Countability, Assignment 3, and Final Exam

After learning computability and impossible algorithms like halt, we moved onto the topic of countability. When we count, we automatically start off like "1... 2... 3..." and etc. So "counting" is actually just enumerating the natural numbers. So, we say the set N is countable, and any set A that satisfies |A| ≤ N is countable as well. So, the set of integers is countable, and, to my surprise, the set of rational numbers (Q) is countable as well (using diagonalization). Moreover, we learned that infinite sets does not necessarily have the same size. However, if two sets (finite or infinite) can be matched up 1-1 and onto, then they have the same size. 

Assignment 3 is due tomorrow at night. I am still working on it and I am going to office hours tomorrow to get help. With that being said, the Final is in 10 days and I need to start studying my butt off.