Talk:Schröder-Bernstein property/Draft

Three remarks

Nice, Boris. I have only minor comments:

1. I think the "noncommutative counterpart" needs some more explanation.
2. What do you think of discussing the relation to antisymmetry of order?
3. What about more structure by (sub)headings?

--Peter Schmitt 23:55, 25 September 2010 (UTC)

1. "noncommutative counterpart" — on one hand, I am waiting for a book from our library about this point; but on the other hand, it is anyway beyond the form "If X is similar to a part of Y and also Y is similar to a part of X then X and Y are similar (to each other)" and only inspired by it.

2. "relation to antisymmetry of order" — you are right, this should be noted.

3. "structure by (sub)headings" — I also feel the need, but the article is so short, I do not see which headings; do you? Boris Tsirelson 06:23, 26 September 2010 (UTC)

As for headings: "Examples" is obvious, I think.

The introduction could say something like: "(Remark) In contrast to most mathematical terms this only gives the general form, the pattern, of a statement instead of a definite and precise definition."

Then the explanation following it could have the heading "The general pattern" (or similar). For tactical reasons :-) I do not make changes myself.

--Peter Schmitt 12:41, 28 September 2010 (UTC)

Being unsure I did the change in my sandbox; please look there. Is it close to what you mean? Boris Tsirelson 13:48, 28 September 2010 (UTC)

Yes, that is what I meant. What do you think? In the introduction, I would exchange the displayed definition with the second sentence -- but this is only a matter of taste. And -- perhaps -- it is not necessary to repeat this in the first section? --Peter Schmitt 23:52, 28 September 2010 (UTC)

(unindent) Peter, I feel that our interaction model "author - approver" is restrictive. A good unapproved article is better than a bad approved one. Thus I propose to leave the approval to a remote future and do the wiki: you edit as you like, and me, and so on.

The problem is that you have an idea how it should be, but I fail to guess it. I do not feel that the version in my sandbox is better. Yes, it has some headings, and this is good. However, it is not for free. In the old version an example appears early and illustrates the general idea. In the new version they are separated, and so, "the general pattern" section is quite dry. Of course, the reader can jump to examples and return. But still, I am not convinced that the advantage overweight the drawback. Trying to implement your last remarks I make more mess.

A more general remark. I feel you have some rather firm idea of a good article. Could you please publish your idea? (Say, on your home page, or mine, or talk, or even my sandbox, no matter where.) It would help. It seems you implicitly assume that others have the same idea but are lazy to follow it; this is not so.

And another general remark. Your phrase "In my opinion, good and high-quality articles cannot and should not be "whipped up". They require much thought and careful planning." is a bit frightening. It would be OK in a prestigious publishing house with high salaries for authors. But here? We know what the set of active math authors is today. I am inclined to say "Yes - but not now." Boris Tsirelson 09:08, 4 October 2010 (UTC)