Sections 8.1 and 8.2, due on February 18th

It's currently 62 degrees in Newport Beach.  For some reason, I find myself in Fashion Island Mall with my computer and my math book, surrounded by palm trees, wealth, and some kids next to me playing games.  What a random, awesome world.

Anyways, sections 8.1 and 8.2

Let's talk about Relations and Properties of Relations.  And just so you know, I'm not talking about relations of people.  If you want to get my thoughts on stuff that's more than just math, go to spanishnap.blogspot.com

What Did I Find Difficult

For this reading, I only found difficult the introduction to the concept of relations.  Particularly, I found the following concepts difficult at first, only because they were so new:

• Let A and B be two sets.  By a relation R from A to B we mean a subset A x B.  

• That is, R is a set of ordered pairs, where the first coordinate of the pair belongs to A and the second coordinate belongs to B. 

• If (a.b) \in R, then we say that a is related to b by R and write a R b.  

I believe that with time and with further learning of these concepts I will come to understand them better.  On page 176, it says that "Although this may seem like a fairly simple idea, it is very important that we have a thorough understanding of it."  I did not really understand what it was saying, but after reading that, I went back and tried to understand it more.  I guess it was difficult for me because it is a new way about thinking of ordered pairs.  

What Did I Find Interesting

What I found interesting about this reading was that which I also found difficult - the thinking of ordered pairs in new ways.  It's neat to think about how 

• "A relation R defined on a set A is called reflexive if x R x for every x \in A."  
• "A relation R defined on a set A is called transitive if whenever x R y and y R z, then x R z, for all x, y, z \in A." 
• The distance between two real numbers a and b is |a-b|.

I can see how these ways of thinking about cartesian products and ordered pairs will be helpful in the future.  I look forward to learning more about them and doing more with them.