Sec. 7, 11.3-11.4 due March 23

At the moment I'm rather sleep deprived, so not very much of the sections made much sense.  Finding the GCD was the most confusing thing for today.  The proof puzzled me, but the application thereof made enough sense.  Hopefully I understand better in class.

Sec. 7, 11.1-11.2, Due March 21

The proof for the division algorithm was slightly confusing, but the existence of such a thing does seem logical.  It's nice to be moving back to more familiar things though.  If there is enough class time further review of chapter 10 would be appreciated.  Thus far chapter 11 doesn't seem to horrible.

Sec. 7, 10.5, Due March 19th

Many of the proofs from the section are rather difficult to follow.  They seem convoluted, but the theorem's they provide seem as if they should be useful and easy to apply.  The Axiom of Choice in particular appears to be a powerful tool for proofs.  Hopefully I'm able to reach a more complete understanding of the proofs through lecture.

Sec. 7, 10.4, Due March 16, 2012

As we've already covered this in class there weren't as many potentially confusing thing.  The proof that the power set of A and 2^A are numerically equivalent still doesn't quite make sense though.  That and the proof showing that a bijection doesn't exist between the set A and it's power set.  If we're still on this section it would be helpful to see these again.

Sec. 7, last half of 10.3, due March 14, 2012

The rest of the section appears to have already been covered in class.  It was taken up with the examples proving that (0,1) was numerically equivalent to the set of real numbers.  The main thing that would be beneficial would be to do as many examples as possible during class time with proofs typical of sections 10.2 and 10.3.

Sec. 7, first half of 10.3, due March 12

The main thing I can't understand is the proof by contradiction used to show that (0,1) is an uncountable set.  Somehow they took a1=0.31717..., a2=0.1515..., and a3=.04000....  Because of this it said that the first three digits in the decimal expansion of b are 5, 4, 5, or b=0.545.  Anyway, more explanation of the proof would be helpful.  Once you're able to assume that theorem it should become significantly easier to prove that something is uncountable.

Sec. 7 10.1-10.2, Due March 9

In section 10.2 the main thing I didn't quite understand was the tables that were used to assist in several of the proofs.  Particularly in the case of when proving that Q+ was a denumerable set.  In order for the function they created to be bijective they decided to ignore any numbers within Q+ that would have had the same value so that it would be one to one.