Ullrichsim; Was: Constructibility of X -> X^2 bijection

David C. Ullrich wrote:

On Wed, 01 Aug 2007 12:27:47 -0400, "Stephen J. Herschkorn"
<sjherschko@xxxxxxxxxxxx> wrote:



David C. Ullrich wrote:



On Tue, 31 Jul 2007 08:52:58 -0400, "Stephen J. Herschkorn"
<sjherschko@xxxxxxxxxxxx> wrote:





Herman Jurjus wrote:





Herman Rubin wrote:
[snip]





It is trivial to order the power set of a well-ordered set



Would you care to explain what you have in mind, here?



I am pretty sure that Herman R. refers to the following: Given a well-ordered set X, order F = 2^X as follows. For f, g in F, let x be least such that f(x) != g(x). Then f < g iff f(x) < g(x).

Without referring to 2^X, this becomes: Let A and B be subsets of X. A < B iff and A contains the smallest element in the symmetric difference of A and B. Exercise: Show this is a well-ordering of P(X) without reference to 2^X.




Did you work out a solution to this "exercise" before posting it?




I erred in calling this a well-ordering (as opposed to an ordering), as I acknowledge in a later post. Did you read later posts before responding to this one?

[...]




I am curious. Why did you choose to put the word, "exercise," in quotation marks?


Those are called "scare quotes" - putting "exercise" in quotes
like that is meant to suggest that the word "exercise" was
not really appropriate. An actual _exercise_ should not ask
the student to do something that's not possible.

Since you've been kind enough to lecture me at great length
on how various aspects of how I phrase things, that look
to most of us like utterly unimportant details, are in
fact very very Bad, I'll return the favor:

Anyone can make a mistake. If you'd simply asserted what
you asserted, without calling it an "exercise", I wouldn't
have commented. Just as in that other situation, if you'd
simply made an error without saying you were being intentionally
coy about the details I would have had no problem with that.

But when you make _obviously_ ridiculous statements, calling
them "exercises", or saying that you're leaving out the
details because you're being "intentionally coy", it really
doesn't look good. When you say "exercise" it's like you're
assuring the reader that you're an expert here, you know
what you're talking about, and if he wants to attain wisdom he should follow your advice and humbly try to
work the exercise you've suggested. (No, I know you
didn't _say_ that - I didn't actually say a lot of
things either.) When you make an obviously ridiculous
statement, _framed_ that way, it really looks, um,
I'm having a hard time coming up with exactly the
right adjective, but it's not good.



It appears to me that you are saying the following: A poster makes an error. To you, the error is "obvious." Therefore you elected to post a response whose entire content is a snide remark meant to put down the poster for making the error. You did this after the OP posted a correction. Is that a fair assessment?

If so, that provides another example of your typical rudeness. You could have pointed out the error without such snideness. You could have not posted at all - after all, there is no mathematical content to your post, and the error had already been noted. You chose neither of these options.



[...]


But using exactly one comma there would be definitely
wrong - that would be an instance of something known
as "comma fault".



As in

"He said, although he really had no idea what he was
talking about, that P(X) could be well-ordered this way."

That sentence is fine, but eliminating exactly one of
the commas would give an instance of comma fault.



Another snide innuendo. As was the part of what I snipped above:

(iii) The test asked the student to prove the following. although
Spanier was unaware of the fact that some of the statements
were false.

[...]if (iii) "always" happened that just indicates that
Spanier was not competent to write tests.


Not only do you imply that I *always* make mistakes, but your choice of words is disrespectful towards Spanier (may he rest in peace), who is quite well known and was quite well loved. Better to use a different choice of words and the conditional. For example, "If (iii) always had happened, then that would have indicated that Spanier tended not to check his tests very well."

As you continue to choose such snide modes of expression, I will continue to point them out. For, indeed, you "always" do so.

--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

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