Talk:Schröder-Bernstein theorem/Draft: Difference between revisions

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Definition: A classic theorem of set theory asserting that sets can be ordered by size. [d] [e]

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"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)

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

"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).

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

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

@@ Line 3: / Line 3: @@
 "Details": "the induced induced image"? [[User:Boris Tsirelson|Boris Tsirelson]] 06:29, 26 September 2010 (UTC)
 : Thanks. Corrected. --[[User:Peter Schmitt|Peter Schmitt]] 12:26, 28 September 2010 (UTC)
+"Proof:Proof":
+: <math>  S_1 \subset S \subset A
+          \Rightarrow f_\ast (S_1) \subset f_\ast (S)
+  </math>
+probably should be
+: <math>  S_1 \subset S \subset A
+          \Rightarrow \sigma_\ast (S_1) \subset \sigma_\ast (S)
+  </math>
+"Monotone" in general may be understood as "either increasing or decreasing"; it is meant "(momotonely) increasing" or "isotone".
+"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).
+"Outline": the reader can guess what is denoted by ''f'' and ''g'' (or see the details), but we'd better let him know.
+[[User:Boris Tsirelson|Boris Tsirelson]] 12:19, 5 October 2010 (UTC)