10.5 up to Theorem 10.18 due March 19

So what we are trying to do here is take a function that isn't bijective, and make it bijective by changing the domain. If we have a function that isn't one to one, we can change the domain to make it one to one, and therefore bijective. That sounds like it could be very useful. It's almost as if you could change an uncountable set to be a denumerable set. Dreamin' big here.

As for the thing that confused me and made my brain spin around, The proof of theorem 10.17 has me pretty lost. In my logical attempt to understand the theorem itself, I have determined that the identity function works. That's all good. So we're just proving that it works for proper subsets. Therefore, the set B' must be a proper subset of B? Ok. I continued reading through it, and after a study of the proof, I think I actually get it now. There were just a few too many variables for me to understand it the first time through. But it makes sense.