Friday, March 16, 2012

10.5, due on March 19

A. In Theorem 10.19 they ended using the Schroder-Bernstien Theorem to tie it all together but to get to that point it was hard to follow. It looks like they found a 1-1 function that maps from an interval to the powerset of N then defined a function going the other way so that the powerset of N maps to a set of real numbers within the interval. Then showed that that was 1-1 and applied the theorems to wrap it up.

B. From what I could see, Theorem 10.17 was interesting because is shows that just by restricting the range of the function to exclude the elements which make it not onto, it becomes bijective and numerically equivalent. It just takes the elements on the set within a set that make it work.

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