Show that the sets [2,4] u [6,10] and (-2,2) have the same cardinality.(using the Schroeder-Berstein Theorem) so I have to define f: [2,4] u [6,10] --> (-2,2) by f(x)= any f(x) I get that works... when you inverse it so that I define f: (-2,2) --> [2,4] u [6,10] by g(x)= I can't get to work... can anyone help me?
December 9th 2009, 12:37 PM
when you inverse it...
I am not sure if you mean inversing the first function. If you use Cantor–Bernstein–Schroeder theorem, you don't have to construct a bijection (which has to have an inverse). You just have to provide two injections: one from to and one back.
Well, that should be easy. You can use linear functions for some to map inside , say, into , and into, say, . So, use make two linear functions and then glue them into one using a declaration like if ..., and if ... .