I figured I would do the blog entry early this week since the homework for Wednesday is from 10.2. Aaaaand I forgot to do the blog for today for section 10.1.
1. By far the hardest thing about these denumerable sets is that you have to try to comprehend the idea of two non-equal sets that are related to each other in some way to have the same cardinality. The example in class today with the hotel rooms was helpful though. It's taking me back to my linear algebra days when I had to attempt to comprehend the n-th dimension. It's just counter intuitive to think that you can "count" an infinite set.
2. I am just loving that everything we've learned is packed together in this one section. We've got subsets, cardinality, types of proofs, induction, least elements, well-ordered sets, the identity matrix...it just never ends! I've never been one to understand application, but I always enjoy seeing it, and since this class is so fascinating to me, I will probably put in the time to understand it. My newest idea for comprehending it is imagining a graph that goes from [0,infinity) that has a range from (-infinity, infinity). This is entirely possible, and would have to be a function, and it would have to be one-to-one and onto.
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