Schröder–Bernstein Property
A Schröder–Bernstein property is any mathematical property that matches the following pattern : If, for some mathematical objects ''X'' and ''Y'', both ''X'' is similar to a part of ''Y'' and ''Y'' is similar to a part of ''X'' then ''X'' and ''Y'' are similar (to each other). The name Schröder–Bernstein (or Cantor–Schröder–Bernstein, or Cantor–Bernstein) property is in analogy to the theorem of the same name (from set theory). Schröder–Bernstein properties In order to define a specific Schröder–Bernstein property 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–)Schröder–Bernstein theorem, * objects are sets (maybe infinite), * "a part" is interpreted as a subset, * "similar" is interpreted as equinumerous. Not all statements of this form are true. For example, assume that * objects are triangles, * "a part" means a triangle inside the given t ...
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