "what the projection does"
changes nothing.


So let's test whether you understood the meaning by some exercises:

1) What does the projection do with the sequence of all constructible
real number of the interval [5, 6]?


"what the projection does" is 6 which is finite. The sequence of all
constructible
real numbers in the interval [5, 6] is infinite.



2) What does the projection do with the sequence of all constructible
real number of the interval [5, 6)?

"what the projection does" is <6 which is finite. The sequence of all
constructible
real numbers in the interval [5, 6) is infinite.


3) What does the projection do with the sequence of all negative unit
fractions?

"what the projection does" is <0 which is finite. The sequence of all
negative unit
fractions is infinite.



4) What does the projection do with all lines of the EIT?

"what the projection does" is < aleph_0 which is finite. There are an
infinite
number of lines in the EIT.

Knowing that "what the projection does" with X is finite tells us
nothing about
whether X is finite.

Which bit of " 'what the projection does' is totally irrelevant" do
you fail
to understand.

- William Hughes



.

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