Well this was exciting...we got the teaser in class about how we could add and multiply sets, and today I got to read about them. I actually did the reading over an hour ago and didn't blog about it immediately because I wanted to think about it some more. I felt like there was a jigsaw puzzle starting to put itself together in my mind. Not sure if it's all the way done fitting together...probably not.
I actually figured out that the equivalence classes of Zn was the set of {[0],[1],[2],...,[n-1]}. I had postulated this idea in some form during lecture last time, and then today doing the homework, I did a problem where we were dealing with modulo 5 (n=5) and observed that we were going to have 5 different possibilities for equivalence classes. That's not to say that we will have 5 every time, but we can only have 5 possibilities because you can only have a remainder of 0,1,2,3 or 4. After that it will repeat. This information seems so useful...hopefully it still feels useful later and I can figure out how to use it.
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