Talk:Schröder-Bernstein property/Draft

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Revision as of 17:52, 28 September 2010 by imported>Peter Schmitt (→‎Three remarks: yes)
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 Definition:  A mathematical term used to describe properties that have the same structure as the Schröder-Bernstein theorem of set theory. [d] [e]
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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)
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