Sections 1 and 2


Section 1:
1. The most difficult concept to me was understanding the empty set. On example 1.26, when defining the power set of U, it listed the empty set both by itself and in brackets, and I thought that it already had brackets implied because it itself is a set, so is that saying the power set of U has the empty set as well as a set containing the empty set? I also am having a tough time remembering how complex numbers work, but I think that is mostly due to the fact that I have not used them in several years.

2. What I found the most interesting in the reading was the section about unions, intersections, differences, and complements. I thought it was really cool how the Venn Diagrams illustrated how you can calculate cardinality of a set based on the complement and the other set. It seems like that will really be built on as I learn more about sets.

Section 2:
1. Most of this section seemed clear to me, but there were still a couple things that are unclear. With the example with the alphabet letters and the vowels, how come question 3 is the set of words that contain no standard vowels? I thought it would be the set of words that contain at least one standard vowel. It mentions that there is a slash through the union sign but I wasn't quite sure how that affected that set. I was also a bit confused about the last part, where the products were graphed. It made sense besides the final graph, where they took the union over all x [1,2] and ended up with the triangle on top of the square graph. How did they derive that? And when multiplying two sets to get the Cartesian product, how come the empty set is not included in the cardinality?
2. I think the whole idea that you can graph the union of a set is fascinating. I don't think I would have completely gotten the concept without the vowel and letter example. The intersection when alpha is included in V means that it needs the intersection of all words containing any vowel, and the only words that ALL of those words would have in common is the words that contained all standard vowels. It's still a bit of an abstract concept for me, and all the new notation is taking me some time to fully grasp, but it seems like it is a simple enough concept when you really break down what the problem is saying.

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