Shroeder-Bernstein Theorem

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Sets, Maps and Symmetry Groups Course Discussion List

Shroeder-Bernstein Theorem

Posted by Matt Rozen on December 07, 1999 at 16:16:45:

In Group Project #2, in problem #8 where we are asked to prove the Shroeder-Bernstein Theorem, we are told to let f:A to B and g:B to A denote bijections. Can we do this? We don't know that such bijections exist. We only know that one-to-one functions from A to B and B to A exist. If we knew that such bijections existed, we'd already have proven that A~B and we'd be done with the problem before we started. Should the problem say instead that f and g are one-to-one functions, or is there some flaw in my logic?

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>>In Group Project #2, in problem #8 where we are asked to prove the Shroeder-Bernstein Theorem, we are told to let f:A to B and g:B to A denote bijections.  Can we do this?  We don't know that such bijections exist.  We only know that one-to-one functions from A to B and B to A exist.  If we knew that such bijections existed, we'd already have proven that A~B and we'd be done with the problem before we started.  Should the problem say instead that f and g are one-to-one functions, or is there some flaw in my logic?

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