10.3a, due March 12

Difficult: I don't understand when something is uncountable. I think I get when things are denumberable since I can find a bijective function with the natural numbers, but I have a hard time understanding when you can tell that something is uncountable without just thinking about it. Most of the theorems for this section i didn't understand at first, and sometimes even with the proof i didn't understand it, but then I would sit and think about it in relation to a denumberable set and then I could figure it out. Is there a different way to think about it though?

Reflective: I liked the part that talked about rational and irrational numbers being written as decimals. I think that this will help me with differentiating between rational and irrational numbers in the future because it is an additional way of thinking about it that I never really considered before. This also, in theory, helps with understanding the whole idea of something being uncountable.

10.1-10.2, due on March 9

Difficult: The most difficult concept for me to understand in this reading is the portion about when sets are denumberable in section 10.2. I think the main thing that I am unsure of regarding denumberable sets is the idea of sets that are infinite. Also, I do not really understand what it means for a set to be denumberable, as in how that affects the set.

Reflective: The easiest section of this reading was 10.1. I thought that this section was easy to understand because it is based on what we already know and understand regarding cardinality. It just shows a new way to figure out if two sets have the same cardinality. Then it introduces the term numerically equivalent sets and defines it as two sets that have the same cardinality. All of it is basic and since I already have an understanding of what cardinality is, it was simple to build on that knowledge.

9.6-9.7, due March 2

Difficult: The most difficult part from this reading assignment had to do with permutations in section 9.7. I guess I feel like I am just missing something for this principle. I understand that a permutation is a bijective function so it has to be one-to-one as well as onto. However, I don't understand what the difference between a bijective function and a permutation is. If there is no difference, then why do we need to learn both?

Reflective: For this section I liked reading about inverse relations in section 9.6. I liked inverse relations because it was easy to understand. Its terminology relates to its definition and what it does. This made it make sense very quickly. This then made understanding the idea of an inverse function relatively easy since I already had the foundation for it. However, I would like to work through examples of inverse functions and apply both inverse functions and relations to help my understanding of how to use them.

9.5, due February 29

Difficult: I thought that the most difficult part in this section was the part about associative functions. I think I understand the basics of the idea but I just thought it was difficult to get a clear understanding of the information simply by reading it.

Reflective: I liked reading the part about composition. I liked this section because I already understand the foundation of the principle after having taken calculus. Plus the idea is fairly simple and makes sense to me without having to go into too much detail.

9.3-9.4, February 27

Difficult: The most difficult part of this reading would probably the part about identity functions in section 9.4. At first this concept seemed rather simply, but the more that I read about them, the more that I got confused. I understood the part in the section about bijective functions for the most part, however I am still a little unsure about all of the details on a surjective element. What are the similarities and differences between one-to-one and onto functions?

Reflective: I thought that the most simple concept to understand for this reading was one-to-one functions. I liked this part in the reading because I already have a foundation for this concept. After taking calculus and studying what entails something to be referred to as being one-to-one, it was rather simple to apply new terminology to the old idea. Although I think I understand the basics for onto functions, I'm not very confident with them.

9.1-9.2, due February 24

Difficult: The difficult section for this reading was 9.2. I just don't think i really understood most of it. I didn't understand what it meant by B^(A) and why that notation was chosen or what it really meant.

Reflexive: I enjoyed section 9.1 for this reading which was on functions, domains, codomains, ranges, images, and mapping. I felt like all of these terms were based of fundamental concepts that I already understand. However I don't think that I understood why for f: A > B that A is the domain and B is the codomain.

9.1-9.2, due February 24

Difficult: The difficult section for this reading was 9.2. I just don't think i really understood most of it. I didn't understand what it meant by B^(A) and why that notation was chosen or what it really meant.

Reflexive: I enjoyed section 9.1 for this reading which was on functions, domains, codomains, ranges, images, and mapping. I felt like all of these terms were based of fundamental concepts that I already understand. However I don't think that I understood why for f: A > B that A is the domain and B is the codomain.