Talk:Schröder-Bernstein theorem/Draft

"Details": "the induced induced image"? Boris Tsirelson 06:29, 26 September 2010 (UTC)
 * Thanks. Corrected. --Peter Schmitt 12:26, 28 September 2010 (UTC)

"Proof:Proof":
 * $$ S_1 \subset S \subset A

\Rightarrow f_\ast (S_1) \subset f_\ast (S) $$ probably should be
 * $$ S_1 \subset S \subset A

\Rightarrow \sigma_\ast (S_1) \subset \sigma_\ast (S) $$
 * Oops -- correct but not what is needed. --Peter Schmitt 23:37, 5 October 2010 (UTC)

"Monotone" in general may be understood as "either increasing or decreasing"; it is meant "(momotonely) increasing" or "isotone".


 * Yes, that was negligent. --Peter Schmitt 23:37, 5 October 2010 (UTC)

"Proof:Proof":
 * "By assumption, there are injective functions (...) that induce..."

I'd say
 * "By assumption, there are injective functions (...); they induce..."

because the second part of the phrase is not a part of the assumption (but its consequence).


 * True -- that is better. --Peter Schmitt 23:37, 5 October 2010 (UTC)

"Outline": the reader can guess what is denoted by f and g (or see the details), but we'd better let him know.


 * I forgot that I did not introduce it before. --Peter Schmitt 23:37, 5 October 2010 (UTC)

"Details": probably also (4) is needed, explaining what are A2, B1 and B2 (which is easy) and why B1 is the image of A1 under f and A2 is the image of B2 under g (which is less easy).


 * I was lazy -- I thought this is "obvious". --Peter Schmitt 23:37, 5 October 2010 (UTC)

Boris Tsirelson 12:19, 5 October 2010 (UTC)


 * Done. Thanks. --Peter Schmitt 23:37, 5 October 2010 (UTC)