User:Boris Tsirelson/Sandbox1: Difference between revisions
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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. | 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". | |||
==Notes and references== | ==Notes and references== | ||
{{reflist}} | {{reflist}} | ||
Revision as of 10:06, 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".