User:Boris Tsirelson/Sandbox1: Difference between revisions
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* what is meant by "a part", | * what is meant by "a part", | ||
* what is meant by "similar". | * what is meant by "similar". | ||
In the classical Cantor–Bernstein–Schroeder theorem | |||
* ''X'' and ''Y'' are sets (maybe infinite), | |||
* "a part" is interpreted as "a subset", | |||
* "similar" is interpreted as | |||
==Notes and references== | ==Notes and references== | ||
{{reflist}} | {{reflist}} |
Revision as of 10:08, 1 September 2010
The general idea of the Cantor–Bernstein–Schroeder theorem and related results may be formulated as follows. If X is similar to a part of Y and at the same time Y is similar to a part of X then X and Y are similar. In order to be specific one should decide
- what kind of mathematical objects are X and Y,
- what is meant by "a part",
- what is meant by "similar".
In the classical Cantor–Bernstein–Schroeder theorem
- X and Y are sets (maybe infinite),
- "a part" is interpreted as "a subset",
- "similar" is interpreted as