Re: Review of Mueckenheims book.

In article <1173301900.682090.90170@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@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.

The projection is, by definition, a set that contains all the members of
all the sets called lines.

A common set-theoretic name for such a set is the union of all those
lines.

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]?

There is no such sequence, merely such a set, until a countable well
ordering of them has been established and imposed upon them.

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

There is no such sequence, merely such a set, until a countable well
ordering of them has been established and imposed upon them.


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

What "projection" is that? Are you projecting onto the real line?

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

What "projection" is that? Are you projecting onto the union of all
those lines of the EIT, or some superset? If not, you have no apparent
target for your projections.
.

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