11.5

Relatively Prime Numbers
Relavively Prime Numbers mean that two number have no gcf other than one.  So the number might not be prime on its own, but when paired with another number they are both relatively prime,  like 20 and 7.  I think that Euclid's Lemma will be very useful when working with relatively Prime numbers and make proof quite a bit easier. 

11.3-11.4

29000!!!!

Last night I went to the Hunger Games Movie, and thus I forgot to BLog, but I figured if I did this morning before class, that that would be okay. 

11.3 Greatest Common Divisors: This section was a nice review about greatest common divisors.   And it was cool to see the proofs and why this worked. 

11.4 The Euclidean Algorithm: This is a cool way to find the gcd, I liked how you just start dividing and deviding by the numbers you get, and it leads you to the gcd once you have to add 0 to get the number before. Math is cool.

11.1-11.2

The first section was simple because it was math I have been farmilar with for quite some time, Divisibility properties of integers.  The division algorithm will be a little harder to understand, but it makes sence the formula b=aq+r with a= some number, q=quotient devided by, and r=remainder after the division.  It doesn't seem too tricky. 

10.5

The Schroder-Bernsein Theorem!!  I'm so happy we are finally learning how to use this theorem.  It makes a lot of sense, that if you prove A is less than or equal to B as well as B being less than or equal to A that A=B, and thus meaning the have the same cardiality.  It is just hard for me to know the equation to pick, when deciding what to map them to.  I also liked reading the history about the earlier mathematicians.  They were smart smart men.

10.4

I was really confused yesterday in class because we talked about this section before I had read the whole thing,  But now that I have read it, It makes a lot more sense.  I wonder if the continuum hypothesis is true or false! It is kinda mind blowing that some things in math still can't be proven or disproven.  I also heard the Schrolder-Bernstein Theorem makes this stuff a lot easier, so I'm excited to read/talk about that next class.

The rest of 10.3

I feel like I really understood the rest of 10.3, I had to read over it to do the last few homework problems.  It isn't difficult to prove that it is a bijection, because we have been working on that for quite some time, what is going to be difficult is figuring out what function to use to ensure that it maps to the correct points in the set. 

10.3

I thought it was really interessting how the fraction 1/2 is equal to .50000 as well as .49999 i have never thought of that before, but it makes perfect sense.  I am still having a real hard time understanding what denumerable means exactly.  I don't understand how denumerable and uncountable are connected, or even if they are at all.  I way don't understand how every 2 denumerable sets are numerically equivalent, wouldn't that mean ALl denumerable sets are equivalent?

10.1-10.-2

I thought it was crazy the history lesson at the start of this chapter and it said Galileo was in jain the last nine years of his life! So many people didn't get the credit they deserved until after they had died.  numerically equivalent is pretty strait forward and I don't think I'll have  a problem with that, I do however have don't understand how a set can be countably infinite, you can't count to infinity. and denumerable is confusing too, I hope it is a little more clear after lecture tomorrow!

Examm # 2

I expect some mathematical induction problems to be on the exam, and I really need a review on them since we did them so long ago.  I also think the test will have a lot on = classes, as well as funtions, since we spent a lot of time on those.  I think there will be lot of proofs on the exam.  I hope it goes better than the last exam did, or I'll be introuble.

9.6-9.7

Inverse Functions was pretty easy for me to understand, one part I didn't get was when it says
R - {2} -> R - {3} ,  I know it has to do with the domain, but I don't quite get how you use then in the problem.  I thought permutations looked fun and not too bad.