The most difficult part of the reading was the section over equivalence classes. The proofs for transitive, symmetric, and reflexive really are not all that new, but the analysis of equivalence classes took a while to understand. I am interested in what they are useful for as I understand they are partitions. I assume we will learn later.
The most interesting part of the material that I got to read was simply the new definition of equivalence as something that is reflexive, transitive, and also symmetric. I had never though of equivalence in that way, but it makes sense. I also thought it was interesting they used the word class in equivalence class. I do not recall anything being called a class in math, and now that I think about it, it is not often used in physics or chemistry. In biology of course we have kingdom, phylum, class, genus, order, family, species, but that is not a very mathematical definition but more of an arbitrary classification.
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