Section 28 due Nov 13

1. So, our earlier experience with cardinality defined it as the number of elements in a set, but this section treats it primarily in relation to a bijective function. (Exactly how that's applied is still a little fuzzy for me) Anyway, it just seems backwards to me that they use the fact that it's bijective to deduce that there are the same number of elements. I was just expecting the number of elements to be the primary defining characteristic of a given cardinality, when they treat the bijective quality as such.  So, my question is, is that really how we should mainly think of cardinality? Is thinking about  numbers of elements within the set too simplistic of an approach?


2. Infinity is fascinating to think about. Also, it's mind blowing that there are different sizes of infinity. It seems like most of the theorems in this section are basically thought experiments... and while they are interesting and are for the most part intuitive (if framed in the right way) I can't help but wonder what the practical value is? What do we gain as a society from knowing that there are sets that are countably infinite and sets that are uncountably infinite? That would be interesting to know. I guess most theorists don't know what practical value their theorems may have, they leave that to the engineers. For instance, Einstein's theories of general relativity are used today to correct for time dilation in GPS satellite mapping. He had no idea that we'd actually be applying the theory that way but we did.